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Experimental study on evolution of lacustrine shallow-water delta
Catena 182 (2019) 104125
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Experimental study on evolution of lacustrine shallow-water delta b
Weiyan Xin , Yuchuan Bai a b
a,b
, Haijue Xu
a,b,⁎
T
State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China Institute for Sediment, River and Coast Engineering, Tianjin University, Tianjin 300072, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Delta Evolution Lacustrine shallow-water Flow regime Sediment transport Topographic deposition
In the process of delta evolution, the flow regime and sediment transport change with the development of topography. Flow is the dynamic factor of shaping topography, while sediment scouring and silting is the direct cause of topography formation, and they are constrained and influenced by topographic changes simultaneously. In order to explore rules of water and sediment movement and topographic sedimentation of delta under microscale conditions, we studied the phenomena, rules and evolution mechanism of flow movement, sediment transport, particle sorting, topographic sedimentation, and flow path generation, merger and recombination under microscale conditions from the perspective of physical experiment. The influence of different external conditions on lacustrine shallow-water delta evolution and the self-organization of delta evolution are studied through comparative experiments under the condition of distinct sediment supplied rates or lake levels and repeatability experiments under the same conditions. Some rules of flow movement, sediment transport and topographic sedimentation such as characteristics of each stage during the process of evolution of lacustrine shallow-water delta, the periodic change of flow regime and the prediction model, the characteristics of sedimentary morphology under different conditions, and the influence of stochastic factors on delta evolution are summarized. The experiments suggest coupled linkage of interaction of water and sediment, self-organization of flow path evolution and the equilibrium tendency of delta structure under the action of coupling interaction of multiple factors of water, sediment and topographic sedimentation.
1. Introduction Lacustrine shallow-water delta is a widespread morphological feature at borders between alluvial rivers and lakes, which is the product of dynamic decrease and sediment deposition in estuarine area. The process of its formation and evolution is an important component of the evolution of alluvial rivers. A well-known example is Gan River-Fu River trail delta in Jiangxi Province in China. The evolution of lacustrine shallow-water delta will be affected by the basin holding its own characteristic, which can be expected to be different from other types of delta. Delta systems are controlled by both upstream and downstream conditions. However, the previous focus has been mainly put on the effects of upstream conditions on delta evolution. Kim and Jerolmack (2008) and Hoyal and Sheets (2009) conducted experiments, which emphasized the importance of the downstream boundary to the morphodynamics of delta. Numerical and physical models have shown that there are certain rules on delta morphology and dynamics: cycles of aggradation, incision (Humphrey and Heller, 1995; Coulthard et al., 2002; Nicholas and Quine, 2007a, 2007b) and avulsion processes
⁎
(Bryant et al., 1995; Mackey and Bridge, 1995; Ashworth et al., 2004): the trend of growth of margin position follows a function of time (Swenson et al., 2000; Reitz et al., 2010); sheet flow was alternated with channelized flow during the experiments (Clarke et al., 2010); Bryant et al. (1995) proposed that the experimental fan developed in three stages, and flow regime and channel configuration in each stage are described respectively in detail, which is also observed and summarized similarly by Clarke et al. (2010). Under similar extrinsic forcing, deltas are not always in the same stage of evolution (Ritter, 1967; Wells and Harvey, 1987) and autogenic behavior is introduced to explain the difference of geomorphic development (Schumm and Parker, 1973; Schumm et al., 1987; Humphrey and Heller, 1995; Whipple et al., 1998; Coulthard et al., 2002). . Due to the difficulty of studying flow regime alternation, morphology and deposition directly and effectively in natural environment over a long timescale and large distance scale, in most cases previous delta studies have only focused on delta classification or morphology description. In addition, it is not easy to separate many influencing factors to conduct quantitative studies respectively in field conditions,
Corresponding author at: State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China. E-mail address: [email protected] (H. Xu).
https://doi.org/10.1016/j.catena.2019.104125 Received 7 September 2018; Received in revised form 3 May 2019; Accepted 10 June 2019 0341-8162/ © 2019 Elsevier B.V. All rights reserved.
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P
so our understanding of the mechanism and rules of lacustrine shallowwater delta formation and evolution remains limited. The physical experiment can reproduce the characteristic process similar to natural delta and it can also shorten the duration by reasonable design which is conductive to study delta system in a controlled range of time and space. And the method of experiment makes it possible to quantify the effect of each factor. Therefore, experimental methods have advantages to be used in studies of delta. Thus far, lacustrine shallow-water delta experiment has rarely been applied to delta study. Advances in understanding characteristics of flow and sediment movement and deposition of lacustrine shallowwater delta, periodic transition of flow regime, the influence of the external forcing on morphology, and stochastic expression of delta require a further study of lacustrine shallow-water delta laboratory experiment. In this study, experiments were conducted under different lake levels and sediment supply rates to study delta evolution process, periodic transition of flow regime and roles of external forcing on lacustrine shallow-water delta formation and evolution. It was also conducted under the same condition to show stochastic expression of delta morphology and influence factors have been explored at laboratory scale. Six groups of evolution processes which were shown as the procedure from instability to stability were observed and recorded. Each complete evolution process was characterized by six phases through summarizing and comparing staged evolutionary characteristics. Periodic changes of flow regime were observed, and estimation method for cycle period by several easily obtained variables was proposed. We compared the performances in deposit morphology of six runs, and deposit morphology characteristics under comparative conditions were shown and summarized through a set of schematic models, which are of great significance to study delta evolution. Stochastic expression of delta morphology under conditions of complex bed, flow structure and sediment distribution observed in our control group and repetitive group provides insight into how apparently stochastic changes occurred and how this stochasticity affected the pattern of delta evolution.
P
P
P P
P P
Inlet channel
Delta
Water
P
Outlet
Sediment feeder Lake region
Digital camera
Tailgate
Video recorder
Sediment feeder Delta Water Slope Fig. 1. Sketch of the experimental flume.
on Run1 and Run1-a; Run 1, Run2 and Run3; Run1, Run4 and Run5. Run1 was conducted as the control group. Run1 and Run1-a were conducted under the same condition; Run1, Run2 and Run3 were conducted under the same condition except for sediment feed rate, which were multiplied and reduced to 75% of that of Run1 in Run2 and Run3 respectively; Run1, Run4 and Run5 were conducted under the same conditions except for height of tail gate, which were 1.5 cm and 2.5 cm in Run4 and Run5 respectively, see Table 1, where Q is the water discharge; Sv is the sediment volume concentration. Equal-diameter foam balls were poured above the inlet of the artificial channel as tracer particles. An overhead video recorder was employed to record tracer particles motion with flow at the end of each hour through the experiment. PTV software was used to process videos to obtain flow field (Bai and Xu, 2007). The experimental process was also recorded by a digital camera located above the flume, and images of delta evolution were taken on five minutes interval. The topographic data were measured every 3 h by fixing the laser rangefinder with accuracy of 1 mm to make the distance from it to the initial bed surface constant. The duration of each experiment is shown above in Table 1 (the progradation rate of Run2 oscillated to zero when it was run to 17 h when the experiment was stopped owing to a greater sediment supplied rate; a higher lake level limited the progradation, and the progradation rate of Run4 gradually dropped to zero when it was run to 20 h when the experiment was stopped), not including the pauses at the end of every 1 h for flow field measurement and every 3 h for topography survey. An experimental lacustrine shallow-water delta was used to reproduce similar phenomenon that occurred in the process of delta evolution in reality, which requiring low Froude number (e.g.: the Froude number of Mississippi River is about 0.1; the Froude number of Gan River-Fu River trail delta is about 0.12; the Froude number of our delta is about 0.09) and bedload dominated, such as key trends in spatial and temporal patterns of flow regime, morphology and topography. That means that the geometry, kinematic and dynamic characteristics of the experimental system are not exactly scaled to a specific prototype but follow Hooke's (1968) ‘similarity of processes and performance’ theory. The values of condition variables were tested by a series of preparatory experiments to make sure that they can show aspects of the mesoscale structure and surface processes. The final
2. Laboratory model Delta morphology is related to factors such as lake level and sediment supply (Harvey, 2005; Postma, 1990). Our study posed a significant question about the roles of lake level and sediment supply on delta formation and evolution. The comparison between the control group and the repetitive group was expected to provide information about stochastic expression of morphology of lacustrine shallow-water delta. The work for this experiment was carried out in Tianjin University. The setting consisted of a flume (3.6 m long, 1.7 m wide and 0.2 m high) with discharge changeable and sediment supply controlled, a water reservoir, a sand basin and a circulating system (see Fig. 1). A variable-speed sediment feeder system supplied the sediment at a predetermined rate to the inlet channel where sediment could be mixed with water. And the mixture would be fed to the delta apex during each experiment. Noncohesive sediment (median diameter d50 = 0.62 mm, density ρs = 2650 kg/m3) was used in our experiment, supplied at the inlet channel and distributed on the bottom of flume with a thickness of 5 cm which can prevent the erosion from reaching the bottom. Grainsize distributions are shown below in Fig. 2. A desired slope can be obtained by adjusting the bottom bearing at one end of flume and we made a gentle slope of 1% in each experiment. It was confirmed that sediment was transported mainly as bedload under the discharge used through our observations, just as alluvial deltas that were dominated by bed load transport. We conducted six runs with three sediment supplied rates and three heights of tail gate (Table 1). Each of experiments was run until the progradation rate gradually dropped to zero, i.e. the sediment supplied was covered on delta deposits formed previously. Our study will focus 2
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100 90
d50= 0.62 mm Cu=d60/d10=2.387
Cumulative weight(%)
80 70 60 50 40 30 20 10 0 0.01
0.1
0.6
1
10
Sediment Size (mm) Fig. 2. Grain-size distribution of sediment.
