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Bedforms controlled by residual current vortices in a subtropical estuarine tidal channel
Journal Pre-proof Bedforms controlled by residual current vortices in a subtropical estuarine tidal channel O.G. Cruz, A.M. Noernberg PII:
S0272-7714(19)30161-1
DOI:
https://doi.org/10.1016/j.ecss.2019.106485
Reference:
YECSS 106485
To appear in:
Estuarine, Coastal and Shelf Science
Received Date: 18 February 2019 Revised Date:
28 October 2019
Accepted Date: 12 November 2019
Please cite this article as: Cruz, O.G., Noernberg, A.M., Bedforms controlled by residual current vortices in a subtropical estuarine tidal channel, Estuarine, Coastal and Shelf Science (2019), doi: https:// doi.org/10.1016/j.ecss.2019.106485. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
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Bedforms controlled by residual current vortices in a subtropical estuarine
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tidal channel.
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Cruz O. G., Noernberg A. M.
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22 23 24 25
Center for Marine Studies, Federal University of Paraná, 83255-976 Pontal do Paraná, PR, Brazil
[email protected]
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Abstract
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The objective of the present work was to analyze the bottom morphology, the genesis of the
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bedforms, and the patterns of current and sediment transport of the internal portion of the
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south mouth in Paranaguá Bay, Paraná - Brazil. This region was used as a laboratory field to
30
study the geomorphology of a dune field on a tide channel, with features of flood delta in the
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inner portion and ebb delta in the direction of the continental shelf. A sediment hydrodynamic
32
model was used to calculate the direction and magnitude of the sediment transport and the
33
residual current flows. A map of apparent roughness was used in the numerical model,
34
obtained through the soundings of a sidescan sonar (Starfish Sonar) and estimated from the
35
classification of the dune field, so it is possible to obtain simulations with higher
36
correspondence with reality. It was observed two vortices of residual circulations near the
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shores of Pontal do Sul and Ilha do Mel, with directions towards the continental shelf. The
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residual circulation vortex is responsible for the triangular shape of the large dunes near the
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Pontal do Sul margin. In the flood, the sediment material is conducted inward forming small
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ripples and accumulating sediment material on large dunes. During the ebb, these ripples are
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supposedly destroyed and attached to the large dunes or to the water column. On the other
42
hand, the bedforms of Saco do Limoeiro are formed due to the effects of the tide when
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entering the mouth and the confinement of the water mass in the region until the next moment
44
of padding.
45 46 47
Keywords: Sediment Transport, Estuarine Dunes, Numerical Modelling.
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INTRODUCTION
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Due to currents within the estuary, sand movements lead to the development of
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bedforms with heights ranging from centimeters to meters. Ripples with elevations in the
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scale from decimeters to meter are commonly called dunes or mega ripples. The combination
53
of tidal oscillation with the depth and size of the grain produces distinct dune fields, with the
54
orientation inferred by the crest of the dunes following the selected direction of the flood or
55
ebb tide. The shape, size, and interactions that the various types of dunes present are directly
56
related to current velocities and sediment characteristics. The minimum velocity of current for
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the formation of dunes is 0.5m/s, with a grain size of at least 0.13mm, the limit between fine
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sand and medium sand. There is no depth limit for the development of small ripples as long as
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current velocities are higher than 0.3m/s (Ashley and Chairperson, 1990). In general, the
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asymmetry of the bedforms indirectly represents the direction of the preferential current and
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the migration direction of the dunes, although, locations, where the migration direction is
62
opposite to the dune shape, have already been sighted (Hanes, 2012).
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The particles at the beginning of the movement form small ripples or dunes to the point
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of balance, and after some distance they are destroyed, while new ones are created right after.
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Small ripples adjust more quickly to currents than larger dunes. Thus, the roughness of the
66
bottom is essential to estimate the direction and magnitude of the sediment transport
67
accurately, since it depends heavily on the type of bedform, which is generated by the
68
transported sediment material itself (Van Rijn, 1993). Typically, the migration direction and
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asymmetry of the bedforms are good indicators to estimate the patterns of sediment transport;
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however, these characteristics can lead to a misinterpretation of the residual sediment
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transport when all the processes acting on the genesis of the bedforms are not taken into
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account. For example the time-scale being analyzed, the effects of current oscillation and the
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spatial variation of sediment transport. On bidirectional flows with a dominant and
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subordinate transport the bedforms have an obliquity in relation to the resultant transport, the
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current oscillation must be taken into consideration because they may be creating a single
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bedform orientation, all transport should be considered to have a positive effect (Rubin &
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Ikeda, 1990).
78
Numerical models provide alternatives for analyzing hydrodynamic flows and sediment
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transport in tidal channels. When properly calibrated and field-tested, the model offers a
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synoptic view of the entire studied area, where the current patterns and the turns in the flow
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patterns can be estimated and observed. Examples of usage in numerical modeling in
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conjunction with geological evidence are seen in the following studies: in Chu et al., (2009) to
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determine the morphological behavior of the mouth of the Yangtze estuary, China; in Zhang
84
et al., (2015) to examine transport trends around the Yellow River Delta, China; and in
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Bonaldo et al., (2014), Fraccascia et al., (2016) and Kubicki et al., (2016) to determine the
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processes acting on the genesis of the bedforms and the patterns of sediment transport and
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current.
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In this present study, the geomorphology of a dune field on a tide channel, with
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features of flood delta in the inner portion and ebb delta in the direction of the continental
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shelf, were examined. The region is used as a laboratory field to study the geomorphologic
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processes occurring on tide deltas, dune fields and also if the characteristics of the bedforms
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are always good indicators of sediment transport. To elucidate the geomorphologic processes,
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we analyzed the genesis of bedforms, sedimentary flows, and residual current patterns. The
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analyzes were made through a baroclinic hydrodynamic and sediment model during
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December 2015. The apparent roughness map used in the numerical model was estimated
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from the individual roughness values (flat areas, small ripples, and dunes) and the
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classification of the dune field, so it is possible to obtain simulations with better
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correspondence with reality. Besides, the results presented can be applied in coastal zone
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management and navigation channel actions.
100 101
STUDY AREA
102 103
The object of this study is the dune field located at the southern Estuarine Complex of
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Paranagua (CEP), in Parana - Brazil, between the Galheta channel and the region of Ponta do
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Poço (Fig. 1). The navigation channel, with depths of 14m and maintained by dredges, is used
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by the ports of Paranaguá and Antonina. Paranaguá is considered the largest bulk port in Latin
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America and the second most important in Brazil (APPA, 2013). The dune field's greatest
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depths, of around 23m, lie in the region of Ponta do Poço. In the region of Saco do Limoeiro,
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the depths are less than 2m (Araújo, 2001).The CEP is characterized as a partially mixed
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estuary (type b) governed by the tide and the river discharge. The tide is semi-diurnal, with an
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average spring tide oscillation of 1.7m near the mouth and 2.7m in its interior (Lana et al.,
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2001). The sediment composition is mainly of medium and fine sand, from moderately to
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very well sorted, due to the influence of the marine environment (Lamour, 2000). In the Saco
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do Limoeiro, the particle size distribution tends to be thin and very thin, well-selected to
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poorly sorted sand (Araújo, 2001).
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The Galheta shoals occur in the external portion of the mouth, which is a development
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of a large bank of sand with depths ranging from 1.5m to 5.0m. It is formed by the flows of
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ebb and the preferred transport from south to north of the shore drift over the mouth delta
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(Angulo, 1999). In the Galheta shoals, typical features of ebb delta are found, such as
120
spreading bars, submerged bars, and flood channel margins. In the Saco do Limoeiro, one can
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observe typical features of the flood delta, with a main flood tide, a flood ramp and an ebb
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spur (Veiga et al., 2005).
123 124 125 126 127 128 129 130 131 132
Figure 1. Location of the studied area, with isobath depths and the navigation channel. The yellow lines demonstrate the longitudinal and transverse sections, with the points where the tidal ellipses were estimated (A, B, C, D, E, F, and G). On the point of observation (PO), the amount of sediment material leaving and entering the channel was observed. The location and extent of the submerged bars were removed and modified according to the study done by Veiga et al., 2005. The red frames over the study area are the extent indicators of figure 6 and 9.
MATERIAL AND METHODS
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Bedform Estuarine Analysis
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The bathymetric data and mapping were obtained with a multibeam probe (Reson
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7125) and a side-scan sonar (Starfish Sonar - 200Hz), between February and April 2017, by
137
the Port Administration of Paranaguá and Antonina (APPA). The multibeam probe coverage
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of the bottom was done only within the channel boundary, while for the Side-Scan Sonar
139
(SSS) the coverage was done from Pontal do Sul margins until the flood delta (Fig. 1 – SSS
140
mapping). The vessels location and movement were constantly corrected with a GPS of high
141
accuracy (Trimble) and a wave compensator (Octans) the bathymetric data was also reduced
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to the lowest tidal level according to the local navy norms. SSS data collection was conducted
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along several parallel lines at a constant ideal speed of 5 knots, with the length of submerged
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cable being constantly measured for post-processing, the backscatter data was then mosaic to
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a resolution of 10cm.
