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Tidal eddies in a semi-enclosed basin: a model study
MARINE ENVIRONMENTAL RESEARCH Marine Environmental Research 59 (2005) 519–532 www.elsevier.com/locate/marenvrev
Tidal eddies in a semi-enclosed basin: a model study P. Vethamony *, G.S. Reddy 1, M.T. Babu, E. Desa, K. Sudheesh National Institute of Oceanography, Dona Paula, Goa 403 004, India Received in revised form 14 August 2004; accepted 27 August 2004
Abstract A modeling study has been carried out to support a Marine Management Plan for the Gulf of Kachchh, India and here the hydrodynamic part of the programme is described. The hydrodynamic model accurately predicts the tides and tidal currents present in the Gulf and these have been validated with the measured data, albeit at only a few locations. The time averaged residual currents obtained from the model for one lunar cycle clearly reproduce the complex, small-scale, topographically induced flows with several eddies. The existence of a dynamic barrier along Sikka–Mundra section, which divides the Gulf into two distinct dynamic systems, is very evident. The model is further used to predict the movement of surface floating particles launched at different locations in the Gulf, as an aid to determining floating pollutants. The results indicate that industries discharging wastes upstream of the barrier should use extreme caution, as these will remain in the vicinity for at least one lunar cycle. 2004 Elsevier Ltd. All rights reserved. Keywords: Gulf of Kachchh; Hydrodynamic model; Currents; Tidal eddies; Dynamic barrier; Particle tracking; Industrial wastes
*
Corresponding author. Tel.: +91 832 2450473; fax: +91 832 2450602/2450603/2450604. E-mail addresses: [email protected], [email protected] (P. Vethamony). 1 Environ Software Pvt. Ltd., Wilson Garden, Bangalore 560 030, India.
0141-1136/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.marenvres.2004.08.002
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P. Vethamony et al. / Marine Environmental Research 59 (2005) 519–532
1. Introduction The Gulf of Kachchh (GoK) is a semi-enclosed basin located in the northern part of west coast of India and opens to the Arabian Sea (Fig. 1). It has grown in economic importance due to acceleration of industrial developments in recent years. Refineries, fertilizer, chemical and cement industries, power plants, minor and major ports and salt works are the major industries, which make use of GoK. Most of these developments are concentrated along the southern shore of GoK, where eco-sensitive areas like Marine Sanctuaries (MS) and Marine National Parks (MNP) are located. Four Single Point Moorings (SPMs) are operational and two more are under consideration along the southern Gulf. The northern Gulf is also being considered for establishing SPMs. In addition, the ports at Okha, Navlakhi, Kandla, Mandvi and Jakhau in the Gulf handle a variety of cargoes, especially petroleum products, and are responsible for considerable tanker traffic in the Gulf. The Gulf may face severe environmental stress, and in due course the impact will be felt on the MNP and MS, if the usage of Gulf is not properly planned. It has therefore become important that a holistic view of the Gulf is taken, vis-a`-vis its ecosystem and existing developments, to properly plan and manage future activities in the Gulf. The National Institute of Oceanography, Goa has been carrying out several projects for industries in the Gulf region for the past three decades, but limited to specific locations. Therefore, a detailed model study has been undertaken under the major project ‘‘Integrated Management of the Marine Environment of the Gulf of Kachchh’’ to understand hydrodynamics, temperature-salinity distributions, water
Fig. 1. The major morphological features of the Gulf of Kachchh.
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quality, oil spill movements and carrying capacity of the entire Gulf. This project takes into account all the environmental data collected in the Gulf so far. The results of hydrodynamic modeling, especially the significance of residual currents and tidal eddies to pollutant transport, are presented in this paper. Tides and tidal currents in the Gulf have been modeled by a few researchers to assess the tidal potential, track the oil spill trajectories and understand the tidal amplification and resonance (Anon., 1999; Shetye, 1999; Unnikrishnan, Gouveia, & Vethamony, 1999; Vaidyaraman, Ghosh, & Gokhale, 1987). No previous study carried out in the Gulf has brought out the dynamic barrier feature or the implication of tidal eddies to pollutant transport in the Gulf. This study relates the significance of tidal eddies and dynamic barrier while planning the Gulf for installing marine facilities to the east of Mundra–Sikka sector. Only a few tidal stations are available in the Gulf. Hence, this model can be used to predict tides at any location in the Gulf. Regions such as Gulf of Oman, Gulf of Aden, Persian Gulf and Gulf of Cambay (India) are very similar to the GoK in several aspects including geographical location, surface meteorology, oceanography, tidal conditions and tanker-traffic are concerned, and the present study can find applications to such regions also. The topographic small scale eddies are very complex, but their presence is evident in the flow pattern. Falconer, Wolanski, and Mardapitta Hadjipandeli (1986) used a 2D depth averaged numerical model to study the main features of measured eddies near Rattray Island, North Queensland. It is residual currents/eddies, rather than instantaneous tidal flows, which contribute to the net transport of materials from the system. Flushing of lagoons is faster if topographically induced tidal eddies are present (Wolanski and King, 1990). The tidal eddies that form behind the Bardsey Island during flood and ebb tides showed that they persist during the period of slack waters (Elliott, Bowers, & Jones, 1995). The factors contributing to the formation of topographic tidal eddies are lateral gradients (Morales-Perez & RamirezLeon, 1996), shear due to bathymetric variations and tides (Takeoka & Murano, 1993). It is therefore important for scientists and environmental managers concerned with the ecosystem of the Gulf to understand the hydrodynamics and the role of residual tidal eddies in the transport of pollutants.