experimental area, and it helped to make a lake area at downstream of the flume to simulate the state of river entering lake. The tail gate height was set as 1.5 cm, 2 cm and 2.5 cm, respectively, which made the best of the length of the flume and the lake areas under several working conditions were obviously different.
Table 1 Details of the experimental scenarios. Run
Q (cm3/s)
1 1-a 2 3 4 5
50 50 50 50 50 50
Sv 0.2% 0.2% 0.4% 0.15% 0.2% 0.2%
Slope
Height of tail gate (cm)
Duration (h)
1% 1% 1% 1% 1% 1%
2 2 2 2 2.5 1.5
30 30 17 30 20 30
3. Results and discussion 3.1. Observations of delta evolution The delta of all runs typically went through six stages, while the time spent in each stage was different between runs.
decision of experimental conditions was based on comprehensive consideration of previous experiments, laboratory conditions, characteristics of natural large-scale lacustrine deltas and pre-experimental results. The adjustment range of flowmeter is 0 cm3/s–50 cm3/s, and the selection of inflow amount mainly considered that the upstream flow velocity should be larger than the sediment incipient velocity and make the morphological evolution more remarkable in the predicted duration. Therefore, the maximum value of flowmeter 50 cm3/s was selected; the selection of grain size mainly considered that sediment particles were easy to flocculate if they were too fine, while the sediment of grain size between 0.5 mm and 0.65 mm was beneficial to the formation of tree-shaped delta and surface channels also with the observation of the merger and reorganization of channels and flow regime transition (Hoyal and Sheets, 2009; Lai and Wei, 1994). And natural sediment of median grain size d50 = 0.62 mm was selected in our experiment; according to experimental studies of Hoyal and Sheets (2009) and Clarke et al. (2010), river morphology is obviously easy to observe when sediment non-uniformity coefficient is 1.6–2.5, so the sediment with non-uniformity coefficient of 2.387 was selected in the experiment. Non-uniformity coefficient Cu is calculated by the following formula:
Cu =
d60 d10
a. Sheet flow dominated, as shown in Fig. 3. The surface of deposit was smooth, where there was no clear channel and bifurcation. Sediment fell into artificial channel at a certain rate and was mixed with flow at the inlet of the plot. Constrained by narrow channel, flow and sediment possessed great energy while their speed decreased rapidly after rushing out of channel, which led to a rapid growth of deposit. As the forward flow had more energy than both sides, sediment could be transported forward farther with water covering the entire surface in the form of sheet flow because of a low height of deposit without channel, which lead to a tongue-shaped deposit with smooth boundary and surface. Sediment had shown sorting, and the grain size of upper delta was small while that of middle delta to the
(1)
The sediment concentration is usually set at about 0.2% in shallowwater delta experiments (Hoyal and Sheets, 2009; Clarke et al., 2010; Zhang et al., 2016). Considering that the amount of sediment coming into the upper reaches of natural shallow-water delta is small, the sediment concentration of control group was set at 0.2%; pre-experimental results showed that the increase of incision was not conducive to the formation of deposit and the observation of flow and sediment movement when the slope was too large, so 1% was chosen as the overall slope; the tail gate can avoid the rapid outflow in the
Fig. 3. Delta morphology at 1 h of Run1. 3
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b.
c.
d.
e.
f.
front showed clear upward coarsening because of the steep slope of the delta front, which was similar to that observed by Ogami et al. (2015). Channels formation. As the deposit gradually accumulated in vertical direction, radial rills started from delta apex. The rills continued to deepen and merge under the interaction between water and sediment with incision initiating downstream and migrating upstream. Several unstable and shallow channels appeared. The sediment at flanks of the upper delta and the middle part of lower delta showed upward coarsening, as shown in Fig. B.1. One main channel in the upper delta was established, and lateral channels disappeared. The degree of flow scouring bed surface forward was more intense due to inertia. Natural levees gradually developed and the main straight channel was formed in the middle. The flow in the upper delta turned into channelized flow, while that of lower delta still showed clear characteristic of sheet flow. Delta surface was cut into several small areas incremental by the sand emerging from the water surface. The crevasse of the natural levee in the middle and the formation of mouth bar in the lower region made the flow bifurcated. After that, small channelized flow formed at the front of the deposit, see Fig. B.2, which was in agreement with what was observed by Bryant et al. (1995). The vertical upward coarsening of the upper delta disappeared gradually, and there was an obvious upward coarsening trend at flanks of the middle delta and the middle of the front. Backfilling. The deposit of the front was constantly silting up, and the lateral flow appeared downstream. With the increase of siltation elevation, the coverage area of lateral flow increased, and the intersection point of the downstream channel moved upward resulting in a decreased transport capacity for upstream sediment transported to the downstream and channel backfilling upstream, which is consistent with the phenomenon observed by Hoyal and Sheets (2009). As the lateral flow coverage area downstream increased, the flow gradually turned into sheet flow, as shown in Fig. B.3. Backfilling sediment on delta flanks and in channels of the middle part showed clear upward coarsening which developed toward the edge of deposit. Slope increased with upstream sediment accumulation, preparing for the next incision. The deposition of the mouth bar at the front prevented the flow movement forward and the flow turned to other directions. Crevasse position changes of the natural levee in the middle delta and the alternation of new and old mouth bars downstream led to the intersection point and flow direction migration. The deposit highly developed, and the area of the outcropping mouth bars increased, which made the flow downstream bifurcate and it encouraged the sedimentation of mouth bar simultaneously. In the latter stage, the delta front developed into the lake area. The sediment rushed out and its velocity decreased rapidly because of the resistance from the lake, which led to progradation rate decline. The water depth was small, and the flow downstream was channelized. The crevasse and mouth bars cut the deposit, which made the deposit no longer continuous. Sediment of large grain size scattered on the delta uncovered by the water surface, as shown in Fig. B.4. Progradation rate oscillated to zero. The sediment carried by the inlet flow deposited on the upper delta, and delta entered a strong aggradation phase, as shown in Fig. B.5.
Fig. 4. Schematic of generalized shape of deposit.