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A grid with a spacing of 100m was created on the bedforms’ maps (775 points). The
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average wavelength (λ) of the bedforms (dunes and small ripples) were measured and
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classified for each point, according to Ashley and Chairperson (1990). The height of the
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dunes (∆) was estimated according to Flemming (1988) and validated with the dredged
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channel's bathymetry data. In areas with data absence and difficult interpretation, the closest
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bedform was adopted and interpolated between neighboring points. In this region, there is a
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small quantity of data of this nature. Consequently, the mapping used in the numerical model
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was elaborated from a compilation of data available in the literature.
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The roughness of the bedform is essential to correctly estimate the direction and
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magnitude of the sediment transport since the sediment transport depends heavily on the
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bottom type, which is usually generated by the sediment transported. The map of apparent
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roughness was drawn from the preformed bedform classification and by the individual
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roughness values (flat areas, small ripples, and dunes), described by Van Rijn (1993).
159
=
+
160
= 1.1
161
= 20
(Eq. 1) 1−
.
(Eq. 2) (Eq. 3)
=3
162
For flat areas, apparent roughness is given by
, which is the average grain size of
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90% of the samples. For areas with the presence of bedforms the apparent roughness is given
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by the sum of the individual roughness values (Eq. 1), where
is the roughness referring to
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the small ripples; and
the roughness for large and very large dunes, which are calculated
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by equations 2 and 3. γ = 1 for bottoms consisting only of small ripples, and 0.7 for bottoms
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with a superposition of large or very large dune, γ = 0.7 for normal channel conditions.
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Numerical Simulation
169 170
The sea-level oscillation, the residual currents and the sediment transport were
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simulated through the FLOW module of the Delft3D modeling software. The model
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calibrated and validated by Krelling et al. (2017) was used in the boundary conditions to
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propagate the hydrodynamic fluxes, the tide variations, and the salinity dilution. The 14-layer
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baroclinic model was modeled over a curvilinear grid with resolutions between 40 and 375m.
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The roughness was updated with the apparent roughness map obtained in this study. The
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bathymetry and the bathymetric outlines were also remodeled according to the data from
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APPA and Angulo (1999). Since the bathymetric data provided by APPA only covers the
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dredged channel and not the entire estuary. The simulations were carried out during
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September to December 2015, characterized as a period with the highest precipitation rates,
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consequently more significant river discharge, and more intense hydrodynamic fluxes
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(Mantovanelli, 1999).
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Numerical model elaborated was validated with currents and tide measurements
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collected by a upward-looking 0.75 MHz Sontek Argonaut-XR Acoustic Doppler Current Profiler
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(ADCP) over a complete cycle of semidiurnal tide and average time-interval of 30 minutes,
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from September 1 to September 16 of 2016. Model quality was quantified through the use o
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root-mean-square error (RMSE) and the Willmott et al. (2012) improved index of agreement.
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In general, numerical model was able to reproduce tidal elevation and along channel current
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with satisfactory results, with dr = 0.79 for tidal elevation and dr = 0.77 for along channel
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current. For cross channel current the model underestimated the amplitude of flows, with dr =
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0.62 and a mean error of 0.17m/s-1. See Fig 1 – Append A.
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Several formulae to estimate the bed-load transport rate (
) are described in the
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literature with different methods to solve the turbulence behavior of the flow or particle
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motion (Meyer-Peter & Müller, 1948; Kalinske, 1947; Einstein, 1950; Bagnold, 1966; Van
194
Rijn, 2007). Van Rijn's (1993) approach was chosen because
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of the flow conditions and particle diameter it considers that the movement of the particles is
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dominated by the saltation of particles, under the influence of hydrodynamic and gravitational
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forces. Besides, this approach has already been tested (Nabi et al., 2013; Van Den Berg, 1987)
rates are solved as a function
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and implemented in other studies with good results for real-life situations (Lesser et al.,
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2004). With this in mind, December 27th and 28th were the dates chosen to demonstrate the
200
patterns of
201
hydrodynamic fluxes.
because they indicated higher tidal oscillations and more intense sediment and
202 203
Tidal Currents Analysis
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The tidal currents were analyzed by the least square method, associated with harmonic
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constituents of tides, ensuring greater robustness in the interpretation of the data. (Valle-
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Levinson and P. Atkinson, 1999; Vindenes et al., 2018). The sea-level oscillation data was
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extracted from the proposed numerical model in this study (Point C on the cross-section - Fig.
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1), from December 1 to December 31, 2015. The PACMARE software was used to calculate
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the harmonic constituents over the frequency domain, described by (Franco, 1997). The time
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series size is sufficient to solve the dominant tide constituents in the diurnal frequency (K1,
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O1) and semi-diurnal (L2, M2, N2, S2).
213 214
RESULTS
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Distribution of Bedforms
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The large dunes, with wavelengths ranging from 40 to 100m, were concentrated in the
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mouth, and the majority of them were superimposed by small ripples with some occasional
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flat areas. The largest overlapping dunes were sighted between Ponta do Poço and Ilha do
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Mel, reaching a wavelength up to 94m (∆/λ max - Fig. 3). Large and simple dunes, with
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wavelengths up to 30m, were sighted near Ponta do Poço, but only in lower depths. In the
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central region, they were also sighted, but with an average wavelength of 15m. In the region
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of Ponta do Poço, a limited number of ripples was observed, only in depths less than 17m.
225
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Figure 2. The spatial distribution of the dunes at the southern mouth of the CEP, according to their wavelengths.
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Figure 3. The spatial distribution of the dunes at the southern mouth of the CEP, according to their heights. At
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Heights of large dunes were validated by a longitudinal section made with the dredged
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channel's bathymetric data (Fig. 3), with an average height of 1.7m and an average
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wavelength of 76m, showing good consistency with the estimated data, according to
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Flemming (1988) (Table 1). The small ripples validation is impractical since the bathymetry's
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resolutions made with multibeam were 1 - 5m.
237 238 239
the chart below, the longitudinal bathymetric section in the final portion of the dredged channel is represented by a black line.
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Dunes size (m) Mean size in meters
240 241
Small
Medium
Large
Large with superposition
Height (∆):
0,22
0,62
1,24
1,87
Wavelength (λ):
4,35
15,41
37,82
60,32
Table 1: The average height and length of the dunes, according to the classification of Ashley and Chairperson, (1990).
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Figure 4 illustrates the various types of bedforms found in this study. The areas with
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two shades of dark gray, with heights between 1 and 3m, indicate areas with small ripples
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overlapping larger dunes and of large dunes without overlapping. The angle between the
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overlapping ripples and the larger dunes is oblique with the crest of the dunes (Fig. 4D). This
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interaction occurs because the small ripples are more subject to flow variations, and they form
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more rapidly than the larger dunes.
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Figure 4. The varieties of bedforms found. A) Large dunes passing longitudinally in small ripples and laterally in flat areas. B) Small ripples steering southeast. C) Medium and simple dunes with a northwest direction. D) Small ripples towards north overlapping large dunes with a northwest/west direction.
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Residual Circulation
255 256
The residual current was calculated through the average values of current, during a
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fortnightly cycle of semi-diurnal tides by integrating the entire water column. Thus, the
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orientation and the asymmetry of the currents are described by elucidating the
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geomorphological processes occurring in the dune field.
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In the region, near the banks of Pontal do Sul and Morro do Miguel, two areas with
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residual circulation towards the continental shelf were sighted. The residual circulation in the
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dredged canal, from Pontal do Sul up to Ponta do Poço, is estuary inward. On the right side of
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the dredged canal, adjacent to the Saco do Limoeiro, the direction is southeast. The residual
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circulation forms three main vortices. One is located in the Ponta do Poço, between the
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continental margin and the left side of the dredged canal. The other two are on both sides of
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the main channel, at the mouth, near the Saco do Limoeiro and the shores of Pontal do Sul
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(Fig. 5).
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Figure 5. The direction and the magnitude of the residual circulation calculated during a fortnightly tide cycle, between December 15th and December 31st, 2015. The black arrows outline the preferred route of the residual currents, considering only the vectors' direction.