2. Gulf setting The Gulf is about 170 km long and 75 km wide at the mouth. It is a very complex water body, encompassing several tidal inlets, creeks, small islands, shoals, coral reefs, tidal flats and rocky regions (Fig. 1). The Gulf is relatively shallow with maximum water depth varying from 60 m at the mouth to 20 m at the head. The topography of the mouth and the mid-gulf is relatively more rugged compared to the head. A coastal plain with indentation, inlets, offshore islands and coral reefs marks the southern Gulf. The northern Gulf, consisting of sand and mud, is marked by numerous sandy shoals. The sediments derived from land are limited, as the whole region is arid. The suspended sediment load varies from 0.19 to 0.51 g/l and 0.11 to 3.60 g/l
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during pre-monsoon and post-monsoon, respectively. The complex bathymetry, rugged bottom topography and undulations in the shoreline produce highly non-linear tidal interactions. The Gulf circulation is dominated by a strong tidal signal with amplitudes increasing considerably upstream. For example, the mean high water spring of 3.5 m at the mouth (Okha) increases to 5.4 m at Sikka and 7.2 m at the head (Navlakhi). The Fresh water discharge into the Gulf is negligible. The time series data of sea surface temperature (SST) and air temperature collected at a few locations show that during morning hours the sea surface is warmer than the air. As the day progresses the air becomes warmer than the sea surface. Vertical profiles of temperature and salinity measured at several locations over a period of 25 years reveal a nearly homogeneous water column with no vertical stratification due to intense tidally-driven turbulence mixing. The water temperature measured at three levels (surface, mid-depth and bottom) at different locations in the Gulf during different seasons also shows that the water temperature undergoes a diurnal variation – relatively higher for surface than the bottom waters. Strong evaporation and scanty rainfall make the Gulf a highly saline water body. The salinity values averaged over the period 1976–1999 show that the maximum salinity ranges from 36.6 psu (off Okha) to 45.5 psu (off Navlakhi). In the Indian coastal region, we have observed this sort of range in salinity as well as high values only in the GoK. In general, surface currents range from 0.75 to 1.25 m/s in the mouth to 1.5– 2.5 m/s in the head. Measurements show that surface and bottom currents are nearly the same, except off Vadinar and Positra (Fig. 2), where the presence of numerous shoals and reefs pose an obstruction to bottom currents. For example, during spring tide, the surface currents measured off Positra in pre-monsoon (February 1997) have a peak speed of about 1.0 m/s (the direction is SE during flood and NW during ebb), and the bottom currents about 0.5 m/s (the direction is SE during flood and N during ebb). The bottom currents reflect the effect of local topography. The currents recorded in September 1997 (post-monsoon) show a similar pattern. In order to substantiate that there is no vertical stratification in the Gulf, the currents measured using a Doppler Current Meter at 6 levels off Sikka (water depth = 20 m) in May 1996 (Fig. 3) have been analysed. In the Gulf region, winds are relatively stronger only during monsoon months (May–August) and wind effect will be felt at the surface, as tidal forcing is stronger than wind forcing in the subsurface layers. This is evident from Fig. 3, where the monsoon wind influence is seen only on the surface currents (1 and 4 m) and not on the sub-surface currents. The sub-surface currents are nearly of the same order of magnitude.
3. Model description Since the waters are generally vertically homogeneous, a 2D model should reproduce the tides and currents in the Gulf.
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Fig. 2. Scatter plot of surface and bottom currents at select locations in the Gulf.
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Fig. 3. Vertical current pattern off Sikka.
3.1. Governing equations Simulation of tides and currents has been carried out by solving the following 2D shallow water equations of mass and momentum: og ouH ovH þ þ ¼ 0: ot ox oy
ð1Þ
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The two depth-averaged momentum equations can be written as: ouH ou2 H ouvH og o ou o ou þ þ ¼ fvH gH þ H Kx Ky þH ot ox oy ox ox ox oy oy þ swx sbx ;
ð2Þ
ovH ovuH ov2 H og o ov o ov þ þ ¼ fuH gH þ H Kx Ky þH ot ox oy oy ox ox oy oy þ swy sby ;
ð3Þ
where t = time; x,y = Cartesian coordinates; u,v = depth averaged velocity components in the x and y directions, respectively; f = Coriolis parameter; g = acceleration due to gravity; Kx, Ky = diffusion coefficients in the x and y directions, respectively; g = water elevation with respect to mean sea level; H = total water depth at any instant; swx,swy = wind stress in x and y directions; sbx,sby = bottom stress in x and y directions. 3.2. Boundary fitted coordinate system In the Cartesian or rectilinear coordinate system, it is difficult to represent the complex coastline accurately since the grid size remains the same at all locations. The present model makes the computations in the boundary-fitted or generalized curvilinear coordinate system (Fig. 4) in order to resolve complex geometry accurately in the horizontal direction. The boundary fitted coordinate (BFC) system takes care of coastal shape and makes fine mesh near the coastline. In case of narrow
Fig. 4. Computational mesh (BFC) for the Gulf of Kachchh.