The shape of deposit is generalized to a rectangle, as shown in Fig. 4 below: where p is the maximum distance from the apex to the margin position; B is medial delta width, i.e., the delta width at 0.5p way down the delta from the apex; b is medial channel width, i.e., the channel width at 0.5p way down the delta from the apex. These three variables can be obtained by direct measurement. Delta developed by sheet flow deposition at initial phase. In Run1 the tendency toward channelization increased at around 4 h and channelized flow predominately changed to sheet flow dominated at around 6 h. Observations showed that the incision was promoted in longitudinal direction when flow regime started to change from sheet flow to channelized flow, which was similar to works of Fisher et al. (2007a, 2007b) and Clarke et al. (2010);, incision was limited with channel widening promoted and channels became wide but shallow when flow regime transited from channelized state to sheet flow. The transverse expansion ability of flow was greater than the constraint from terrain, which promoted the transition to sheet flow; otherwise channelization was promoted. We defined relative channel width as b/ B. It can be considered that the flow will achieve a periodic maximum state of sheet flow when b/B reaches a maximum value; and the flow will achieve a periodic maximum state of channelized flow when b/B reaches a minimum value. Therefore flow regime can be distinguished both from a visual perspective and value of relative channel width. From the time when obvious channels can be observed in each experiment, the value of relative channel width of Run1, 2 and 3 with distinct sediment supplied rate, and Run1, 4 and 5 with lake level varied was plotted in Fig. 5 respectively: Instantaneous water depth was regarded as constant. As the sediment deposited continuously and rose to water surface, the fluctuation of the sediment surface would cause the flow to divert or bifurcate whose continuous action on the surface led to channelization, so sediment outcropping water surface was taken as a sign of flow regime entering channelized flow state; while the sediment-laden flow acted on the outcropping sediment, the sediment carried by flow was backfilled into the channel. As flow and topographic conditions were no longer conducive to maintaining channelized flow, the flow showed the characteristic of sheet flow. So we took sediment filling channel which made flow covering the sediment surface in a thin layer as a sign of flow regime entering sheet flow state (refer to Fig. 6 for schematic diagrams of the two processes respectively). It is possible to estimate the flow regime cycle (sheet flow-channelized flow and channelized flow-sheet flow) period. The cycle period T can be estimated as follows:
3.2. The characteristics of flow movement and sediment transport 3.2.1. Periodic transition of flow regime and period prediction model Cycles of sheet and channelized flow occurred during the formation and evolution of delta of each run, which was in agreement with that observed by Dijk et al. (2012). Run1 is taken as an example to explore influencing factors of flow regime and estimation method for cycle period.
T=
h v
where h is typical depth; v is delta aggradation rate: 4
(2)
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(A) 0.5
Run1 Run2 Run3
0.4
b/B
0.3
0.2
0.1
0.0 0
200
400
600
800
1000
1200
1400
1600
1800
2000
Time(min)
(B) 0.5
Run1 Run4 Run5
0.4
b/B
0.3
0.2
0.1
0.0 0
200
400
600
800
1000
1200
1400
1600
1800
2000
Time(min) Fig. 5. Relative channel width. (A) Relative channel width of Run1, Run2 and Run3. (B) Relative channel width of Run1, Run4 and Run5.
v=
Qs Bp
where Qs is Because difficult to transported
h=
(3)
Y
(4)
where Q is the known water discharge; vf is the estimate of flow velocity in channel at 0.5p way down the delta from the apex based on particle image velocimetry and takes the value of the mean velocity of channel centrelines. Flow field contour map at 10 h of Run1 based on particle image velocimetry was taken as an example and shown in Fig. 7 below.
the sediment supplied rate. of the small depth of water during the experiment, it is measure directly. The discharge was considered to be mainly by channel, and the depth can be estimated from:
(A)
Q bvf
(B)
water surface
sediment
water surface h
h
Y
sediment
Fig. 6. Schematic of the transition process of flow regime: (A) Transition from sheet flow to channelized flow, (B) transition from channelized flow to sheet flow. 5
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level (see Fig. 8(A)) made the lake inundate even middle delta segment. As the lake level was high, the length and transverse width of delta were small with a large thickness of deposition. The width from the middle to the lower part did not change greatly, and lateral deposition on flanks of apex was obvious. The front was smooth and thick. The main channel can extend to the front, with few discontinuous radial rills and channels occurring on the surface. Therefore, the high lake level limited both the horizontal and vertical movement of sediment, being insufficient to trigger incisions as much as shallow level. When the sediment carried by the sediment-laden flow could not be transported farther away from the apex by the combined mechanism of longitudinal energy gradient and flow energy, the sediment would fall and deposit in the upper delta. Compared with a low sediment supplied rate (see Fig. 8(D)), under the condition of great sediment supplied rate (see Fig. 8(C)), the deposition thickness was large with a great length and a slightly larger width. The width from the middle to the lower part changed greatly, and the front was protruding, smooth and thick. No obvious deposition occurred on flanks of apex. The main channel could not reach the front, and continuous radial rills and channels occurred on the surface. A great sediment supplied rate would lead to improving the sediment movement range both in transverse and longitudinal directions and vertical deposition thickness, promoting continuous incisions. 3.2.3. Comparison between control group and repetitive group Conditions of Run1 and Run1-a were kept the same under an observable precision. Although many similar evolution rules existed between the two runs, the flow regime, the channel generation, the location and extent of sediment transport and deposition as well as the morphology at a certain time were different, which was identified as stochastic expression of delta morphology. The delta geometries changing over time of Run1 and Run1-a are plotted respectively in Fig. 9 (the delta contours of 14 h, 22 h, 26 h, 27 h and 29 h of Run 1 and 26 h of Run 1-a are covered). From the microscopic view, whether the channel bifurcate or migrate at a certain time depends on the anti-scouring characteristic of a certain pinch of sediment and the scouring characteristic of fluid on the sediment, which determines flow direction, flow regime, the formation and merging of flow paths suggesting flow path self-organization, and the morphological characteristic of sedimentary body and so on. The discussion on anti-scouring characteristic of sediment and the scouring characteristic of fluid can help to explore the influencing factors of stochastic expression of delta morphology. We assumed that the fluid intensity was constant, sediment incipient motion depended on the grain size distribution and the cohesive force existed between sediment particles. For the non-cohesive sediment used in our experiment, the critical shear stress acting on noncohesive sediment on gentle slope can be calculated as follows according to Wang and Shen's (1985) and Zhang's (1990) method:
Fig. 7. Contour map of flow field at 10 h of Run1.
Take Run1 as an example to illustrate the calculation process. During the first 3 h when it was in the typical sheet flow stage, there was no obvious channel, so the calculation was started from the fourth hour. As shown in Fig. 5(A), starting from 4 h, the first observation of the maximum state of channelized flow should be between 6 h and 7 h since the flow field was measured at the end of each hour. The interval from the 4th hour to the moment around 6 h is the duration that flow regime began to change from sheet flow to channelized flow, indicated by ΔT ≈ 2–3 h, while the predicted period based on the data at 4 h ΔTp ≈ 7844.35 s ≈ 2.1790 h (T = 240 min: h = 0.2958 cm, B = 39.9549 cm, p = 65.0451 cm, Qs = 0.098 cm3/s). The same goes for other nodes and intervals in Fig. 5(A). The calculation results of Run 1–5 are listed in Appendix A, where T is the time point for calculating; h is the estimated water depth through formula (4) based on particle image velocimetry; B is the medial delta width; p is the maximum distance from the apex to the margin position; Qs is the sediment supplied rate; ΔTp is the cycle period of flow regime transition through calculation; ΔT is the cycle period of flow regime transition that relative channel width in Fig. 10 reflects. The calculation results were in excellent agreement with what was observed and the value of relative width of channel.
sin 2ϕ ⎞ τc = K ∗ (γs − γ ) d w ⎜⎛1 − ⎟ sin 2β ⎠ ⎝
3.2.2. Delta deposition and morphology In order to compare the morphological characteristics of the delta under several working conditions better, the characteristics of the delta in terms of length, transverse width, deposition thickness, width variation from the middle to the lower part, deposition at the top flanks, front contour and thickness, types and quantities of surface channels under working conditions 2, 3, 4 and 5 are summarized and compared in Fig. 8. Schematic models of delta morphology under conditions of high and low lake level, great and small sediment supplied rates were obtained and shown in Fig. 8. Groups of experiments showed the spatial similarity (tree shape) of structural characteristics after the evolution process was stable, but the final morphology obtained by each experiment was different. Compared with the experiment under the condition of low lake level (see Fig. 8(B)) whose shoreline just reached the delta front, a high lake
(5)
where τc is the incipient shear stress; K* is the coefficient of sediment incipient motion; ϕ is the angle between slope and horizontal plane; β is sediment friction angle; dw is the representative size of sediment. From Eq. (5), it can be seen that when flow condition is constant and ϕ is small enough which is same as our experiment, the shear stress is mainly controlled by grain size and sediment gravity, i.e., sediment properties. The sediment adopted in this experiment was naturally nonuniform, so the grain size and gravity of the sediment laying at the bottom of the flume differed both in horizontal and vertical directions before the experiment began, the same applied to the sediment supplied at the inlet. According to Ferguson's (2003) method，the shear stress of fluid can be calculated as follows: 6
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Fig. 8. Schematic models of delta morphology. (A) Run2. (B) Run3. (C) Run4. (D) Run5.