Sediment Transport and Tidal Currents
274 275
In the region of the Saco do Limoeiro, the modeled tendency of bed-load transport
276
shows moderate similarity in relation to the migration direction of small ripples and large
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dunes, identified by Angulo (1999). The magnitude of bed-load transport is higher during ebb
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than in flood period (Fig. 12). It is possible to conclude that the small ripples on the dorsum of
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medium dunes happen during the flood, and the medium and large dunes form through a
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combination of flood and ebb currents. The flood ramp identified by Angulo (1999) is
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represented in this study through the vector of bed-load transport near the Morro do Miguel
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(Fig. 12c).
283
The harmonic constituents calculated at point C of the cross-section are listed in the
284
table below. Several combinations between the diurnal and semi-diurnal components were
285
tested by the minimum square method. The combination that obtained the highest
286
concordance index was used to calculate the parameters of the tidal ellipse and the phase
287
difference.
288 Harmonic constituents Daytime Lunar-solar declination Minor elliptical lunar Main lunar Semi daytime Minor elliptical lunar Main lunar Minor elliptical lunar Main solar
Symbol Frequency Amplitude Phase K1 M1 O1
15,04 14,49 13,94
8,43 0,91 11,67
188,01 243,83 73,69
L2 M2 N2 S2
29,52 28,98 28,43 30
0,73 40,35 6,01 28,77
90,94 83,52 170,25 101,41
289 290 291
Table 2. The harmonic constituents extracted and used in the harmonic analysis of the velocity components U and V. The frequency is given per hour in degrees, the amplitude in centimeters, and the phase in degrees.
292 293
The behavior of the currents, associated with harmonic constituents of tides, had better
294
accordance between components M2 and K1, with a concordance index of 0.93 for the U
295
component and 0.92 for the V component of velocity (Fig. 7). The tide currents of the main
296
channel (points A through D) are approximately 4 times larger (0.39 and 0.097, respectively)
297
than those of the Saco do Limoeiro (points E, F, G) (Fig. 6).
298
At all points, the M2 component was more prominent than the K1. The values of the
299
semi-major axis of the tidal ellipse range from 0.40 m/s to 0.59 m/s in the middle of the
300
channel (Fig. 6a, 6b, 6c and 6d), and from 0.08 m/s to 0.17 m/s in the Saco do Limoeiro (Fig.
301
6e, 6f, 6g). The orientation of the tidal ellipse is approximately 133° at the main channel and
302
104° at Saco do Limoeiro.
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Fig. 6. The tidal ellipses calculated on the A, B, C, D, E, F, and G points of the cross-section from the harmonic
306 307 308
Figure 7. The variation of the tidal current calculated from the sum of the Harmonic constituents M2 and K1
constituent M2 in blue and K1 in red.
(black) and the modeled (red).
309 310
The phase variation along the cross-section (Fig. 8), calculated from the main lunar
311
component (M2), shows a maximum difference of 15° (30 minutes) between the main channel
312
and the Saco do Limoeiro. The phase difference between the bottom layer and the surface is
313
approximately 1 degree (2 min) in the main channel, and up to 5 degrees (10 min) near the
314
banks of the Saco do Limoeiro.
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315 316 317 318 319
Figure 8. The phase difference along the cross-section, calculated from the Harmonic constituent M2 and concerning the geographic north; 1 degree corresponds to approximately 2 minutes. From 12/27/15, at 4:00 AM until 12/28/15, at 2:00 PM.
320
Bed-load transport during ebb and flood, shows the hydrodynamic complexity of the
321
area near the Pontal do Sul's margin, where the formation of a vortex occurs (Fig. 12). The
322
sediment transport vectors modeled are aligned with the direction of the large overlapping
323
dunes (Fig.12a and 12b). The triangular format, slightly inclined to the east of the large dunes,
324
indicates that the features were formed by a combination of the dominant sediment transport
325
of flood and the subordinate ebb. It was observed that in the areas where large and composed
326
dunes are formed, the sediments are trapped because of this combination between the
327
hydrodynamic fluxes.
328
Contrary to what was seen at the Saco do Limoeiro, an erosive process occurs due to
329
anthropic action on the other side of the channel. Between 1954 and 1980, the coastline
330
reached back to 150m and the beach morphology changed from sandy spurs (Fig. 9a) to a cliff
331
and tidal flats (Angulo et al., 2016). In the numerical simulation, the macro-drainage channel
332
and the Techint pier were not considered, but it is still possible to see how the obstruction of
333
the coastal drift occurs. During the flood the total sediment transport rate was parallel to the
334
margin (W-NO) removing sedimentary material from the sand bars and coastal drift to the
335
estuary. During the ebb, this sedimentary material is transported back. The coastal works
336
blocked the sediment source causing erosion at the beach.
337
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338 339 340 341
Figure 9. Aerial photographs of the coastline between Pontal do Sul and Ponta do Poço. (A) 1954, (B) 1980, ( modified from (Rodolfo José Angulo et al., 2016). In C the total sediment transport rate (suspended+bed-load) during flood, December 27th, 2015, at 7:30 AM, and ebb, December 27th, 2015, at 10:30 AM.
342 343
The cumulative sediment transport consists of the sum of the total sediment transport
344
rate (bed-load + suspension) during a semi-diurnal tide cycle (12.5h). Hence, it is possible to
345
estimate the positive or negative balance of sedimentary material being mobilized in each tide
346
cycle over a monthly cycle (December 1st to 31st). The negative values for the U component
347
show that the sediment material is being withdrawn from the location to the platform, and the
348
positive values into the estuary.
349
The total sediment transport occurs in the spring tide days, being almost null during the
350
neap. The average amount of sediment material being mobilized per tidal cycle is 0.39 ton/m,
351
approximately 0.61 ton/m entering the estuary and 0.17 ton/m exiting the estuary (Fig. 10a).
352
On average, about 71% of the sediment material is deposited on-site, a 0.43ton/m per tide,
353
representing an increase of 3cm concerning depth (Fig. 10b). However, there is a reversal in
354
sediment transport patterns from the middle of the channel towards the margins, as seen in the
355
current pattern residuals (Fig. 5). The amount of sediment material towards the platform
356
exceeds the amount entering the estuary.
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357
358 359 360 361
Figure 10. Sediment transport at the observation point (Fig. 1 - PO). (A) Cumulative sediment transport of entrance and exit. (B) Quantity of sediment material deposited in relation to the sediment transport of entrance and exit.
362 363
DISCUSSION
364 365
In this study, the types of bedforms at the southern mouth of the CEP and the factors
366
controlling its shape and genesis were described. Numerical modeling, in conjunction with the
367
bedform maps, allowed us to explore the direction of the sediment transport and the amount
368
of sediment material entering and leaving the south mouth during a tide cycle. The largest
369
dunes (∆ = 1-3m, λ = 40-100m) were found to be directly related to the magnitude of the bed-
370
load transport. The areas with small ripples had lower bed-load transport than the regions with
371
large dunes.
372
The large dunes, near the Pontal do Sul margin, have a triangular shape with small
373
overlapping ripples of north and south directions. Since the angle of the face and the dorsum
374
inclination of the large dunes is determined by the relative force between the flood velocities
375
and ebb (Allen, 1980), the triangular shape slightly inclined to the east indicate that the
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376
sediment transport of ebb is equated to the prevailing flood flow. During flood periods, the
377
sediment material is conducted into the estuary in the middle of the channel, forming small
378
ripples and accumulating material on the large dunes (Fig. 11b). During the ebb, these ripples
379
are supposed to be eroded and attached to the large dunes or the water column (Fig. 11a).
380 381 382 383 384 385
Figure 11. Sediment transport by bed-load (m3/s/m) during maximum flood - December 26th, 2015, at 4:00 PM (B) - and ebb - December 26th, 2015 at 9:00 PM (A). The figures on the left show the insertion area of the red square, with the reflectance maps of the seafloor overlapped by the bedform transport vectors. The figures on the left, represented by black areas, are the very large dunes with and without overlaps.
386
Previous studies have pointed out that the main transport tendencies at the south mouth
387
are directed inward the estuary with E/NE direction (Lamour et al., 2007; Lamour, 2000). In
388
this study, the bed-load transport flows and the residual currents also show an estuary inward
389
tendency in the dredged channel, and formation of vortices with seaward sediment transport,
390
near the borders of Pontal do Sul and Ilha do Mel (Fig. 5). In addition, it is possible to
Página 20 de 29
391
conclude that the submerged bars are formed from these vortices and the sediment transport
392
interacting with the coastal drift. After the vortex, near Pontal do Sul, sediment transport
393
flows return to the estuary inward until the south of Ponta do Poço, where a vortex formation
394
occurs clockwise. On the right side of the dredged channel, near the Morro do Miguel,
395
hydrodynamic flows have E-S directions (Fig. 5). This innermost region of the mouth shows
396
us the importance of spatial variation in estimating sedimentary transport by the dune field. In
397
the case of using small sampling area, such as the middle of the channel or near the margins,
398
it would hide the inlet and outlet dynamics and the formation of a sediment trap vortex.