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head, flux boundary conditions should be used. The model treats the islands, as drying and flooding options are available. Once the coastal shape is defined, BFC system generates orthogonal and nonorthogonal grids automatically by defining number of grids in x and y directions. The grid is non-uniform both in x and y directions and it is a skewed mesh. This necessitates the transformation of the governing equations into boundary-fitted coordinates (1,r). The (x,y) coordinates are transformed in such a way that their components are perpendicular to the (1,r) coordinate lines. This is accomplished by employing the chain rule transformation. The momentum equation in the x direction can be written in BFC system as oðuH Þ oðu2 H Þ oðu2 H Þ oðuvH Þ oðuvH Þ þ 1x þ rx þ 1y þ ry fvH ot o1 or o1 or og og þ gH 1x þ rx o1 or 2 2 ou ou o2 u 2o u 2o u þ ðrx Þ þ 21x rx HK x 1xx þ rxx þ ð1x Þ o1 or o1 or o1or 2 2 ou ou o2 u 2o u 2o u þ ð1y Þ þ ðry Þ þ 21y ry HK y 1yy þ ryy swx þ sbx o1 or o1 or o1or ¼ 0;
ð4Þ
where 1x, 1y, rx, ry, 1xx, 1yy, rxx, ryy = grid transformation parameters, h = water depth up to mean sea level H ¼ h þ g:
ð5Þ
Similarly, the momentum equation in y direction can be written in the BFC coordinate system. More details about transformation of basic governing equations of flow from Cartesian to BFC is found in Reddy (1997). The transformed governing equations of flow have been discretised on a staggered grid and solved using Leapfrog trapezoidal scheme through a predictor and corrector step method. The numerical scheme is based on finite difference method and fully centered in space and time. In the BFC system, grid size varies both in the x and y directions and accordingly time step (Dt) also changes. Dt is chosen in such a way that it satisfies the CFL criterion, Dt < 0.5Dx(gH)0.5. The stability analysis of Leapfrog scheme has been analysed by Wang (1998) and Wang and Ikeda (1997). They reported that the scheme is conditionally stable for u.(Dt/Dx) = 0.8. The same scheme has been used in the present study, and correction has been done at every time step. 3.3. Model setup The computational domain of the model is selected from Okha to beyond Kandla between the longitudes 69 02ÕE and 70 18ÕE and the latitudes 22 17ÕN and 22 53ÕN. The model domain is divided into 110 · 50 grids in x and y directions, respectively. Fig. 4 shows the computational grid for the entire Gulf. The bathymetry is selected from the hydrographic chart.
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The horizontal diffusion coefficients Kx and Ky are calculated as follows: pffiffiffiffiffiffiffiffiffiffiffiffiffiffi K x ¼ ax g u2 þ v2 =C 2 ; K y ¼ ay g
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi u2 þ v2 =C 2 ;
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ð6Þ ð7Þ
where ax and ay are the constants in depth averaged eddy viscosity coefficients in x and y directions and C (in m1/2/s) is the Chezy coefficient. The diffusion coefficients for horizontal exchange of momentum vary in space. The wind stress in the x and y directions (swx and swy) can be written as: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð8Þ swx ¼ qa C d U w ðU 2w þ V 2w Þ; swy ¼ qa C d V w
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðU 2w þ V 2w Þ;
ð9Þ
where qa = air density; Cd = drag coefficient; Uw, Vw = wind components in the x and y directions. The bottom stress in the x and y directions (sbx,sby) can be written as: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð10Þ sbx ¼ gu ðu2 þ v2 Þ=C 2 ; sby ¼ gv
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðu2 þ v2 Þ=C :
ð11Þ
The bottom roughness in the GoK varies according to bed sediment size. The bed is composed of clay, sand, silt and rock soils. Depending upon bed configuration and sediment particle size, the d50 size (mean sediment particle size in mm) is selected to compute the ManningÕs roughness values. The boundary conditions selected are as follows: (i) along the western open boundary (from Okha to north corner), predicted Okha tide of October 1994 available in the Indian Tide Tables (Anon., 1994) has been imposed to force the model as no tidal station or measured data is available on/for the northern corner; (ii) no flux across the closed boundary near Kandla; (iii) no flux along the northern and southern boundaries of the Gulf. As the predicted tides are given at larger time interval (6 h), cubic spline interpolation technique has been applied to calculate the value at each computational time step.
4. Results and discussion 4.1. Calibration and verification The model has been calibrated by providing two sets of bed roughness coefficients, estimated from d50 sediment size and bed configuration. Based on the available information, we find that these two sets of coefficients are the most suitable for the GoK. The computational runs have been executed for the two sets of bed roughness coefficients till computed and measured tides off Sikka match (Fig. 5). The discrepancy, both in phase and amplitude, is within the acceptable
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Measured Computed with bed coeff1 Computed with bed coeff2
7
Tide elevation (m)
6 5 4 3 2 1 0 -1 0
2
4
6
8
10
12
Time in days
Fig. 5. Comparison of measured and computed tides during 1–12, October 1994 at Sikka with variable bed roughness coefficients.
range for tides computed using bed roughness coefficient 1. Therefore, bed roughness coefficient 1 is used in all subsequent simulations. The results indicate that nearly two tidal cycles are required for the model to reach dynamical equilibrium from the cold start. Several model runs have been carried out to test the model efficiency in reproducing tides and currents in the entire computational domain. For validation, the model has been forced with March 94 tide data at Okha. The simulated tides and currents have been validated with those measured at the monitoring points, which include the moorings off Vadinar, Sikka and Mundra. As a typical case, here we present the validation of Vadinar currents. The simulated and measured currents off Vadinar (Fig. 6) show a discrepancy of the order of 10 cm/s in magnitude. This may be due to the following three reasons: (i) depth-averaged form of the numerical model; (ii) lack of measured or predicted input tide data at the northern corner of western open boundary; (iii) the leapfrog scheme tends to overestimate the phase speed, while the implicit scheme tends to slow down the phase speed (Wang & Ikeda, 1997); (iv) the bottom topography and geomorphological features of the southern Gulf change abruptly within a few kilometers, and this causes mismatch in the measured and simulated currents, especially when the measurement location does not coincide with the model location (of the order of a few hundred meters in the present case). 4.2. Tides and tidal currents The model clearly reproduces the tidal variation at various locations all along the Gulf. In general, the tidal currents flow in the ENE direction during flood and WSW during ebb, with relatively high currents along the central Gulf (reaching upto 1.5 m/s). A typical variation of tides during ebb condition in October 1994 is shown
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Measured
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Computed
0.9
Current speed (m/s)
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 9.0
9.5
10.0
10.5
11.0
11.5
12.0
12.5
13.0
13.5
14.0
Time (in days)
Fig. 6. Comparison of measured and computed currents off Vadinar during 9–14 March 1994.
in Fig. 7. The tidal elevation and tidal currents computed at various locations agree with those measured at the same locations during different seasons and years (please refer to the section: Gulf setting). 4.3. Tidal circulation and eddies The residual currents in the Gulf computed by integrating velocities over a period of one month in October 1994 are presented in Fig. 8. In the eastern half of the Gulf, the circulation shows a net transport towards Kandla (along the northern
Fig. 7. A typical ebb current system in the Gulf.