qS 0.67 τp = ρg ⎛ ⎞ ⎝C⎠
(6)
where τp is the shear stress of fluid; ρ is fluid density; q is unit discharge; S is unit slope; C is Chezy's coefficient. The fluid that each unit sediment received is assumed to be same in density and Chezy's coefficient but the discharge that each unit sediment receives and the unit slope change with spatial location of unit sediment, so the shear stress produced by flow to a pile of sediment also differs. A schematic of interaction of water and sediment and flow path selection is shown as follows: where bed sediment is divided into n squares and each square contains a pinch of sediment; the white square is the representation of the sediment that can move with the fluid while the black square is the sediment that cannot move; the arrow indicates the direction of the flow. As shown in Fig. 10, for white squares, scouring effects on them are greater than that of anti-scouring, and they can be carried away by
Fig. 10. Schematic of interaction of water and sediment and flow path selection.
Fig. 9. Delta geometries. (A) Run1. (B) Run1-a. 7
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fluid. Sediment that cannot move will still be left at black squares. Flow path will form at the place where white squares are connected, and two paths can even merge if the sediment in black squares between them are moved down by fluid then. And during the movement of sedimentladen flow, the bed load at the bottom of the flow merged with the surface ahead to form a new surface, which was also the interaction process between flow and new surface. The stochasticity of incoming water and sediment, the stochasticity of sediment gradation and gravity, and the stochasticity of bed conditions determined the stochasticity of micro-channel formation and the process of flow and sediment action. Therefore, delta evolution is a dialectical unity of variable hydrodynamic intensity, alternation of distribution space and stochastic process of bed change. Certainty is contained within stochasticity while the unification of instability and tendency is brewed in certainty, which determines the similarity and diversity of spatial evolution of Run1 and Run1-a.
channel width; a high lake level limited both the horizontal and vertical movement of sediment being insufficient to trigger incisions as much as shallow level, and a great sediment supplied rate would lead to improve the sediment movement range both in transverse and longitudinal directions and vertical deposition thickness promoting continuous incisions; factors influencing stochastic expression of delta morphology have been explored through the comparison between control and repetitive group. Phenomenon in our physical system showed that delta evolution was a process of simultaneous representation of similarity and stochasticity. Our experimental results have potential to provide data concerning revealing the process of water and sediment, the process of channel formation and siltation, the mechanism of lacustrine shallow-water delta evolution. The physical models have important reference value for inversing the process of historical siltation of delta and studying the response of lacustrine shallow-water delta to varied conditions of lake level and sediment supplied.
4. Conclusions
Acknowledgments
Our results presented in this paper provide insight into delta evolution process, periodic transition of flow regime, the influence of lake level and sediment supplied rate on delta morphology and process and factors of delta stochastic expression. The experimental process of each run was characterized by six phases; periodic transition of flow regime was observed and the period of flow regime transition was estimated by several easily available variables. The calculation results are in good agreement with the flow regime observed and indicated by relative
This work was supported by the National Natural Science Foundation of China, China (51879182, 41576093 and 51279124), the Natural Science Foundation of Tianjin City, China (No. 14JCZDJC39800) and the Science Fund for Creative Research Groups of the National Natural Science Foundation of China, China (No. 51621092). We appreciate Chenfei Xue and Yu Zhao for their help to the experiment. Comments from the editor and the anonymous reviewers are sincerely thanked.
Appendix A. Schedule Calculation results of Run 1–5
Run
T (min)
1 1 1 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 5 5 5 5 5 5 5
240 360 480 600 840 1080 1380 1620 120 240 360 540 780 60 180 300 480 720 1080 1140 1560 1740 240 420 540 660 780 900 1020 180 420 780 1020 1140 1320 1500
h (cm)
B (cm)
p (cm)
0.2958 0.2237 0.2502 0.3096 0.2425 0.2723 0.1942 0.1667 0.2503 0.2493 0.2108 0.2374 0.2263 0.5743 0.1823 0.2562 0.2195 0.2157 0.1197 0.1969 0.0717 0.1833 0.3457 0.1465 0.1486 0.1169 0.1373 0.1181 0.1816 0.3955 0.3296 0.2289 0.0685 0.0924 0.0825 0.1398
39.9549 62.3476 36.7523 49.1131 51.1002 67.9209 68.0584 74.1039 70.3620 76.8474 88.0646 97.655 103.7543 23.0516 58.8874 46.2839 52.5590 69.0794 78.9048 85.4360 90.8102 90.3656 42.8986 69.4080 77.0381 74.7147 77.0061 81.8889 83.3672 68.0520 77.5503 85.8645 104.3972 116.4751 122.3610 117.1275
65.0451 95.2601 114.0744 114.9506 114.9049 113.4576 114.1011 122.8454 91.4031 106.3328 148.1207 142.3953 144.6134 52.9854 56.6059 86.7035 99.8296 102.7728 107.7557 120.7531 125.9180 128.7131 84.9728 85.7466 91.6286 90.0102 93.2906 99.2147 98.7701 60.7935 94.7280 119.6551 123.0315 122.3340 122.9100 131.6432
8
Qs (cm3/s)
ΔTp (h)
ΔT (h)
0.098 0.098 0.098 0.098 0.098 0.098 0.098 0.098 0.196 0.196 0.196 0.196 0.196 0.074 0.074 0.074 0.074 0.074 0.074 0.074 0.074 0.074 0.098 0.098 0.098 0.098 0.098 0.098 0.098 0.098 0.098 0.098 0.098 0.098 0.098 0.098
2.1790 3.7659 2.9733 4.9543 4.0359 5.3073 4.2746 4.3091 2.2814 2.8871 3.8970 4.6786 4.8122 2.6331 2.2811 3.8593 4.3232 4.9808 3.8204 7.6252 3.0432 8.0030 3.5719 2.4714 2.9732 2.7278 2.7958 2.7197 4.2385 4.6378 6.8631 5.7137 2.4938 3.7318 3.5169 6.1099
2–3 3–4 2–3 4–5 4–5 5–6 4–5 – 2–3 2–3 3–4 4–5 – 2–3 2–3 3–4 4–5 4–5 3–4 7–8 3–4 – 3–4 2–3 2–3 2–3 2–3 2–3 – 4–5 6–7 5–6 2–3 3–4 3–4 –
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Appendix B
B.1
B.2
B.3
B.4
B.5
Fig. B. 1. Delta morphology at 4 h of Run1. 2. Delta morphology at 9 h of Run1. 3. Delta morphology at 14 h of Run 1. 4. Delta morphology at 25 h of Run1. 5. Delta morphology at 30 h in Run1.
Clarke, L.E., Quine, T.A., Nicholas, A.P., 2010. An experimental investigation of autogenic behaviour during alluvial fan evolution. Geomorphology 115, 278–285. Coulthard, T.J., Macklin, M.G., Kirkby, M.J., 2002. A cellular model of Holocene upland river basin and alluvial fan evolution. Earth Surf. Process. Landf. 27, 269–288. Dijk, M.V., Kleinhans, M.G., Postma, G., Kraal, E., 2012. Contrasting morphodynamics in alluvial fans and fan deltas: effect of the downstream boundary. Sedimentology 59 (7), 2125–2145. Ferguson, R.I., 2003. The missing dimension: effects of lateral variation on 1-D calculations of fluvial bedload transport. Geomorphology 56, 1–14.