399
The process of interaction between the coastal drift and the sediment transport near the
400
mouth observed in this study is also investigated in the Changjiang Delta. The recirculation
401
vortices and the residual transport that occurs in the mouth’s boundaries are associated with
402
the accretion trend of the navigation channel and the expansion of the mouth towards the sea
403
of the mouth (Chu et al., 2009; Saito et al., 2001).
404
In the flood delta region of Saco do Limoeiro, three types of bedforms occur: large
405
dunes, medium dunes, and small ripples (Angulo, 1999). The largest bedforms have a
406
wavelength up to 200m, with NNE and NNW directions. The medium dunes present
407
wavelengths up to 10m and SSW-NNE and SW-NE directions. The flood ramp beginning is
408
located near the Moro do Miguel, just after the vortex near Ponta do Caraguatá (Fig. 5).
409
Although the dunes were flooded oriented, the hydrodynamic surveys of Araújo (2001)
410
indicate the trend of ebb transport of non-cohesive sediments, during spring tide days in calm
411
sea conditions. The geomorphological evolution of the Saco do Limoeiro also shows that it
412
tends to export sediments in long term. On the beach between Pontal do Sul and Ponta do
413
Poço there is also erosive process, but caused by the influence of the jetty built in the macro-
414
drainage channel. It blocks the sediment transport during flood period changing the beach
415
morphology.
416
This contradiction between the direction of the dunes migration and the
417
geomorphological evolution of the flood delta is explained by the effects of the oscillation in
418
the tidal current and the influence of low bathymetry in the region, in the propagation of the
419
tidal wave. The tidal wave, crossing the gap between Pontal do Sul and Ponta do Caraguatá,
420
progressively gains NE direction when entering the flood delta, while in the dredged channel
421
the direction is NW, explaining the direction trends of the small ripples (Fig. 12a). Due to
422
depth variations and bedform friction effects, the tidal wave moves more slowly in the flood
423
delta than in the main channel, confining water in the delta region. The current maximums 30
Página 21 de 29
424
minutes phase difference between the flood delta and the channel demonstrates this
425
confinement of water. The ebb current starts with W-SW direction (Fig. 12b), and gradually
426
moves counterclockwise to SE. This type of flood tidal delta shows how the direction of the
427
sediment transport inferred by the dune field may be mistaken with the geomorphological
428
evolution of the bottom. The direction SW of the largest bedforms give a false impression of
429
deposition, when the current oscillation is eroding the flood delta. The current pattern and the
430
erosion processes of the Saco do Limoeiro region are illustrated by bed-load transport
431
patterns. (Fig. 12).
432 433 434 435 436
Figure 12. The sediment transport by bed-load transport (m3/s/m) during the ebb - December 28th, 2015, at 8:30 PM (B) - and flood - December 28th, 2015 at 3:00 PM (C). (A) Migration direction assumed through the crests of the bedform, small ripples, medium dunes, and large dunes, modified from Angulo, (1999).
Página 22 de 29
437
Similarly, a tide asymmetry was identified in Denmark's Wadden Inlet Channel (Knude
438
Dyb), and a flow separation with a recirculation vortex was developed approximately 1h
439
before the next flood period, between the main channel and the tidal plain. These processes
440
were associated with the depth differences between the main channel and the tidal plain.
441
Besides, recirculation vortices are found with the direction of migration of the large dunes
442
(approximately 2.3m height and 155m wavelength), following the direction of the residual
443
circulation flows (Fraccascia et al., 2016; Ridderinkhof et al., 2016). A similar physical
444
process was demonstrated in this case study, but with different magnitudes and delay of the
445
tidal current maximums.
446
Contrary to what was observed in the Saco do Limoeiro, in the Lobos Point and Bonita
447
Point bay, the recirculation vortices, formed from the rocky headlands, show the sediment
448
transport being retained and transported back to the ebb-tidal delta, being that these areas with
449
flood dominance were attributed to the stability of Baker Beach (Elias and Hansen, 2013). In
450
McDonald Bank, Whangarei Harbor, there is a similar process of sediment accumulation with
451
the presence of recirculation vortices and sediment transport occurring in closed cycles. From
452
the flood ramp, the flood residual streams follow uninterruptedly to north of the Snake Bank,
453
reversing the direction in Shoal Bay and McDonald Bank to the south of Darch Point where
454
ebb residual currents rapidly decelerate (Black et al., 1989; Black and Healy, 1986).
455
The distinction between the sedimentation/erosion processes occurring in the Saco do
456
Limoeiro and in the Lobos Point and the McDonald Bank are due to the preferred direction of
457
the flood residual streams in relation to the mouth. In the Point Lobos and the McDonald
458
Bank, the recirculation vortex has a clockwise direction and the residual streams of flood
459
enter perpendicularly to the mouth. For the Saco do Limoeiro, the vortex has a
460
counterclockwise direction and the angle of entry of residual streams is oblique.
461 462
CONCLUSION
463 464
The bedforms and the sediment transport of the south mouth of the Paranaguá Bay were
465
investigated through mapping together with a hydrodynamic and sediment model. The
466
preferential direction of the sediment transport was inferred by the geomorphology of the
467
dunes and supplemented with the direction of the sediment transport obtained by the
468
numerical model. The main results obtained in this study are the following:
469
Página 23 de 29
470
- The residual current vortices, near Pontal do Sul are responsible for the overlap of small
471
ripples to windward of the dunes, and also the triangular shapes of the large dunes. From the
472
interaction of this vortex and the coastal drift the submerged bars are formed and continuously
473
remodeled.
474
- At the flood delta (Saco do Limoeiro) was demonstrated how the genesis of the bedforms
475
could lead to a false interpretation of geomorphologic evolution. The erosion tendency of the
476
flood delta was illustrated by the residual circulation patterns when entering the mouth and by
477
the water confinement, identified in the analysis of the tidal currents.
478 479
ACKNOWLEDGMENTS
480 481
The authors would like to kindly thanks APPA for providing the data that made this
482
study possible, and also Mihael Machado de Souza for your support with the numerical model
483
that was used at the boundaries conditions. The Center of Marine Studies of Federal
484
University of Paraná (CEM-UFPR) and the Coastal and Oceanic Systems Graduate Program
485
(PGSISCO) were also essential to complete this study by providing fundings, scientific
486
knowledge and the computational framework for this research paper. The authors would also
487
like to thank the two anonymous reviewers of this journal for helpful comments and insights.
488 489
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Zhang, L., Chen, S.L., Yi, L., 2015. The Sediment Source and Transport Trends around the
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Abandoned Yellow River Delta, China. Mar. Georesources Geotechnol. 0, 1–10.
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Appendix A
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Figure 13. Model validation results (red) in relation to field data (black). For along channel current on first chart, cross channel current on intermediate, and tides on last chart.
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Figure 14. Map of apparent roughness calculated through bedform classification and by sum of the individual roughness values.
HIGHLIGHTS - The bedforms and the sediment transport of the south mouth of the Paranaguá Bay were investigated through mapping together with a hydrodynamic and sediment model.
- The residual current vortices, near Pontal do Sul are responsible for the overlap of small ripples to windward of the dunes, and also the triangular shapes of the large dunes.
- At the flood delta (Saco do Limoeiro) was demonstrated how the genesis of the bedforms could lead to a false interpretation of geomorphologic evolution. The erosion tendency of the flood delta was illustrated by the residual circulation patterns when entering the mouth and by the water confinement, identified in the analysis of the tidal currents.
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
Port Administration of Paranaguá and Antonina (APPA) provided the data multibeam and backscatter data that made this study possible and the numerical model that was used at the boundaries conditions was provided by Mihael Machado de Souza. The Center of Marine Studies of Federal University of Paraná (CEM-UFPR) and the Coastal and Oceanic Systems Graduate Program (PGSISCO) were also essential to complete this study by providing fundings, scientific knowledge and the computational framework for this research paper.
S0272-7714(19)30161-1
DOI:
https://doi.org/10.1016/j.ecss.2019.106485
Reference:
YECSS 106485
To appear in:
Estuarine, Coastal and Shelf Science
Received Date: 18 February 2019 Revised Date:
28 October 2019
Accepted Date: 12 November 2019
Please cite this article as: Cruz, O.G., Noernberg, A.M., Bedforms controlled by residual current vortices in a subtropical estuarine tidal channel, Estuarine, Coastal and Shelf Science (2019), doi: https:// doi.org/10.1016/j.ecss.2019.106485. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
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Bedforms controlled by residual current vortices in a subtropical estuarine
14
tidal channel.
15 16 17 18 19
Cruz O. G., Noernberg A. M.