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Fig. 8. Average residual currents and eddies.
rim of the Gulf) with a tendency to form a clockwise circulation. On the contrary, in the western Gulf, the residual circulation presents anti-clockwise eddies of different sizes, except one clockwise eddy in the northern Gulf (off Mandvi). It is evident from Fig. 8 that the net transport from the open ocean into the Gulf is through the southern side of the mouth, and the net outward transport is through the northern side, forming an anti-clockwise circulation in the western part. Tidal eddies shed by coastal features such as coral reefs and islands play a vital role in transporting materials. The geometry of the Gulf is such that the tides enter into it through the southern side and pushes the water inside. As the Gulf width suddenly drops at the mid-Gulf and coastal orientation changes abruptly thereafter (Fig. 1), the water flow is deflected towards north, and forms a dynamic barrier across Sikka–Mundra section. One branch of this northern flow contributes to the westward flow (outflow of the Gulf), and the other branch to the eastward flow, both along the northern rim of the Gulf. This dynamic barrier retards the flushing of the Gulf, which is a matter of concern when industrial wastes are released. 4.4. Particle trajectories In the field, usually drogues are released at desired locations, and their positions over space and time are tracked to calculate the surface drift. In the present study, numerical experiments have been conducted to further illustrate the flow pattern – by releasing particles at six select locations in the vicinity of the dynamic barrier and tracking their trajectories (Fig. 9). The results show that particles follow the eddy system present in the Gulf. Wang (2001) has used a model to predict surface trajectories of oil spills and floating objects utilising surface current, wind speed
P. Vethamony et al. / Marine Environmental Research 59 (2005) 519–532 trajectory 1 trajectory 2 trajectory 3
Start point End point
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trajectory 4 trajectory 5 trajectory 6
22.9
Latitude (Deg)
22.8 22.7
6
2
1
22.6
4
3 1
5
22.5 5 22.4
2
3
4 6
22.3 22.2 69.1
69.2
69.3
69.4
69.5
69.6
69.7
69.8
69.9
70.0
70.1
70.2
70.3
Longitude (Deg)
Fig. 9. Trajectories of particles launched in the mid Gulf on either side of the dynamic barrier.
and random flight. Only the tidal residual current has been used to drive the trajectories. One qualitative validation to the eastward flow (along the northern rim) from the dynamic barrier is as follows: a wave rider buoy which was deployed off Mundra got cut off, and after a month it was located around 70E (near Kandla). The path of wave rider buoy and the time taken to reach Kandla match very well with that of Particle No. 1 released off Mundra (Fig. 9). As the deployment location is eastward of the dynamic barrier, the buoy drifted towards Kandla. This incident and the numerical experiments indicate the probable path of pollutants on either side of the dynamic barrier. As several major industries, in addition to the existing, are likely to come up along the Gulf coast, proper care should be taken while identifying locations for discharging industrial wastes.
5. Conclusions A calibrated hydrodynamic model has been used to study the flow pattern present in the Gulf. The results show the presence of several eddies and pathways of net transport through the Gulf mouth. The dynamic barrier has a great role to play in the transport of wastes discharged from shore-based industries located along the upstream of the Gulf. The results further prove that the basic hydrodynamic model formulated for the Gulf could be coupled with the water quality model to study the Gulf water quality as envisaged under the project. A long-term observational plan
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has been prepared for the Gulf to measure all the coastal and oceanographic parameters and use them for modeling the Gulf.
Acknowledgements We are grateful to the Department of Environment & Forest, Government of Gujarat, India for providing funds to carry out the project ‘‘Integrated Management of Marine Environment of the Gulf of Kachchh’’. We thank all the team members of the above project who contributed directly to the project. The suggestions given by the two unknown reviewers greatly helped to improve the quality of this paper. This is NIO contribution number 3919.