References Ashworth, P.J., Best, J.L., Jones, M., 2004. The relationship between sediment supply and avulsion frequency in braided rivers. Geology 32, 21–24. Bai, Y.C., Xu, D., 2007. Study on particle tracking velocity measurement in complex surface flow field. In: The 20th National Symposium on Hydraulics, pp. 9. Bryant, M., Falk, P., Paola, C., 1995. Experimental study of avulsion frequency and rate of deposition. Geology 23, 358–365.
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W. Xin, et al. Fisher, J.A., Nichols, G.J., Waltham, D.A., 2007a. Unconfined flow deposits in distal sectors of fluvial distributary systems: examples from the Miocene Luna and Huesca Systems, northern Spain. Sediment. Geol. 195 (1), 55–73. Fisher, J.A., Waltham, D.A., Nichols, G.J., Krapt, C.B., Lang, S.C., 2007b. A quantitative model for deposition of thin fluvial sand sheets. J. Geol. Soc. 164 (1), 67–71. Harvey, A.M., 2005. Differential effects of base-level, tectonic setting and climatic change on Quaternary alluvial fans in the northern Great Basin, Nevada, USA. Geol. Soc. Lond. Spec. Publ. 251 (1), 117–131. Hooke, R.L., 1968. Model geology: prototype and laboratory streams: discussion. Geol. Soc. Am. Bull. 79, 391–394. Hoyal, D.C.J.D., Sheets, B.A., 2009. Morphodynamic evolution of experimental cohesive deltas. J. Geophys. Res. Earth Surf. 114 (F2). Humphrey, N.F., Heller, P.L., 1995. Natural oscillations in coupled geomorphic systems: an alternative origin for cyclic sedimentation. Geology 23, 499–502. Kim, W., Jerolmack, D.J., 2008. The pulse of calm deltas. Geology 116, 315–330. Lai, Z.Y., Wei, Z., 1994. Sedimentary simulation experiments on the formation and evolution of tongue-shaped delta and bird-foot delta. Acta Sedimentol. Sin. 12 (2), 38–43. Mackey, S.D., Bridge, J.S., 1995. Three dimensional alluvial stratigraphy: theory and application. J. Sediment. Res. 65, 7–31. Nicholas, A.P., Quine, T.A., 2007a. Crossing the divide: representation of channels and processes in reduced-complexity river models at reach and landscape scales. Geomorphology 90, 318–339. Nicholas, A.P., Quine, T.A., 2007b. Modelling alluvial landform change in the absence of external environmental forcing. Geology 35, 527–530. Ogami, T., Sugai, T., Fujiwara, O., 2015. Dynamic particle segregation and accumulation
processes in time and space revealed in a modern river-dominated delta: a spatiotemporal record of the Kiso River delta, central Japan. Geomorphology 235, 27–39. Postma, G., 1990. An analysis of the variation in delta architecture. Terra Nova 2, 124–130. Reitz, M.D., Jerolmack, D.J., Swenson, J.B., 2010. Flooding and flow path selection on alluvial fans and deltas. Geophys. Res. Lett. 37 (6), 6401. Ritter, D.F., 1967. Terrace development along the front of the Beartooth Mountains, southern Montana. Geol. Soc. Am. Bull. 78, 467–484. Schumm, S.A., Parker, R.S., 1973. Implications of complex response of drainage systems for Quaternary alluvial stratigraphy. Nature 243, 99–100. Schumm, S.A., Mosley, M.P., Weaver, W.E., 1987. Experimental Fluvial Geomorphology. John Wiley and Sons, New York, pp. 413. Swenson, J.B., Voller, V.R., Paola, C., Parker, G., Marr, J.G., 2000. Fluvio-deltaic sedimentation: a generalized Stefan problem. Eur. J. Appl. Math. 11, 433–452. Wang, Sany-yi, Shen, Hsieh Wen, 1985. Incipient sediment motion and riprap design. J. Hydraul. Eng. 111, 520–538. Wells, S.G., Harvey, A.M., 1987. Sedimentologic and geomorphic variations in stormgenerated alluvial fans, Howgill Fells, northwest England. Geol. Soc. Am. Bull. 98, 182–198. Whipple, K.X., Parker, G., Paola, C., Mohrig, D.C., 1998. Channel dynamics, sediment transport and the slope of alluvial fans: experimental study. J. Geol. 106, 677–693. Zhang, Haiyan, 1990. River Evolution Engineering. Science Press, Beijing, pp. 62–65. Zhang, X.F., Wang, S.Q., Wu, X., Xu, S., Li, Z.Y., 2016. The development of a laterally confined laboratory fan delta under sediment supply reduction. Geomorphology 257, 120–133.
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Catena journal homepage: www.elsevier.com/locate/catena
Experimental study on evolution of lacustrine shallow-water delta b
Weiyan Xin , Yuchuan Bai a b
a,b
, Haijue Xu
a,b,⁎
T
State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China Institute for Sediment, River and Coast Engineering, Tianjin University, Tianjin 300072, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Delta Evolution Lacustrine shallow-water Flow regime Sediment transport Topographic deposition
In the process of delta evolution, the flow regime and sediment transport change with the development of topography. Flow is the dynamic factor of shaping topography, while sediment scouring and silting is the direct cause of topography formation, and they are constrained and influenced by topographic changes simultaneously. In order to explore rules of water and sediment movement and topographic sedimentation of delta under microscale conditions, we studied the phenomena, rules and evolution mechanism of flow movement, sediment transport, particle sorting, topographic sedimentation, and flow path generation, merger and recombination under microscale conditions from the perspective of physical experiment. The influence of different external conditions on lacustrine shallow-water delta evolution and the self-organization of delta evolution are studied through comparative experiments under the condition of distinct sediment supplied rates or lake levels and repeatability experiments under the same conditions. Some rules of flow movement, sediment transport and topographic sedimentation such as characteristics of each stage during the process of evolution of lacustrine shallow-water delta, the periodic change of flow regime and the prediction model, the characteristics of sedimentary morphology under different conditions, and the influence of stochastic factors on delta evolution are summarized. The experiments suggest coupled linkage of interaction of water and sediment, self-organization of flow path evolution and the equilibrium tendency of delta structure under the action of coupling interaction of multiple factors of water, sediment and topographic sedimentation.
1. Introduction Lacustrine shallow-water delta is a widespread morphological feature at borders between alluvial rivers and lakes, which is the product of dynamic decrease and sediment deposition in estuarine area. The process of its formation and evolution is an important component of the evolution of alluvial rivers. A well-known example is Gan River-Fu River trail delta in Jiangxi Province in China. The evolution of lacustrine shallow-water delta will be affected by the basin holding its own characteristic, which can be expected to be different from other types of delta. Delta systems are controlled by both upstream and downstream conditions. However, the previous focus has been mainly put on the effects of upstream conditions on delta evolution. Kim and Jerolmack (2008) and Hoyal and Sheets (2009) conducted experiments, which emphasized the importance of the downstream boundary to the morphodynamics of delta. Numerical and physical models have shown that there are certain rules on delta morphology and dynamics: cycles of aggradation, incision (Humphrey and Heller, 1995; Coulthard et al., 2002; Nicholas and Quine, 2007a, 2007b) and avulsion processes
⁎
(Bryant et al., 1995; Mackey and Bridge, 1995; Ashworth et al., 2004): the trend of growth of margin position follows a function of time (Swenson et al., 2000; Reitz et al., 2010); sheet flow was alternated with channelized flow during the experiments (Clarke et al., 2010); Bryant et al. (1995) proposed that the experimental fan developed in three stages, and flow regime and channel configuration in each stage are described respectively in detail, which is also observed and summarized similarly by Clarke et al. (2010). Under similar extrinsic forcing, deltas are not always in the same stage of evolution (Ritter, 1967; Wells and Harvey, 1987) and autogenic behavior is introduced to explain the difference of geomorphic development (Schumm and Parker, 1973; Schumm et al., 1987; Humphrey and Heller, 1995; Whipple et al., 1998; Coulthard et al., 2002). . Due to the difficulty of studying flow regime alternation, morphology and deposition directly and effectively in natural environment over a long timescale and large distance scale, in most cases previous delta studies have only focused on delta classification or morphology description. In addition, it is not easy to separate many influencing factors to conduct quantitative studies respectively in field conditions,
Corresponding author at: State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China. E-mail address: [email protected] (H. Xu).
https://doi.org/10.1016/j.catena.2019.104125 Received 7 September 2018; Received in revised form 3 May 2019; Accepted 10 June 2019 0341-8162/ © 2019 Elsevier B.V. All rights reserved.