20 21
22 23 24 25
Center for Marine Studies, Federal University of Paraná, 83255-976 Pontal do Paraná, PR, Brazil
[email protected]
Página 2 de 29
26
Abstract
27
The objective of the present work was to analyze the bottom morphology, the genesis of the
28
bedforms, and the patterns of current and sediment transport of the internal portion of the
29
south mouth in Paranaguá Bay, Paraná - Brazil. This region was used as a laboratory field to
30
study the geomorphology of a dune field on a tide channel, with features of flood delta in the
31
inner portion and ebb delta in the direction of the continental shelf. A sediment hydrodynamic
32
model was used to calculate the direction and magnitude of the sediment transport and the
33
residual current flows. A map of apparent roughness was used in the numerical model,
34
obtained through the soundings of a sidescan sonar (Starfish Sonar) and estimated from the
35
classification of the dune field, so it is possible to obtain simulations with higher
36
correspondence with reality. It was observed two vortices of residual circulations near the
37
shores of Pontal do Sul and Ilha do Mel, with directions towards the continental shelf. The
38
residual circulation vortex is responsible for the triangular shape of the large dunes near the
39
Pontal do Sul margin. In the flood, the sediment material is conducted inward forming small
40
ripples and accumulating sediment material on large dunes. During the ebb, these ripples are
41
supposedly destroyed and attached to the large dunes or to the water column. On the other
42
hand, the bedforms of Saco do Limoeiro are formed due to the effects of the tide when
43
entering the mouth and the confinement of the water mass in the region until the next moment
44
of padding.
45 46 47
Keywords: Sediment Transport, Estuarine Dunes, Numerical Modelling.
Página 3 de 29
48
INTRODUCTION
49 50
Due to currents within the estuary, sand movements lead to the development of
51
bedforms with heights ranging from centimeters to meters. Ripples with elevations in the
52
scale from decimeters to meter are commonly called dunes or mega ripples. The combination
53
of tidal oscillation with the depth and size of the grain produces distinct dune fields, with the
54
orientation inferred by the crest of the dunes following the selected direction of the flood or
55
ebb tide. The shape, size, and interactions that the various types of dunes present are directly
56
related to current velocities and sediment characteristics. The minimum velocity of current for
57
the formation of dunes is 0.5m/s, with a grain size of at least 0.13mm, the limit between fine
58
sand and medium sand. There is no depth limit for the development of small ripples as long as
59
current velocities are higher than 0.3m/s (Ashley and Chairperson, 1990). In general, the
60
asymmetry of the bedforms indirectly represents the direction of the preferential current and
61
the migration direction of the dunes, although, locations, where the migration direction is
62
opposite to the dune shape, have already been sighted (Hanes, 2012).
63
The particles at the beginning of the movement form small ripples or dunes to the point
64
of balance, and after some distance they are destroyed, while new ones are created right after.
65
Small ripples adjust more quickly to currents than larger dunes. Thus, the roughness of the
66
bottom is essential to estimate the direction and magnitude of the sediment transport
67
accurately, since it depends heavily on the type of bedform, which is generated by the
68
transported sediment material itself (Van Rijn, 1993). Typically, the migration direction and
69
asymmetry of the bedforms are good indicators to estimate the patterns of sediment transport;
70
however, these characteristics can lead to a misinterpretation of the residual sediment
71
transport when all the processes acting on the genesis of the bedforms are not taken into
72
account. For example the time-scale being analyzed, the effects of current oscillation and the
73
spatial variation of sediment transport. On bidirectional flows with a dominant and
74
subordinate transport the bedforms have an obliquity in relation to the resultant transport, the
75
current oscillation must be taken into consideration because they may be creating a single
76
bedform orientation, all transport should be considered to have a positive effect (Rubin &
77
Ikeda, 1990).
78
Numerical models provide alternatives for analyzing hydrodynamic flows and sediment
79
transport in tidal channels. When properly calibrated and field-tested, the model offers a
80
synoptic view of the entire studied area, where the current patterns and the turns in the flow
Página 4 de 29
81
patterns can be estimated and observed. Examples of usage in numerical modeling in
82
conjunction with geological evidence are seen in the following studies: in Chu et al., (2009) to
83
determine the morphological behavior of the mouth of the Yangtze estuary, China; in Zhang
84
et al., (2015) to examine transport trends around the Yellow River Delta, China; and in
85
Bonaldo et al., (2014), Fraccascia et al., (2016) and Kubicki et al., (2016) to determine the
86
processes acting on the genesis of the bedforms and the patterns of sediment transport and
87
current.
88
In this present study, the geomorphology of a dune field on a tide channel, with
89
features of flood delta in the inner portion and ebb delta in the direction of the continental
90
shelf, were examined. The region is used as a laboratory field to study the geomorphologic
91
processes occurring on tide deltas, dune fields and also if the characteristics of the bedforms
92
are always good indicators of sediment transport. To elucidate the geomorphologic processes,
93
we analyzed the genesis of bedforms, sedimentary flows, and residual current patterns. The
94
analyzes were made through a baroclinic hydrodynamic and sediment model during
95
December 2015. The apparent roughness map used in the numerical model was estimated
96
from the individual roughness values (flat areas, small ripples, and dunes) and the
97
classification of the dune field, so it is possible to obtain simulations with better
98
correspondence with reality. Besides, the results presented can be applied in coastal zone
99
management and navigation channel actions.
100 101
STUDY AREA
102 103
The object of this study is the dune field located at the southern Estuarine Complex of
104
Paranagua (CEP), in Parana - Brazil, between the Galheta channel and the region of Ponta do
105
Poço (Fig. 1). The navigation channel, with depths of 14m and maintained by dredges, is used
106
by the ports of Paranaguá and Antonina. Paranaguá is considered the largest bulk port in Latin
107
America and the second most important in Brazil (APPA, 2013). The dune field's greatest
108
depths, of around 23m, lie in the region of Ponta do Poço. In the region of Saco do Limoeiro,
109
the depths are less than 2m (Araújo, 2001).The CEP is characterized as a partially mixed
110
estuary (type b) governed by the tide and the river discharge. The tide is semi-diurnal, with an
111
average spring tide oscillation of 1.7m near the mouth and 2.7m in its interior (Lana et al.,
112
2001). The sediment composition is mainly of medium and fine sand, from moderately to
113
very well sorted, due to the influence of the marine environment (Lamour, 2000). In the Saco
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114
do Limoeiro, the particle size distribution tends to be thin and very thin, well-selected to
115
poorly sorted sand (Araújo, 2001).
116
The Galheta shoals occur in the external portion of the mouth, which is a development
117
of a large bank of sand with depths ranging from 1.5m to 5.0m. It is formed by the flows of
118
ebb and the preferred transport from south to north of the shore drift over the mouth delta
119
(Angulo, 1999). In the Galheta shoals, typical features of ebb delta are found, such as
120
spreading bars, submerged bars, and flood channel margins. In the Saco do Limoeiro, one can
121
observe typical features of the flood delta, with a main flood tide, a flood ramp and an ebb
122
spur (Veiga et al., 2005).
123 124 125 126 127 128 129 130 131 132
Figure 1. Location of the studied area, with isobath depths and the navigation channel. The yellow lines demonstrate the longitudinal and transverse sections, with the points where the tidal ellipses were estimated (A, B, C, D, E, F, and G). On the point of observation (PO), the amount of sediment material leaving and entering the channel was observed. The location and extent of the submerged bars were removed and modified according to the study done by Veiga et al., 2005. The red frames over the study area are the extent indicators of figure 6 and 9.
MATERIAL AND METHODS
Página 6 de 29
133
Bedform Estuarine Analysis
134 135
The bathymetric data and mapping were obtained with a multibeam probe (Reson
136
7125) and a side-scan sonar (Starfish Sonar - 200Hz), between February and April 2017, by
137
the Port Administration of Paranaguá and Antonina (APPA). The multibeam probe coverage
138
of the bottom was done only within the channel boundary, while for the Side-Scan Sonar
139
(SSS) the coverage was done from Pontal do Sul margins until the flood delta (Fig. 1 – SSS
140
mapping). The vessels location and movement were constantly corrected with a GPS of high
141
accuracy (Trimble) and a wave compensator (Octans) the bathymetric data was also reduced
142
to the lowest tidal level according to the local navy norms. SSS data collection was conducted
143
along several parallel lines at a constant ideal speed of 5 knots, with the length of submerged
144
cable being constantly measured for post-processing, the backscatter data was then mosaic to
145
a resolution of 10cm.