References Anonymous. (1994). The Indian tide tables – Part I, Dehra Dun, India: Survey of India. Anonymous. (1999). Carrying capacity of southern Gulf of Kachchh with respect to accidental petroleum hydrocarbon discharges at SPMs. Report submitted to BORL, Mumbai, India. Elliott, A. J., Bowers, D. G., & Jones, B. (1995). Tidal currents near Bardsey Sound. Hydrography Journal, 78, 13–18. Falconer, R. A., Wolanski, E., & Mardapitta Hadjipandeli, L. (1986). Integrated field measurements and numerical model simulations of tidal eddies. In Proceedings of the international conference on measuring techniques of hydraulics phenomena in offshore, coastal and inland waters (pp. 43–60), London, UK. Morales-Perez, R. A., & Ramirez-Leon, H. (1996). The simulation of dispersion by tidal eddies in coastal waters. In A. A. Aldama, J. Aparicio, C. A. Brebbia, W. G. Gray, I. Herrera, & G. F. Pinder (Eds.). Computational methods in water resources-XI (2, pp. 347–354). UK: Computational Mechanics Publications. Reddy, G. S. (1997). Aspects of a computational model for predicting the flow and pollutant transport in rivers, estuaries and seas. In International conference on coastal engineering 97, La Coruna, Spain, 23– 25 June, 1997. Shetye, S. R. (1999). Tides in the Gulf of Kachchh, India. Continental Shelf Research, 19, 1771–1782. Takeoka, H., & Murano, H. (1993). Tidal currents influenced by topographic eddies in Uchiumi Bay. Journal of Oceanography, 49, 491–501. Unnikrishnan, A. S., Gouveia, A. D., & Vethamony, P. (1999). Tidal regime in Gulf of Kachchh, West Coast of India by 2D model. Journal of Waterway, Port, Coastal, and Ocean Engineering, 125(6), 276–284. Vaidyaraman, P. P., Ghosh, L. K., & Gokhale, D. P. (1987). Mathematical modeling of tidal propagation in the Gulf of Kachchh. In Proceedings of the coast and port engineering in developing countries (Vol. II, pp. 2165–2173), China: Nanjing Hydraulic Research Institute. Wang, J. (1998). A two-channel laterally averaged estuarine circulation model (LAECIM). Journal of Geophysical Research, 103(C9), 18381–18391. Wang, J. (2001). A nowcast/forecast system for coastal ocean circulation using simple nudging data assimilation. Journal of Atmospheric and Oceanic Technology, 18(6), 1037–1047. Wang, J., & Ikeda, M. (1997). Inertial stability and phase error of time integration schemes in ocean general circulation models. Monthly Weather Review, 125, 2316–2327. Wolanski, E., & King, B. (1990). Flushing of Bowden Reef lagoon, Great Barrier Reef. Estuarine, Coastal and Shelf Science, 31, 789–804.
Tidal eddies in a semi-enclosed basin: a model study P. Vethamony *, G.S. Reddy 1, M.T. Babu, E. Desa, K. Sudheesh National Institute of Oceanography, Dona Paula, Goa 403 004, India Received in revised form 14 August 2004; accepted 27 August 2004
Abstract A modeling study has been carried out to support a Marine Management Plan for the Gulf of Kachchh, India and here the hydrodynamic part of the programme is described. The hydrodynamic model accurately predicts the tides and tidal currents present in the Gulf and these have been validated with the measured data, albeit at only a few locations. The time averaged residual currents obtained from the model for one lunar cycle clearly reproduce the complex, small-scale, topographically induced flows with several eddies. The existence of a dynamic barrier along Sikka–Mundra section, which divides the Gulf into two distinct dynamic systems, is very evident. The model is further used to predict the movement of surface floating particles launched at different locations in the Gulf, as an aid to determining floating pollutants. The results indicate that industries discharging wastes upstream of the barrier should use extreme caution, as these will remain in the vicinity for at least one lunar cycle. 2004 Elsevier Ltd. All rights reserved. Keywords: Gulf of Kachchh; Hydrodynamic model; Currents; Tidal eddies; Dynamic barrier; Particle tracking; Industrial wastes
*
Corresponding author. Tel.: +91 832 2450473; fax: +91 832 2450602/2450603/2450604. E-mail addresses: [email protected], [email protected] (P. Vethamony). 1 Environ Software Pvt. Ltd., Wilson Garden, Bangalore 560 030, India.
0141-1136/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.marenvres.2004.08.002
520
P. Vethamony et al. / Marine Environmental Research 59 (2005) 519–532
1. Introduction The Gulf of Kachchh (GoK) is a semi-enclosed basin located in the northern part of west coast of India and opens to the Arabian Sea (Fig. 1). It has grown in economic importance due to acceleration of industrial developments in recent years. Refineries, fertilizer, chemical and cement industries, power plants, minor and major ports and salt works are the major industries, which make use of GoK. Most of these developments are concentrated along the southern shore of GoK, where eco-sensitive areas like Marine Sanctuaries (MS) and Marine National Parks (MNP) are located. Four Single Point Moorings (SPMs) are operational and two more are under consideration along the southern Gulf. The northern Gulf is also being considered for establishing SPMs. In addition, the ports at Okha, Navlakhi, Kandla, Mandvi and Jakhau in the Gulf handle a variety of cargoes, especially petroleum products, and are responsible for considerable tanker traffic in the Gulf. The Gulf may face severe environmental stress, and in due course the impact will be felt on the MNP and MS, if the usage of Gulf is not properly planned. It has therefore become important that a holistic view of the Gulf is taken, vis-a`-vis its ecosystem and existing developments, to properly plan and manage future activities in the Gulf. The National Institute of Oceanography, Goa has been carrying out several projects for industries in the Gulf region for the past three decades, but limited to specific locations. Therefore, a detailed model study has been undertaken under the major project ‘‘Integrated Management of the Marine Environment of the Gulf of Kachchh’’ to understand hydrodynamics, temperature-salinity distributions, water
Fig. 1. The major morphological features of the Gulf of Kachchh.