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P
so our understanding of the mechanism and rules of lacustrine shallowwater delta formation and evolution remains limited. The physical experiment can reproduce the characteristic process similar to natural delta and it can also shorten the duration by reasonable design which is conductive to study delta system in a controlled range of time and space. And the method of experiment makes it possible to quantify the effect of each factor. Therefore, experimental methods have advantages to be used in studies of delta. Thus far, lacustrine shallow-water delta experiment has rarely been applied to delta study. Advances in understanding characteristics of flow and sediment movement and deposition of lacustrine shallowwater delta, periodic transition of flow regime, the influence of the external forcing on morphology, and stochastic expression of delta require a further study of lacustrine shallow-water delta laboratory experiment. In this study, experiments were conducted under different lake levels and sediment supply rates to study delta evolution process, periodic transition of flow regime and roles of external forcing on lacustrine shallow-water delta formation and evolution. It was also conducted under the same condition to show stochastic expression of delta morphology and influence factors have been explored at laboratory scale. Six groups of evolution processes which were shown as the procedure from instability to stability were observed and recorded. Each complete evolution process was characterized by six phases through summarizing and comparing staged evolutionary characteristics. Periodic changes of flow regime were observed, and estimation method for cycle period by several easily obtained variables was proposed. We compared the performances in deposit morphology of six runs, and deposit morphology characteristics under comparative conditions were shown and summarized through a set of schematic models, which are of great significance to study delta evolution. Stochastic expression of delta morphology under conditions of complex bed, flow structure and sediment distribution observed in our control group and repetitive group provides insight into how apparently stochastic changes occurred and how this stochasticity affected the pattern of delta evolution.
P
P
P P
P P
Inlet channel
Delta
Water
P
Outlet
Sediment feeder Lake region
Digital camera
Tailgate
Video recorder
Sediment feeder Delta Water Slope Fig. 1. Sketch of the experimental flume.
on Run1 and Run1-a; Run 1, Run2 and Run3; Run1, Run4 and Run5. Run1 was conducted as the control group. Run1 and Run1-a were conducted under the same condition; Run1, Run2 and Run3 were conducted under the same condition except for sediment feed rate, which were multiplied and reduced to 75% of that of Run1 in Run2 and Run3 respectively; Run1, Run4 and Run5 were conducted under the same conditions except for height of tail gate, which were 1.5 cm and 2.5 cm in Run4 and Run5 respectively, see Table 1, where Q is the water discharge; Sv is the sediment volume concentration. Equal-diameter foam balls were poured above the inlet of the artificial channel as tracer particles. An overhead video recorder was employed to record tracer particles motion with flow at the end of each hour through the experiment. PTV software was used to process videos to obtain flow field (Bai and Xu, 2007). The experimental process was also recorded by a digital camera located above the flume, and images of delta evolution were taken on five minutes interval. The topographic data were measured every 3 h by fixing the laser rangefinder with accuracy of 1 mm to make the distance from it to the initial bed surface constant. The duration of each experiment is shown above in Table 1 (the progradation rate of Run2 oscillated to zero when it was run to 17 h when the experiment was stopped owing to a greater sediment supplied rate; a higher lake level limited the progradation, and the progradation rate of Run4 gradually dropped to zero when it was run to 20 h when the experiment was stopped), not including the pauses at the end of every 1 h for flow field measurement and every 3 h for topography survey. An experimental lacustrine shallow-water delta was used to reproduce similar phenomenon that occurred in the process of delta evolution in reality, which requiring low Froude number (e.g.: the Froude number of Mississippi River is about 0.1; the Froude number of Gan River-Fu River trail delta is about 0.12; the Froude number of our delta is about 0.09) and bedload dominated, such as key trends in spatial and temporal patterns of flow regime, morphology and topography. That means that the geometry, kinematic and dynamic characteristics of the experimental system are not exactly scaled to a specific prototype but follow Hooke's (1968) ‘similarity of processes and performance’ theory. The values of condition variables were tested by a series of preparatory experiments to make sure that they can show aspects of the mesoscale structure and surface processes. The final
2. Laboratory model Delta morphology is related to factors such as lake level and sediment supply (Harvey, 2005; Postma, 1990). Our study posed a significant question about the roles of lake level and sediment supply on delta formation and evolution. The comparison between the control group and the repetitive group was expected to provide information about stochastic expression of morphology of lacustrine shallow-water delta. The work for this experiment was carried out in Tianjin University. The setting consisted of a flume (3.6 m long, 1.7 m wide and 0.2 m high) with discharge changeable and sediment supply controlled, a water reservoir, a sand basin and a circulating system (see Fig. 1). A variable-speed sediment feeder system supplied the sediment at a predetermined rate to the inlet channel where sediment could be mixed with water. And the mixture would be fed to the delta apex during each experiment. Noncohesive sediment (median diameter d50 = 0.62 mm, density ρs = 2650 kg/m3) was used in our experiment, supplied at the inlet channel and distributed on the bottom of flume with a thickness of 5 cm which can prevent the erosion from reaching the bottom. Grainsize distributions are shown below in Fig. 2. A desired slope can be obtained by adjusting the bottom bearing at one end of flume and we made a gentle slope of 1% in each experiment. It was confirmed that sediment was transported mainly as bedload under the discharge used through our observations, just as alluvial deltas that were dominated by bed load transport. We conducted six runs with three sediment supplied rates and three heights of tail gate (Table 1). Each of experiments was run until the progradation rate gradually dropped to zero, i.e. the sediment supplied was covered on delta deposits formed previously. Our study will focus 2
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100 90
d50= 0.62 mm Cu=d60/d10=2.387
Cumulative weight(%)
80 70 60 50 40 30 20 10 0 0.01
0.1
0.6
1
10
Sediment Size (mm) Fig. 2. Grain-size distribution of sediment.
experimental area, and it helped to make a lake area at downstream of the flume to simulate the state of river entering lake. The tail gate height was set as 1.5 cm, 2 cm and 2.5 cm, respectively, which made the best of the length of the flume and the lake areas under several working conditions were obviously different.
Table 1 Details of the experimental scenarios. Run
Q (cm3/s)
1 1-a 2 3 4 5
50 50 50 50 50 50
Sv 0.2% 0.2% 0.4% 0.15% 0.2% 0.2%
Slope
Height of tail gate (cm)
Duration (h)
1% 1% 1% 1% 1% 1%
2 2 2 2 2.5 1.5
30 30 17 30 20 30
3. Results and discussion 3.1. Observations of delta evolution The delta of all runs typically went through six stages, while the time spent in each stage was different between runs.
decision of experimental conditions was based on comprehensive consideration of previous experiments, laboratory conditions, characteristics of natural large-scale lacustrine deltas and pre-experimental results. The adjustment range of flowmeter is 0 cm3/s–50 cm3/s, and the selection of inflow amount mainly considered that the upstream flow velocity should be larger than the sediment incipient velocity and make the morphological evolution more remarkable in the predicted duration. Therefore, the maximum value of flowmeter 50 cm3/s was selected; the selection of grain size mainly considered that sediment particles were easy to flocculate if they were too fine, while the sediment of grain size between 0.5 mm and 0.65 mm was beneficial to the formation of tree-shaped delta and surface channels also with the observation of the merger and reorganization of channels and flow regime transition (Hoyal and Sheets, 2009; Lai and Wei, 1994). And natural sediment of median grain size d50 = 0.62 mm was selected in our experiment; according to experimental studies of Hoyal and Sheets (2009) and Clarke et al. (2010), river morphology is obviously easy to observe when sediment non-uniformity coefficient is 1.6–2.5, so the sediment with non-uniformity coefficient of 2.387 was selected in the experiment. Non-uniformity coefficient Cu is calculated by the following formula:
Cu =
d60 d10
a. Sheet flow dominated, as shown in Fig. 3. The surface of deposit was smooth, where there was no clear channel and bifurcation. Sediment fell into artificial channel at a certain rate and was mixed with flow at the inlet of the plot. Constrained by narrow channel, flow and sediment possessed great energy while their speed decreased rapidly after rushing out of channel, which led to a rapid growth of deposit. As the forward flow had more energy than both sides, sediment could be transported forward farther with water covering the entire surface in the form of sheet flow because of a low height of deposit without channel, which lead to a tongue-shaped deposit with smooth boundary and surface. Sediment had shown sorting, and the grain size of upper delta was small while that of middle delta to the
(1)
The sediment concentration is usually set at about 0.2% in shallowwater delta experiments (Hoyal and Sheets, 2009; Clarke et al., 2010; Zhang et al., 2016). Considering that the amount of sediment coming into the upper reaches of natural shallow-water delta is small, the sediment concentration of control group was set at 0.2%; pre-experimental results showed that the increase of incision was not conducive to the formation of deposit and the observation of flow and sediment movement when the slope was too large, so 1% was chosen as the overall slope; the tail gate can avoid the rapid outflow in the
Fig. 3. Delta morphology at 1 h of Run1. 3
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b.