146
A grid with a spacing of 100m was created on the bedforms’ maps (775 points). The
147
average wavelength (λ) of the bedforms (dunes and small ripples) were measured and
148
classified for each point, according to Ashley and Chairperson (1990). The height of the
149
dunes (∆) was estimated according to Flemming (1988) and validated with the dredged
150
channel's bathymetry data. In areas with data absence and difficult interpretation, the closest
151
bedform was adopted and interpolated between neighboring points. In this region, there is a
152
small quantity of data of this nature. Consequently, the mapping used in the numerical model
153
was elaborated from a compilation of data available in the literature.
154
The roughness of the bedform is essential to correctly estimate the direction and
155
magnitude of the sediment transport since the sediment transport depends heavily on the
156
bottom type, which is usually generated by the sediment transported. The map of apparent
157
roughness was drawn from the preformed bedform classification and by the individual
158
roughness values (flat areas, small ripples, and dunes), described by Van Rijn (1993).
159
=
+
160
= 1.1
161
= 20
(Eq. 1) 1−
.
(Eq. 2) (Eq. 3)
=3
162
For flat areas, apparent roughness is given by
, which is the average grain size of
163
90% of the samples. For areas with the presence of bedforms the apparent roughness is given
164
by the sum of the individual roughness values (Eq. 1), where
is the roughness referring to
Página 7 de 29
165
the small ripples; and
the roughness for large and very large dunes, which are calculated
166
by equations 2 and 3. γ = 1 for bottoms consisting only of small ripples, and 0.7 for bottoms
167
with a superposition of large or very large dune, γ = 0.7 for normal channel conditions.
168
Numerical Simulation
169 170
The sea-level oscillation, the residual currents and the sediment transport were
171
simulated through the FLOW module of the Delft3D modeling software. The model
172
calibrated and validated by Krelling et al. (2017) was used in the boundary conditions to
173
propagate the hydrodynamic fluxes, the tide variations, and the salinity dilution. The 14-layer
174
baroclinic model was modeled over a curvilinear grid with resolutions between 40 and 375m.
175
The roughness was updated with the apparent roughness map obtained in this study. The
176
bathymetry and the bathymetric outlines were also remodeled according to the data from
177
APPA and Angulo (1999). Since the bathymetric data provided by APPA only covers the
178
dredged channel and not the entire estuary. The simulations were carried out during
179
September to December 2015, characterized as a period with the highest precipitation rates,
180
consequently more significant river discharge, and more intense hydrodynamic fluxes
181
(Mantovanelli, 1999).
182
Numerical model elaborated was validated with currents and tide measurements
183
collected by a upward-looking 0.75 MHz Sontek Argonaut-XR Acoustic Doppler Current Profiler
184
(ADCP) over a complete cycle of semidiurnal tide and average time-interval of 30 minutes,
185
from September 1 to September 16 of 2016. Model quality was quantified through the use o
186
root-mean-square error (RMSE) and the Willmott et al. (2012) improved index of agreement.
187
In general, numerical model was able to reproduce tidal elevation and along channel current
188
with satisfactory results, with dr = 0.79 for tidal elevation and dr = 0.77 for along channel
189
current. For cross channel current the model underestimated the amplitude of flows, with dr =
190
0.62 and a mean error of 0.17m/s-1. See Fig 1 – Append A.
191
Several formulae to estimate the bed-load transport rate (
) are described in the
192
literature with different methods to solve the turbulence behavior of the flow or particle
193
motion (Meyer-Peter & Müller, 1948; Kalinske, 1947; Einstein, 1950; Bagnold, 1966; Van
194
Rijn, 2007). Van Rijn's (1993) approach was chosen because
195
of the flow conditions and particle diameter it considers that the movement of the particles is
196
dominated by the saltation of particles, under the influence of hydrodynamic and gravitational
197
forces. Besides, this approach has already been tested (Nabi et al., 2013; Van Den Berg, 1987)
rates are solved as a function
Página 8 de 29
198
and implemented in other studies with good results for real-life situations (Lesser et al.,
199
2004). With this in mind, December 27th and 28th were the dates chosen to demonstrate the
200
patterns of
201
hydrodynamic fluxes.
because they indicated higher tidal oscillations and more intense sediment and
202 203
Tidal Currents Analysis
204 205
The tidal currents were analyzed by the least square method, associated with harmonic
206
constituents of tides, ensuring greater robustness in the interpretation of the data. (Valle-
207
Levinson and P. Atkinson, 1999; Vindenes et al., 2018). The sea-level oscillation data was
208
extracted from the proposed numerical model in this study (Point C on the cross-section - Fig.
209
1), from December 1 to December 31, 2015. The PACMARE software was used to calculate
210
the harmonic constituents over the frequency domain, described by (Franco, 1997). The time
211
series size is sufficient to solve the dominant tide constituents in the diurnal frequency (K1,
212
O1) and semi-diurnal (L2, M2, N2, S2).
213 214
RESULTS
215 216
Distribution of Bedforms
217 218
The large dunes, with wavelengths ranging from 40 to 100m, were concentrated in the
219
mouth, and the majority of them were superimposed by small ripples with some occasional
220
flat areas. The largest overlapping dunes were sighted between Ponta do Poço and Ilha do
221
Mel, reaching a wavelength up to 94m (∆/λ max - Fig. 3). Large and simple dunes, with
222
wavelengths up to 30m, were sighted near Ponta do Poço, but only in lower depths. In the
223
central region, they were also sighted, but with an average wavelength of 15m. In the region
224
of Ponta do Poço, a limited number of ripples was observed, only in depths less than 17m.
225
Página 9 de 29
226 227
Figure 2. The spatial distribution of the dunes at the southern mouth of the CEP, according to their wavelengths.
Página 10 de 29
228 229 230 231
Figure 3. The spatial distribution of the dunes at the southern mouth of the CEP, according to their heights. At
232
Heights of large dunes were validated by a longitudinal section made with the dredged
233
channel's bathymetric data (Fig. 3), with an average height of 1.7m and an average
234
wavelength of 76m, showing good consistency with the estimated data, according to
235
Flemming (1988) (Table 1). The small ripples validation is impractical since the bathymetry's
236
resolutions made with multibeam were 1 - 5m.
237 238 239
the chart below, the longitudinal bathymetric section in the final portion of the dredged channel is represented by a black line.
Página 11 de 29
Dunes size (m) Mean size in meters
240 241
Small
Medium
Large
Large with superposition
Height (∆):
0,22
0,62
1,24
1,87
Wavelength (λ):
4,35
15,41
37,82
60,32
Table 1: The average height and length of the dunes, according to the classification of Ashley and Chairperson, (1990).
242 243
Figure 4 illustrates the various types of bedforms found in this study. The areas with
244
two shades of dark gray, with heights between 1 and 3m, indicate areas with small ripples
245
overlapping larger dunes and of large dunes without overlapping. The angle between the
246
overlapping ripples and the larger dunes is oblique with the crest of the dunes (Fig. 4D). This
247
interaction occurs because the small ripples are more subject to flow variations, and they form
248
more rapidly than the larger dunes.
249
Página 12 de 29
250 251 252
Figure 4. The varieties of bedforms found. A) Large dunes passing longitudinally in small ripples and laterally in flat areas. B) Small ripples steering southeast. C) Medium and simple dunes with a northwest direction. D) Small ripples towards north overlapping large dunes with a northwest/west direction.
253 254
Residual Circulation
255 256
The residual current was calculated through the average values of current, during a
257
fortnightly cycle of semi-diurnal tides by integrating the entire water column. Thus, the
258
orientation and the asymmetry of the currents are described by elucidating the
259
geomorphological processes occurring in the dune field.
260
In the region, near the banks of Pontal do Sul and Morro do Miguel, two areas with
261
residual circulation towards the continental shelf were sighted. The residual circulation in the
262
dredged canal, from Pontal do Sul up to Ponta do Poço, is estuary inward. On the right side of
263
the dredged canal, adjacent to the Saco do Limoeiro, the direction is southeast. The residual
264
circulation forms three main vortices. One is located in the Ponta do Poço, between the
265
continental margin and the left side of the dredged canal. The other two are on both sides of
266
the main channel, at the mouth, near the Saco do Limoeiro and the shores of Pontal do Sul
267
(Fig. 5).
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268 269 270 271 272 273
Figure 5. The direction and the magnitude of the residual circulation calculated during a fortnightly tide cycle, between December 15th and December 31st, 2015. The black arrows outline the preferred route of the residual currents, considering only the vectors' direction.
Sediment Transport and Tidal Currents
274 275
In the region of the Saco do Limoeiro, the modeled tendency of bed-load transport
276
shows moderate similarity in relation to the migration direction of small ripples and large
277
dunes, identified by Angulo (1999). The magnitude of bed-load transport is higher during ebb
278
than in flood period (Fig. 12). It is possible to conclude that the small ripples on the dorsum of
279
medium dunes happen during the flood, and the medium and large dunes form through a
280
combination of flood and ebb currents. The flood ramp identified by Angulo (1999) is
Página 14 de 29
281
represented in this study through the vector of bed-load transport near the Morro do Miguel
282
(Fig. 12c).