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quality, oil spill movements and carrying capacity of the entire Gulf. This project takes into account all the environmental data collected in the Gulf so far. The results of hydrodynamic modeling, especially the significance of residual currents and tidal eddies to pollutant transport, are presented in this paper. Tides and tidal currents in the Gulf have been modeled by a few researchers to assess the tidal potential, track the oil spill trajectories and understand the tidal amplification and resonance (Anon., 1999; Shetye, 1999; Unnikrishnan, Gouveia, & Vethamony, 1999; Vaidyaraman, Ghosh, & Gokhale, 1987). No previous study carried out in the Gulf has brought out the dynamic barrier feature or the implication of tidal eddies to pollutant transport in the Gulf. This study relates the significance of tidal eddies and dynamic barrier while planning the Gulf for installing marine facilities to the east of Mundra–Sikka sector. Only a few tidal stations are available in the Gulf. Hence, this model can be used to predict tides at any location in the Gulf. Regions such as Gulf of Oman, Gulf of Aden, Persian Gulf and Gulf of Cambay (India) are very similar to the GoK in several aspects including geographical location, surface meteorology, oceanography, tidal conditions and tanker-traffic are concerned, and the present study can find applications to such regions also. The topographic small scale eddies are very complex, but their presence is evident in the flow pattern. Falconer, Wolanski, and Mardapitta Hadjipandeli (1986) used a 2D depth averaged numerical model to study the main features of measured eddies near Rattray Island, North Queensland. It is residual currents/eddies, rather than instantaneous tidal flows, which contribute to the net transport of materials from the system. Flushing of lagoons is faster if topographically induced tidal eddies are present (Wolanski and King, 1990). The tidal eddies that form behind the Bardsey Island during flood and ebb tides showed that they persist during the period of slack waters (Elliott, Bowers, & Jones, 1995). The factors contributing to the formation of topographic tidal eddies are lateral gradients (Morales-Perez & RamirezLeon, 1996), shear due to bathymetric variations and tides (Takeoka & Murano, 1993). It is therefore important for scientists and environmental managers concerned with the ecosystem of the Gulf to understand the hydrodynamics and the role of residual tidal eddies in the transport of pollutants.
2. Gulf setting The Gulf is about 170 km long and 75 km wide at the mouth. It is a very complex water body, encompassing several tidal inlets, creeks, small islands, shoals, coral reefs, tidal flats and rocky regions (Fig. 1). The Gulf is relatively shallow with maximum water depth varying from 60 m at the mouth to 20 m at the head. The topography of the mouth and the mid-gulf is relatively more rugged compared to the head. A coastal plain with indentation, inlets, offshore islands and coral reefs marks the southern Gulf. The northern Gulf, consisting of sand and mud, is marked by numerous sandy shoals. The sediments derived from land are limited, as the whole region is arid. The suspended sediment load varies from 0.19 to 0.51 g/l and 0.11 to 3.60 g/l
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during pre-monsoon and post-monsoon, respectively. The complex bathymetry, rugged bottom topography and undulations in the shoreline produce highly non-linear tidal interactions. The Gulf circulation is dominated by a strong tidal signal with amplitudes increasing considerably upstream. For example, the mean high water spring of 3.5 m at the mouth (Okha) increases to 5.4 m at Sikka and 7.2 m at the head (Navlakhi). The Fresh water discharge into the Gulf is negligible. The time series data of sea surface temperature (SST) and air temperature collected at a few locations show that during morning hours the sea surface is warmer than the air. As the day progresses the air becomes warmer than the sea surface. Vertical profiles of temperature and salinity measured at several locations over a period of 25 years reveal a nearly homogeneous water column with no vertical stratification due to intense tidally-driven turbulence mixing. The water temperature measured at three levels (surface, mid-depth and bottom) at different locations in the Gulf during different seasons also shows that the water temperature undergoes a diurnal variation – relatively higher for surface than the bottom waters. Strong evaporation and scanty rainfall make the Gulf a highly saline water body. The salinity values averaged over the period 1976–1999 show that the maximum salinity ranges from 36.6 psu (off Okha) to 45.5 psu (off Navlakhi). In the Indian coastal region, we have observed this sort of range in salinity as well as high values only in the GoK. In general, surface currents range from 0.75 to 1.25 m/s in the mouth to 1.5– 2.5 m/s in the head. Measurements show that surface and bottom currents are nearly the same, except off Vadinar and Positra (Fig. 2), where the presence of numerous shoals and reefs pose an obstruction to bottom currents. For example, during spring tide, the surface currents measured off Positra in pre-monsoon (February 1997) have a peak speed of about 1.0 m/s (the direction is SE during flood and NW during ebb), and the bottom currents about 0.5 m/s (the direction is SE during flood and N during ebb). The bottom currents reflect the effect of local topography. The currents recorded in September 1997 (post-monsoon) show a similar pattern. In order to substantiate that there is no vertical stratification in the Gulf, the currents measured using a Doppler Current Meter at 6 levels off Sikka (water depth = 20 m) in May 1996 (Fig. 3) have been analysed. In the Gulf region, winds are relatively stronger only during monsoon months (May–August) and wind effect will be felt at the surface, as tidal forcing is stronger than wind forcing in the subsurface layers. This is evident from Fig. 3, where the monsoon wind influence is seen only on the surface currents (1 and 4 m) and not on the sub-surface currents. The sub-surface currents are nearly of the same order of magnitude.
3. Model description Since the waters are generally vertically homogeneous, a 2D model should reproduce the tides and currents in the Gulf.
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Fig. 2. Scatter plot of surface and bottom currents at select locations in the Gulf.
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Fig. 3. Vertical current pattern off Sikka.
3.1. Governing equations Simulation of tides and currents has been carried out by solving the following 2D shallow water equations of mass and momentum: og ouH ovH þ þ ¼ 0: ot ox oy
ð1Þ
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The two depth-averaged momentum equations can be written as: ouH ou2 H ouvH og o ou o ou þ þ ¼ fvH gH þ H Kx Ky þH ot ox oy ox ox ox oy oy þ swx sbx ;
ð2Þ
ovH ovuH ov2 H og o ov o ov þ þ ¼ fuH gH þ H Kx Ky þH ot ox oy oy ox ox oy oy þ swy sby ;
ð3Þ
where t = time; x,y = Cartesian coordinates; u,v = depth averaged velocity components in the x and y directions, respectively; f = Coriolis parameter; g = acceleration due to gravity; Kx, Ky = diffusion coefficients in the x and y directions, respectively; g = water elevation with respect to mean sea level; H = total water depth at any instant; swx,swy = wind stress in x and y directions; sbx,sby = bottom stress in x and y directions. 3.2. Boundary fitted coordinate system In the Cartesian or rectilinear coordinate system, it is difficult to represent the complex coastline accurately since the grid size remains the same at all locations. The present model makes the computations in the boundary-fitted or generalized curvilinear coordinate system (Fig. 4) in order to resolve complex geometry accurately in the horizontal direction. The boundary fitted coordinate (BFC) system takes care of coastal shape and makes fine mesh near the coastline. In case of narrow
Fig. 4. Computational mesh (BFC) for the Gulf of Kachchh.