c.
d.
e.
f.
front showed clear upward coarsening because of the steep slope of the delta front, which was similar to that observed by Ogami et al. (2015). Channels formation. As the deposit gradually accumulated in vertical direction, radial rills started from delta apex. The rills continued to deepen and merge under the interaction between water and sediment with incision initiating downstream and migrating upstream. Several unstable and shallow channels appeared. The sediment at flanks of the upper delta and the middle part of lower delta showed upward coarsening, as shown in Fig. B.1. One main channel in the upper delta was established, and lateral channels disappeared. The degree of flow scouring bed surface forward was more intense due to inertia. Natural levees gradually developed and the main straight channel was formed in the middle. The flow in the upper delta turned into channelized flow, while that of lower delta still showed clear characteristic of sheet flow. Delta surface was cut into several small areas incremental by the sand emerging from the water surface. The crevasse of the natural levee in the middle and the formation of mouth bar in the lower region made the flow bifurcated. After that, small channelized flow formed at the front of the deposit, see Fig. B.2, which was in agreement with what was observed by Bryant et al. (1995). The vertical upward coarsening of the upper delta disappeared gradually, and there was an obvious upward coarsening trend at flanks of the middle delta and the middle of the front. Backfilling. The deposit of the front was constantly silting up, and the lateral flow appeared downstream. With the increase of siltation elevation, the coverage area of lateral flow increased, and the intersection point of the downstream channel moved upward resulting in a decreased transport capacity for upstream sediment transported to the downstream and channel backfilling upstream, which is consistent with the phenomenon observed by Hoyal and Sheets (2009). As the lateral flow coverage area downstream increased, the flow gradually turned into sheet flow, as shown in Fig. B.3. Backfilling sediment on delta flanks and in channels of the middle part showed clear upward coarsening which developed toward the edge of deposit. Slope increased with upstream sediment accumulation, preparing for the next incision. The deposition of the mouth bar at the front prevented the flow movement forward and the flow turned to other directions. Crevasse position changes of the natural levee in the middle delta and the alternation of new and old mouth bars downstream led to the intersection point and flow direction migration. The deposit highly developed, and the area of the outcropping mouth bars increased, which made the flow downstream bifurcate and it encouraged the sedimentation of mouth bar simultaneously. In the latter stage, the delta front developed into the lake area. The sediment rushed out and its velocity decreased rapidly because of the resistance from the lake, which led to progradation rate decline. The water depth was small, and the flow downstream was channelized. The crevasse and mouth bars cut the deposit, which made the deposit no longer continuous. Sediment of large grain size scattered on the delta uncovered by the water surface, as shown in Fig. B.4. Progradation rate oscillated to zero. The sediment carried by the inlet flow deposited on the upper delta, and delta entered a strong aggradation phase, as shown in Fig. B.5.
Fig. 4. Schematic of generalized shape of deposit.
The shape of deposit is generalized to a rectangle, as shown in Fig. 4 below: where p is the maximum distance from the apex to the margin position; B is medial delta width, i.e., the delta width at 0.5p way down the delta from the apex; b is medial channel width, i.e., the channel width at 0.5p way down the delta from the apex. These three variables can be obtained by direct measurement. Delta developed by sheet flow deposition at initial phase. In Run1 the tendency toward channelization increased at around 4 h and channelized flow predominately changed to sheet flow dominated at around 6 h. Observations showed that the incision was promoted in longitudinal direction when flow regime started to change from sheet flow to channelized flow, which was similar to works of Fisher et al. (2007a, 2007b) and Clarke et al. (2010);, incision was limited with channel widening promoted and channels became wide but shallow when flow regime transited from channelized state to sheet flow. The transverse expansion ability of flow was greater than the constraint from terrain, which promoted the transition to sheet flow; otherwise channelization was promoted. We defined relative channel width as b/ B. It can be considered that the flow will achieve a periodic maximum state of sheet flow when b/B reaches a maximum value; and the flow will achieve a periodic maximum state of channelized flow when b/B reaches a minimum value. Therefore flow regime can be distinguished both from a visual perspective and value of relative channel width. From the time when obvious channels can be observed in each experiment, the value of relative channel width of Run1, 2 and 3 with distinct sediment supplied rate, and Run1, 4 and 5 with lake level varied was plotted in Fig. 5 respectively: Instantaneous water depth was regarded as constant. As the sediment deposited continuously and rose to water surface, the fluctuation of the sediment surface would cause the flow to divert or bifurcate whose continuous action on the surface led to channelization, so sediment outcropping water surface was taken as a sign of flow regime entering channelized flow state; while the sediment-laden flow acted on the outcropping sediment, the sediment carried by flow was backfilled into the channel. As flow and topographic conditions were no longer conducive to maintaining channelized flow, the flow showed the characteristic of sheet flow. So we took sediment filling channel which made flow covering the sediment surface in a thin layer as a sign of flow regime entering sheet flow state (refer to Fig. 6 for schematic diagrams of the two processes respectively). It is possible to estimate the flow regime cycle (sheet flow-channelized flow and channelized flow-sheet flow) period. The cycle period T can be estimated as follows:
3.2. The characteristics of flow movement and sediment transport 3.2.1. Periodic transition of flow regime and period prediction model Cycles of sheet and channelized flow occurred during the formation and evolution of delta of each run, which was in agreement with that observed by Dijk et al. (2012). Run1 is taken as an example to explore influencing factors of flow regime and estimation method for cycle period.
T=
h v
where h is typical depth; v is delta aggradation rate: 4
(2)
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(A) 0.5
Run1 Run2 Run3
0.4
b/B
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0.2
0.1
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1400
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0.4
b/B
0.3
0.2
0.1
0.0 0
200
400
600
800
1000
1200
1400
1600
1800
2000
Time(min) Fig. 5. Relative channel width. (A) Relative channel width of Run1, Run2 and Run3. (B) Relative channel width of Run1, Run4 and Run5.
v=
Qs Bp
where Qs is Because difficult to transported
h=
(3)
Y
(4)
where Q is the known water discharge; vf is the estimate of flow velocity in channel at 0.5p way down the delta from the apex based on particle image velocimetry and takes the value of the mean velocity of channel centrelines. Flow field contour map at 10 h of Run1 based on particle image velocimetry was taken as an example and shown in Fig. 7 below.