283
The harmonic constituents calculated at point C of the cross-section are listed in the
284
table below. Several combinations between the diurnal and semi-diurnal components were
285
tested by the minimum square method. The combination that obtained the highest
286
concordance index was used to calculate the parameters of the tidal ellipse and the phase
287
difference.
288 Harmonic constituents Daytime Lunar-solar declination Minor elliptical lunar Main lunar Semi daytime Minor elliptical lunar Main lunar Minor elliptical lunar Main solar
Symbol Frequency Amplitude Phase K1 M1 O1
15,04 14,49 13,94
8,43 0,91 11,67
188,01 243,83 73,69
L2 M2 N2 S2
29,52 28,98 28,43 30
0,73 40,35 6,01 28,77
90,94 83,52 170,25 101,41
289 290 291
Table 2. The harmonic constituents extracted and used in the harmonic analysis of the velocity components U and V. The frequency is given per hour in degrees, the amplitude in centimeters, and the phase in degrees.
292 293
The behavior of the currents, associated with harmonic constituents of tides, had better
294
accordance between components M2 and K1, with a concordance index of 0.93 for the U
295
component and 0.92 for the V component of velocity (Fig. 7). The tide currents of the main
296
channel (points A through D) are approximately 4 times larger (0.39 and 0.097, respectively)
297
than those of the Saco do Limoeiro (points E, F, G) (Fig. 6).
298
At all points, the M2 component was more prominent than the K1. The values of the
299
semi-major axis of the tidal ellipse range from 0.40 m/s to 0.59 m/s in the middle of the
300
channel (Fig. 6a, 6b, 6c and 6d), and from 0.08 m/s to 0.17 m/s in the Saco do Limoeiro (Fig.
301
6e, 6f, 6g). The orientation of the tidal ellipse is approximately 133° at the main channel and
302
104° at Saco do Limoeiro.
Página 15 de 29
303 304 305
Fig. 6. The tidal ellipses calculated on the A, B, C, D, E, F, and G points of the cross-section from the harmonic
306 307 308
Figure 7. The variation of the tidal current calculated from the sum of the Harmonic constituents M2 and K1
constituent M2 in blue and K1 in red.
(black) and the modeled (red).
309 310
The phase variation along the cross-section (Fig. 8), calculated from the main lunar
311
component (M2), shows a maximum difference of 15° (30 minutes) between the main channel
312
and the Saco do Limoeiro. The phase difference between the bottom layer and the surface is
313
approximately 1 degree (2 min) in the main channel, and up to 5 degrees (10 min) near the
314
banks of the Saco do Limoeiro.
Página 16 de 29
315 316 317 318 319
Figure 8. The phase difference along the cross-section, calculated from the Harmonic constituent M2 and concerning the geographic north; 1 degree corresponds to approximately 2 minutes. From 12/27/15, at 4:00 AM until 12/28/15, at 2:00 PM.
320
Bed-load transport during ebb and flood, shows the hydrodynamic complexity of the
321
area near the Pontal do Sul's margin, where the formation of a vortex occurs (Fig. 12). The
322
sediment transport vectors modeled are aligned with the direction of the large overlapping
323
dunes (Fig.12a and 12b). The triangular format, slightly inclined to the east of the large dunes,
324
indicates that the features were formed by a combination of the dominant sediment transport
325
of flood and the subordinate ebb. It was observed that in the areas where large and composed
326
dunes are formed, the sediments are trapped because of this combination between the
327
hydrodynamic fluxes.
328
Contrary to what was seen at the Saco do Limoeiro, an erosive process occurs due to
329
anthropic action on the other side of the channel. Between 1954 and 1980, the coastline
330
reached back to 150m and the beach morphology changed from sandy spurs (Fig. 9a) to a cliff
331
and tidal flats (Angulo et al., 2016). In the numerical simulation, the macro-drainage channel
332
and the Techint pier were not considered, but it is still possible to see how the obstruction of
333
the coastal drift occurs. During the flood the total sediment transport rate was parallel to the
334
margin (W-NO) removing sedimentary material from the sand bars and coastal drift to the
335
estuary. During the ebb, this sedimentary material is transported back. The coastal works
336
blocked the sediment source causing erosion at the beach.
337
Página 17 de 29
338 339 340 341
Figure 9. Aerial photographs of the coastline between Pontal do Sul and Ponta do Poço. (A) 1954, (B) 1980, ( modified from (Rodolfo José Angulo et al., 2016). In C the total sediment transport rate (suspended+bed-load) during flood, December 27th, 2015, at 7:30 AM, and ebb, December 27th, 2015, at 10:30 AM.
342 343
The cumulative sediment transport consists of the sum of the total sediment transport
344
rate (bed-load + suspension) during a semi-diurnal tide cycle (12.5h). Hence, it is possible to
345
estimate the positive or negative balance of sedimentary material being mobilized in each tide
346
cycle over a monthly cycle (December 1st to 31st). The negative values for the U component
347
show that the sediment material is being withdrawn from the location to the platform, and the
348
positive values into the estuary.
349
The total sediment transport occurs in the spring tide days, being almost null during the
350
neap. The average amount of sediment material being mobilized per tidal cycle is 0.39 ton/m,
351
approximately 0.61 ton/m entering the estuary and 0.17 ton/m exiting the estuary (Fig. 10a).
352
On average, about 71% of the sediment material is deposited on-site, a 0.43ton/m per tide,
353
representing an increase of 3cm concerning depth (Fig. 10b). However, there is a reversal in
354
sediment transport patterns from the middle of the channel towards the margins, as seen in the
355
current pattern residuals (Fig. 5). The amount of sediment material towards the platform
356
exceeds the amount entering the estuary.
Página 18 de 29
357
358 359 360 361
Figure 10. Sediment transport at the observation point (Fig. 1 - PO). (A) Cumulative sediment transport of entrance and exit. (B) Quantity of sediment material deposited in relation to the sediment transport of entrance and exit.
362 363
DISCUSSION
364 365
In this study, the types of bedforms at the southern mouth of the CEP and the factors
366
controlling its shape and genesis were described. Numerical modeling, in conjunction with the
367
bedform maps, allowed us to explore the direction of the sediment transport and the amount
368
of sediment material entering and leaving the south mouth during a tide cycle. The largest
369
dunes (∆ = 1-3m, λ = 40-100m) were found to be directly related to the magnitude of the bed-
370
load transport. The areas with small ripples had lower bed-load transport than the regions with
371
large dunes.
372
The large dunes, near the Pontal do Sul margin, have a triangular shape with small
373
overlapping ripples of north and south directions. Since the angle of the face and the dorsum
374
inclination of the large dunes is determined by the relative force between the flood velocities
375
and ebb (Allen, 1980), the triangular shape slightly inclined to the east indicate that the
Página 19 de 29
376
sediment transport of ebb is equated to the prevailing flood flow. During flood periods, the
377
sediment material is conducted into the estuary in the middle of the channel, forming small
378
ripples and accumulating material on the large dunes (Fig. 11b). During the ebb, these ripples
379
are supposed to be eroded and attached to the large dunes or the water column (Fig. 11a).
380 381 382 383 384 385
Figure 11. Sediment transport by bed-load (m3/s/m) during maximum flood - December 26th, 2015, at 4:00 PM (B) - and ebb - December 26th, 2015 at 9:00 PM (A). The figures on the left show the insertion area of the red square, with the reflectance maps of the seafloor overlapped by the bedform transport vectors. The figures on the left, represented by black areas, are the very large dunes with and without overlaps.
386
Previous studies have pointed out that the main transport tendencies at the south mouth
387
are directed inward the estuary with E/NE direction (Lamour et al., 2007; Lamour, 2000). In
388
this study, the bed-load transport flows and the residual currents also show an estuary inward
389
tendency in the dredged channel, and formation of vortices with seaward sediment transport,
390
near the borders of Pontal do Sul and Ilha do Mel (Fig. 5). In addition, it is possible to
Página 20 de 29
391
conclude that the submerged bars are formed from these vortices and the sediment transport
392
interacting with the coastal drift. After the vortex, near Pontal do Sul, sediment transport
393
flows return to the estuary inward until the south of Ponta do Poço, where a vortex formation
394
occurs clockwise. On the right side of the dredged channel, near the Morro do Miguel,
395
hydrodynamic flows have E-S directions (Fig. 5). This innermost region of the mouth shows
396
us the importance of spatial variation in estimating sedimentary transport by the dune field. In
397
the case of using small sampling area, such as the middle of the channel or near the margins,
398
it would hide the inlet and outlet dynamics and the formation of a sediment trap vortex.