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head, flux boundary conditions should be used. The model treats the islands, as drying and flooding options are available. Once the coastal shape is defined, BFC system generates orthogonal and nonorthogonal grids automatically by defining number of grids in x and y directions. The grid is non-uniform both in x and y directions and it is a skewed mesh. This necessitates the transformation of the governing equations into boundary-fitted coordinates (1,r). The (x,y) coordinates are transformed in such a way that their components are perpendicular to the (1,r) coordinate lines. This is accomplished by employing the chain rule transformation. The momentum equation in the x direction can be written in BFC system as oðuH Þ oðu2 H Þ oðu2 H Þ oðuvH Þ oðuvH Þ þ 1x þ rx þ 1y þ ry fvH ot o1 or o1 or og og þ gH 1x þ rx o1 or 2 2 ou ou o2 u 2o u 2o u þ ðrx Þ þ 21x rx HK x 1xx þ rxx þ ð1x Þ o1 or o1 or o1or 2 2 ou ou o2 u 2o u 2o u þ ð1y Þ þ ðry Þ þ 21y ry HK y 1yy þ ryy swx þ sbx o1 or o1 or o1or ¼ 0;
ð4Þ
where 1x, 1y, rx, ry, 1xx, 1yy, rxx, ryy = grid transformation parameters, h = water depth up to mean sea level H ¼ h þ g:
ð5Þ
Similarly, the momentum equation in y direction can be written in the BFC coordinate system. More details about transformation of basic governing equations of flow from Cartesian to BFC is found in Reddy (1997). The transformed governing equations of flow have been discretised on a staggered grid and solved using Leapfrog trapezoidal scheme through a predictor and corrector step method. The numerical scheme is based on finite difference method and fully centered in space and time. In the BFC system, grid size varies both in the x and y directions and accordingly time step (Dt) also changes. Dt is chosen in such a way that it satisfies the CFL criterion, Dt < 0.5Dx(gH)0.5. The stability analysis of Leapfrog scheme has been analysed by Wang (1998) and Wang and Ikeda (1997). They reported that the scheme is conditionally stable for u.(Dt/Dx) = 0.8. The same scheme has been used in the present study, and correction has been done at every time step. 3.3. Model setup The computational domain of the model is selected from Okha to beyond Kandla between the longitudes 69 02ÕE and 70 18ÕE and the latitudes 22 17ÕN and 22 53ÕN. The model domain is divided into 110 · 50 grids in x and y directions, respectively. Fig. 4 shows the computational grid for the entire Gulf. The bathymetry is selected from the hydrographic chart.
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The horizontal diffusion coefficients Kx and Ky are calculated as follows: pffiffiffiffiffiffiffiffiffiffiffiffiffiffi K x ¼ ax g u2 þ v2 =C 2 ; K y ¼ ay g
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi u2 þ v2 =C 2 ;
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ð6Þ ð7Þ
where ax and ay are the constants in depth averaged eddy viscosity coefficients in x and y directions and C (in m1/2/s) is the Chezy coefficient. The diffusion coefficients for horizontal exchange of momentum vary in space. The wind stress in the x and y directions (swx and swy) can be written as: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð8Þ swx ¼ qa C d U w ðU 2w þ V 2w Þ; swy ¼ qa C d V w
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðU 2w þ V 2w Þ;
ð9Þ
where qa = air density; Cd = drag coefficient; Uw, Vw = wind components in the x and y directions. The bottom stress in the x and y directions (sbx,sby) can be written as: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð10Þ sbx ¼ gu ðu2 þ v2 Þ=C 2 ; sby ¼ gv
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðu2 þ v2 Þ=C :
ð11Þ
The bottom roughness in the GoK varies according to bed sediment size. The bed is composed of clay, sand, silt and rock soils. Depending upon bed configuration and sediment particle size, the d50 size (mean sediment particle size in mm) is selected to compute the ManningÕs roughness values. The boundary conditions selected are as follows: (i) along the western open boundary (from Okha to north corner), predicted Okha tide of October 1994 available in the Indian Tide Tables (Anon., 1994) has been imposed to force the model as no tidal station or measured data is available on/for the northern corner; (ii) no flux across the closed boundary near Kandla; (iii) no flux along the northern and southern boundaries of the Gulf. As the predicted tides are given at larger time interval (6 h), cubic spline interpolation technique has been applied to calculate the value at each computational time step.