399
The process of interaction between the coastal drift and the sediment transport near the
400
mouth observed in this study is also investigated in the Changjiang Delta. The recirculation
401
vortices and the residual transport that occurs in the mouth’s boundaries are associated with
402
the accretion trend of the navigation channel and the expansion of the mouth towards the sea
403
of the mouth (Chu et al., 2009; Saito et al., 2001).
404
In the flood delta region of Saco do Limoeiro, three types of bedforms occur: large
405
dunes, medium dunes, and small ripples (Angulo, 1999). The largest bedforms have a
406
wavelength up to 200m, with NNE and NNW directions. The medium dunes present
407
wavelengths up to 10m and SSW-NNE and SW-NE directions. The flood ramp beginning is
408
located near the Moro do Miguel, just after the vortex near Ponta do Caraguatá (Fig. 5).
409
Although the dunes were flooded oriented, the hydrodynamic surveys of Araújo (2001)
410
indicate the trend of ebb transport of non-cohesive sediments, during spring tide days in calm
411
sea conditions. The geomorphological evolution of the Saco do Limoeiro also shows that it
412
tends to export sediments in long term. On the beach between Pontal do Sul and Ponta do
413
Poço there is also erosive process, but caused by the influence of the jetty built in the macro-
414
drainage channel. It blocks the sediment transport during flood period changing the beach
415
morphology.
416
This contradiction between the direction of the dunes migration and the
417
geomorphological evolution of the flood delta is explained by the effects of the oscillation in
418
the tidal current and the influence of low bathymetry in the region, in the propagation of the
419
tidal wave. The tidal wave, crossing the gap between Pontal do Sul and Ponta do Caraguatá,
420
progressively gains NE direction when entering the flood delta, while in the dredged channel
421
the direction is NW, explaining the direction trends of the small ripples (Fig. 12a). Due to
422
depth variations and bedform friction effects, the tidal wave moves more slowly in the flood
423
delta than in the main channel, confining water in the delta region. The current maximums 30
Página 21 de 29
424
minutes phase difference between the flood delta and the channel demonstrates this
425
confinement of water. The ebb current starts with W-SW direction (Fig. 12b), and gradually
426
moves counterclockwise to SE. This type of flood tidal delta shows how the direction of the
427
sediment transport inferred by the dune field may be mistaken with the geomorphological
428
evolution of the bottom. The direction SW of the largest bedforms give a false impression of
429
deposition, when the current oscillation is eroding the flood delta. The current pattern and the
430
erosion processes of the Saco do Limoeiro region are illustrated by bed-load transport
431
patterns. (Fig. 12).
432 433 434 435 436
Figure 12. The sediment transport by bed-load transport (m3/s/m) during the ebb - December 28th, 2015, at 8:30 PM (B) - and flood - December 28th, 2015 at 3:00 PM (C). (A) Migration direction assumed through the crests of the bedform, small ripples, medium dunes, and large dunes, modified from Angulo, (1999).
Página 22 de 29
437
Similarly, a tide asymmetry was identified in Denmark's Wadden Inlet Channel (Knude
438
Dyb), and a flow separation with a recirculation vortex was developed approximately 1h
439
before the next flood period, between the main channel and the tidal plain. These processes
440
were associated with the depth differences between the main channel and the tidal plain.
441
Besides, recirculation vortices are found with the direction of migration of the large dunes
442
(approximately 2.3m height and 155m wavelength), following the direction of the residual
443
circulation flows (Fraccascia et al., 2016; Ridderinkhof et al., 2016). A similar physical
444
process was demonstrated in this case study, but with different magnitudes and delay of the
445
tidal current maximums.
446
Contrary to what was observed in the Saco do Limoeiro, in the Lobos Point and Bonita
447
Point bay, the recirculation vortices, formed from the rocky headlands, show the sediment
448
transport being retained and transported back to the ebb-tidal delta, being that these areas with
449
flood dominance were attributed to the stability of Baker Beach (Elias and Hansen, 2013). In
450
McDonald Bank, Whangarei Harbor, there is a similar process of sediment accumulation with
451
the presence of recirculation vortices and sediment transport occurring in closed cycles. From
452
the flood ramp, the flood residual streams follow uninterruptedly to north of the Snake Bank,
453
reversing the direction in Shoal Bay and McDonald Bank to the south of Darch Point where
454
ebb residual currents rapidly decelerate (Black et al., 1989; Black and Healy, 1986).
455
The distinction between the sedimentation/erosion processes occurring in the Saco do
456
Limoeiro and in the Lobos Point and the McDonald Bank are due to the preferred direction of
457
the flood residual streams in relation to the mouth. In the Point Lobos and the McDonald
458
Bank, the recirculation vortex has a clockwise direction and the residual streams of flood
459
enter perpendicularly to the mouth. For the Saco do Limoeiro, the vortex has a
460
counterclockwise direction and the angle of entry of residual streams is oblique.
461 462
CONCLUSION
463 464
The bedforms and the sediment transport of the south mouth of the Paranaguá Bay were
465
investigated through mapping together with a hydrodynamic and sediment model. The
466
preferential direction of the sediment transport was inferred by the geomorphology of the
467
dunes and supplemented with the direction of the sediment transport obtained by the
468
numerical model. The main results obtained in this study are the following:
469
Página 23 de 29
470
- The residual current vortices, near Pontal do Sul are responsible for the overlap of small
471
ripples to windward of the dunes, and also the triangular shapes of the large dunes. From the
472
interaction of this vortex and the coastal drift the submerged bars are formed and continuously
473
remodeled.
474
- At the flood delta (Saco do Limoeiro) was demonstrated how the genesis of the bedforms
475
could lead to a false interpretation of geomorphologic evolution. The erosion tendency of the
476
flood delta was illustrated by the residual circulation patterns when entering the mouth and by
477
the water confinement, identified in the analysis of the tidal currents.
478 479
ACKNOWLEDGMENTS
480 481
The authors would like to kindly thanks APPA for providing the data that made this
482
study possible, and also Mihael Machado de Souza for your support with the numerical model
483
that was used at the boundaries conditions. The Center of Marine Studies of Federal
484
University of Paraná (CEM-UFPR) and the Coastal and Oceanic Systems Graduate Program
485
(PGSISCO) were also essential to complete this study by providing fundings, scientific
486
knowledge and the computational framework for this research paper. The authors would also
487
like to thank the two anonymous reviewers of this journal for helpful comments and insights.
488 489
REFERENCES
490
Allen, J.R.L., 1980. Sand waves: A model of origin and internal structure. Sediment. Geol.
491 492 493 494
26, 281–328. doi:10.1016/0037-0738(80)90022-6 Angulo, R.J., 1999. Morphological characterization of the tidal deltas on the coast of the state of Paraná. An. Acad. Bras. Cienc. Araújo, A., 2001. Dinâmica sedimentar e evolução paleogeográfica do Limoeiro's Bag na
495
Honey Island, e sua relação com o canal de acesso ao porto de Paranaguá. Bol. Paraná.
496
Geociências. doi:10.5380/geo.v51i0.4187
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Angulo, R.J., Borzone, C.A., Noernberg, M.A., José, C., Quadros, L. De, Souza, M.C. De, Cruz, L., 2016. Brazilian Beach Systems. doi:10.1007/978-3-319-30394-9 Ashley, G.M., Chairperson, S., 1990. Classification of Large-Scale Subaqueous Bedforms: A
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New Look at an Old Problem-SEPM Bedforms and Bedding Structures 60, 160–172.
501
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Figure 13. Model validation results (red) in relation to field data (black). For along channel current on first chart, cross channel current on intermediate, and tides on last chart.
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Figure 14. Map of apparent roughness calculated through bedform classification and by sum of the individual roughness values.
HIGHLIGHTS - The bedforms and the sediment transport of the south mouth of the Paranaguá Bay were investigated through mapping together with a hydrodynamic and sediment model.
- The residual current vortices, near Pontal do Sul are responsible for the overlap of small ripples to windward of the dunes, and also the triangular shapes of the large dunes.
- At the flood delta (Saco do Limoeiro) was demonstrated how the genesis of the bedforms could lead to a false interpretation of geomorphologic evolution. The erosion tendency of the flood delta was illustrated by the residual circulation patterns when entering the mouth and by the water confinement, identified in the analysis of the tidal currents.
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
Port Administration of Paranaguá and Antonina (APPA) provided the data multibeam and backscatter data that made this study possible and the numerical model that was used at the boundaries conditions was provided by Mihael Machado de Souza. The Center of Marine Studies of Federal University of Paraná (CEM-UFPR) and the Coastal and Oceanic Systems Graduate Program (PGSISCO) were also essential to complete this study by providing fundings, scientific knowledge and the computational framework for this research paper.