4. Results and discussion 4.1. Calibration and verification The model has been calibrated by providing two sets of bed roughness coefficients, estimated from d50 sediment size and bed configuration. Based on the available information, we find that these two sets of coefficients are the most suitable for the GoK. The computational runs have been executed for the two sets of bed roughness coefficients till computed and measured tides off Sikka match (Fig. 5). The discrepancy, both in phase and amplitude, is within the acceptable
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Measured Computed with bed coeff1 Computed with bed coeff2
7
Tide elevation (m)
6 5 4 3 2 1 0 -1 0
2
4
6
8
10
12
Time in days
Fig. 5. Comparison of measured and computed tides during 1–12, October 1994 at Sikka with variable bed roughness coefficients.
range for tides computed using bed roughness coefficient 1. Therefore, bed roughness coefficient 1 is used in all subsequent simulations. The results indicate that nearly two tidal cycles are required for the model to reach dynamical equilibrium from the cold start. Several model runs have been carried out to test the model efficiency in reproducing tides and currents in the entire computational domain. For validation, the model has been forced with March 94 tide data at Okha. The simulated tides and currents have been validated with those measured at the monitoring points, which include the moorings off Vadinar, Sikka and Mundra. As a typical case, here we present the validation of Vadinar currents. The simulated and measured currents off Vadinar (Fig. 6) show a discrepancy of the order of 10 cm/s in magnitude. This may be due to the following three reasons: (i) depth-averaged form of the numerical model; (ii) lack of measured or predicted input tide data at the northern corner of western open boundary; (iii) the leapfrog scheme tends to overestimate the phase speed, while the implicit scheme tends to slow down the phase speed (Wang & Ikeda, 1997); (iv) the bottom topography and geomorphological features of the southern Gulf change abruptly within a few kilometers, and this causes mismatch in the measured and simulated currents, especially when the measurement location does not coincide with the model location (of the order of a few hundred meters in the present case). 4.2. Tides and tidal currents The model clearly reproduces the tidal variation at various locations all along the Gulf. In general, the tidal currents flow in the ENE direction during flood and WSW during ebb, with relatively high currents along the central Gulf (reaching upto 1.5 m/s). A typical variation of tides during ebb condition in October 1994 is shown
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Measured
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Computed
0.9
Current speed (m/s)
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 9.0
9.5
10.0
10.5
11.0
11.5
12.0
12.5
13.0
13.5
14.0
Time (in days)
Fig. 6. Comparison of measured and computed currents off Vadinar during 9–14 March 1994.
in Fig. 7. The tidal elevation and tidal currents computed at various locations agree with those measured at the same locations during different seasons and years (please refer to the section: Gulf setting). 4.3. Tidal circulation and eddies The residual currents in the Gulf computed by integrating velocities over a period of one month in October 1994 are presented in Fig. 8. In the eastern half of the Gulf, the circulation shows a net transport towards Kandla (along the northern
Fig. 7. A typical ebb current system in the Gulf.
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Fig. 8. Average residual currents and eddies.
rim of the Gulf) with a tendency to form a clockwise circulation. On the contrary, in the western Gulf, the residual circulation presents anti-clockwise eddies of different sizes, except one clockwise eddy in the northern Gulf (off Mandvi). It is evident from Fig. 8 that the net transport from the open ocean into the Gulf is through the southern side of the mouth, and the net outward transport is through the northern side, forming an anti-clockwise circulation in the western part. Tidal eddies shed by coastal features such as coral reefs and islands play a vital role in transporting materials. The geometry of the Gulf is such that the tides enter into it through the southern side and pushes the water inside. As the Gulf width suddenly drops at the mid-Gulf and coastal orientation changes abruptly thereafter (Fig. 1), the water flow is deflected towards north, and forms a dynamic barrier across Sikka–Mundra section. One branch of this northern flow contributes to the westward flow (outflow of the Gulf), and the other branch to the eastward flow, both along the northern rim of the Gulf. This dynamic barrier retards the flushing of the Gulf, which is a matter of concern when industrial wastes are released. 4.4. Particle trajectories In the field, usually drogues are released at desired locations, and their positions over space and time are tracked to calculate the surface drift. In the present study, numerical experiments have been conducted to further illustrate the flow pattern – by releasing particles at six select locations in the vicinity of the dynamic barrier and tracking their trajectories (Fig. 9). The results show that particles follow the eddy system present in the Gulf. Wang (2001) has used a model to predict surface trajectories of oil spills and floating objects utilising surface current, wind speed
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Start point End point
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trajectory 4 trajectory 5 trajectory 6
22.9
Latitude (Deg)
22.8 22.7
6
2
1
22.6
4
3 1
5
22.5 5 22.4
2
3
4 6
22.3 22.2 69.1
69.2
69.3
69.4
69.5
69.6
69.7
69.8
69.9
70.0
70.1
70.2
70.3
Longitude (Deg)
Fig. 9. Trajectories of particles launched in the mid Gulf on either side of the dynamic barrier.
and random flight. Only the tidal residual current has been used to drive the trajectories. One qualitative validation to the eastward flow (along the northern rim) from the dynamic barrier is as follows: a wave rider buoy which was deployed off Mundra got cut off, and after a month it was located around 70E (near Kandla). The path of wave rider buoy and the time taken to reach Kandla match very well with that of Particle No. 1 released off Mundra (Fig. 9). As the deployment location is eastward of the dynamic barrier, the buoy drifted towards Kandla. This incident and the numerical experiments indicate the probable path of pollutants on either side of the dynamic barrier. As several major industries, in addition to the existing, are likely to come up along the Gulf coast, proper care should be taken while identifying locations for discharging industrial wastes.
5. Conclusions A calibrated hydrodynamic model has been used to study the flow pattern present in the Gulf. The results show the presence of several eddies and pathways of net transport through the Gulf mouth. The dynamic barrier has a great role to play in the transport of wastes discharged from shore-based industries located along the upstream of the Gulf. The results further prove that the basic hydrodynamic model formulated for the Gulf could be coupled with the water quality model to study the Gulf water quality as envisaged under the project. A long-term observational plan
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has been prepared for the Gulf to measure all the coastal and oceanographic parameters and use them for modeling the Gulf.
Acknowledgements We are grateful to the Department of Environment & Forest, Government of Gujarat, India for providing funds to carry out the project ‘‘Integrated Management of Marine Environment of the Gulf of Kachchh’’. We thank all the team members of the above project who contributed directly to the project. The suggestions given by the two unknown reviewers greatly helped to improve the quality of this paper. This is NIO contribution number 3919.
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