the sediment supplied rate. of the small depth of water during the experiment, it is measure directly. The discharge was considered to be mainly by channel, and the depth can be estimated from:
(A)
Q bvf
(B)
water surface
sediment
water surface h
h
Y
sediment
Fig. 6. Schematic of the transition process of flow regime: (A) Transition from sheet flow to channelized flow, (B) transition from channelized flow to sheet flow. 5
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level (see Fig. 8(A)) made the lake inundate even middle delta segment. As the lake level was high, the length and transverse width of delta were small with a large thickness of deposition. The width from the middle to the lower part did not change greatly, and lateral deposition on flanks of apex was obvious. The front was smooth and thick. The main channel can extend to the front, with few discontinuous radial rills and channels occurring on the surface. Therefore, the high lake level limited both the horizontal and vertical movement of sediment, being insufficient to trigger incisions as much as shallow level. When the sediment carried by the sediment-laden flow could not be transported farther away from the apex by the combined mechanism of longitudinal energy gradient and flow energy, the sediment would fall and deposit in the upper delta. Compared with a low sediment supplied rate (see Fig. 8(D)), under the condition of great sediment supplied rate (see Fig. 8(C)), the deposition thickness was large with a great length and a slightly larger width. The width from the middle to the lower part changed greatly, and the front was protruding, smooth and thick. No obvious deposition occurred on flanks of apex. The main channel could not reach the front, and continuous radial rills and channels occurred on the surface. A great sediment supplied rate would lead to improving the sediment movement range both in transverse and longitudinal directions and vertical deposition thickness, promoting continuous incisions. 3.2.3. Comparison between control group and repetitive group Conditions of Run1 and Run1-a were kept the same under an observable precision. Although many similar evolution rules existed between the two runs, the flow regime, the channel generation, the location and extent of sediment transport and deposition as well as the morphology at a certain time were different, which was identified as stochastic expression of delta morphology. The delta geometries changing over time of Run1 and Run1-a are plotted respectively in Fig. 9 (the delta contours of 14 h, 22 h, 26 h, 27 h and 29 h of Run 1 and 26 h of Run 1-a are covered). From the microscopic view, whether the channel bifurcate or migrate at a certain time depends on the anti-scouring characteristic of a certain pinch of sediment and the scouring characteristic of fluid on the sediment, which determines flow direction, flow regime, the formation and merging of flow paths suggesting flow path self-organization, and the morphological characteristic of sedimentary body and so on. The discussion on anti-scouring characteristic of sediment and the scouring characteristic of fluid can help to explore the influencing factors of stochastic expression of delta morphology. We assumed that the fluid intensity was constant, sediment incipient motion depended on the grain size distribution and the cohesive force existed between sediment particles. For the non-cohesive sediment used in our experiment, the critical shear stress acting on noncohesive sediment on gentle slope can be calculated as follows according to Wang and Shen's (1985) and Zhang's (1990) method:
Fig. 7. Contour map of flow field at 10 h of Run1.
Take Run1 as an example to illustrate the calculation process. During the first 3 h when it was in the typical sheet flow stage, there was no obvious channel, so the calculation was started from the fourth hour. As shown in Fig. 5(A), starting from 4 h, the first observation of the maximum state of channelized flow should be between 6 h and 7 h since the flow field was measured at the end of each hour. The interval from the 4th hour to the moment around 6 h is the duration that flow regime began to change from sheet flow to channelized flow, indicated by ΔT ≈ 2–3 h, while the predicted period based on the data at 4 h ΔTp ≈ 7844.35 s ≈ 2.1790 h (T = 240 min: h = 0.2958 cm, B = 39.9549 cm, p = 65.0451 cm, Qs = 0.098 cm3/s). The same goes for other nodes and intervals in Fig. 5(A). The calculation results of Run 1–5 are listed in Appendix A, where T is the time point for calculating; h is the estimated water depth through formula (4) based on particle image velocimetry; B is the medial delta width; p is the maximum distance from the apex to the margin position; Qs is the sediment supplied rate; ΔTp is the cycle period of flow regime transition through calculation; ΔT is the cycle period of flow regime transition that relative channel width in Fig. 10 reflects. The calculation results were in excellent agreement with what was observed and the value of relative width of channel.
sin 2ϕ ⎞ τc = K ∗ (γs − γ ) d w ⎜⎛1 − ⎟ sin 2β ⎠ ⎝
3.2.2. Delta deposition and morphology In order to compare the morphological characteristics of the delta under several working conditions better, the characteristics of the delta in terms of length, transverse width, deposition thickness, width variation from the middle to the lower part, deposition at the top flanks, front contour and thickness, types and quantities of surface channels under working conditions 2, 3, 4 and 5 are summarized and compared in Fig. 8. Schematic models of delta morphology under conditions of high and low lake level, great and small sediment supplied rates were obtained and shown in Fig. 8. Groups of experiments showed the spatial similarity (tree shape) of structural characteristics after the evolution process was stable, but the final morphology obtained by each experiment was different. Compared with the experiment under the condition of low lake level (see Fig. 8(B)) whose shoreline just reached the delta front, a high lake
(5)
where τc is the incipient shear stress; K* is the coefficient of sediment incipient motion; ϕ is the angle between slope and horizontal plane; β is sediment friction angle; dw is the representative size of sediment. From Eq. (5), it can be seen that when flow condition is constant and ϕ is small enough which is same as our experiment, the shear stress is mainly controlled by grain size and sediment gravity, i.e., sediment properties. The sediment adopted in this experiment was naturally nonuniform, so the grain size and gravity of the sediment laying at the bottom of the flume differed both in horizontal and vertical directions before the experiment began, the same applied to the sediment supplied at the inlet. According to Ferguson's (2003) method，the shear stress of fluid can be calculated as follows: 6
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Fig. 8. Schematic models of delta morphology. (A) Run2. (B) Run3. (C) Run4. (D) Run5.
qS 0.67 τp = ρg ⎛ ⎞ ⎝C⎠
(6)
where τp is the shear stress of fluid; ρ is fluid density; q is unit discharge; S is unit slope; C is Chezy's coefficient. The fluid that each unit sediment received is assumed to be same in density and Chezy's coefficient but the discharge that each unit sediment receives and the unit slope change with spatial location of unit sediment, so the shear stress produced by flow to a pile of sediment also differs. A schematic of interaction of water and sediment and flow path selection is shown as follows: where bed sediment is divided into n squares and each square contains a pinch of sediment; the white square is the representation of the sediment that can move with the fluid while the black square is the sediment that cannot move; the arrow indicates the direction of the flow. As shown in Fig. 10, for white squares, scouring effects on them are greater than that of anti-scouring, and they can be carried away by
Fig. 10. Schematic of interaction of water and sediment and flow path selection.
Fig. 9. Delta geometries. (A) Run1. (B) Run1-a. 7
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fluid. Sediment that cannot move will still be left at black squares. Flow path will form at the place where white squares are connected, and two paths can even merge if the sediment in black squares between them are moved down by fluid then. And during the movement of sedimentladen flow, the bed load at the bottom of the flow merged with the surface ahead to form a new surface, which was also the interaction process between flow and new surface. The stochasticity of incoming water and sediment, the stochasticity of sediment gradation and gravity, and the stochasticity of bed conditions determined the stochasticity of micro-channel formation and the process of flow and sediment action. Therefore, delta evolution is a dialectical unity of variable hydrodynamic intensity, alternation of distribution space and stochastic process of bed change. Certainty is contained within stochasticity while the unification of instability and tendency is brewed in certainty, which determines the similarity and diversity of spatial evolution of Run1 and Run1-a.
channel width; a high lake level limited both the horizontal and vertical movement of sediment being insufficient to trigger incisions as much as shallow level, and a great sediment supplied rate would lead to improve the sediment movement range both in transverse and longitudinal directions and vertical deposition thickness promoting continuous incisions; factors influencing stochastic expression of delta morphology have been explored through the comparison between control and repetitive group. Phenomenon in our physical system showed that delta evolution was a process of simultaneous representation of similarity and stochasticity. Our experimental results have potential to provide data concerning revealing the process of water and sediment, the process of channel formation and siltation, the mechanism of lacustrine shallow-water delta evolution. The physical models have important reference value for inversing the process of historical siltation of delta and studying the response of lacustrine shallow-water delta to varied conditions of lake level and sediment supplied.
4. Conclusions
Acknowledgments
Our results presented in this paper provide insight into delta evolution process, periodic transition of flow regime, the influence of lake level and sediment supplied rate on delta morphology and process and factors of delta stochastic expression. The experimental process of each run was characterized by six phases; periodic transition of flow regime was observed and the period of flow regime transition was estimated by several easily available variables. The calculation results are in good agreement with the flow regime observed and indicated by relative
This work was supported by the National Natural Science Foundation of China, China (51879182, 41576093 and 51279124), the Natural Science Foundation of Tianjin City, China (No. 14JCZDJC39800) and the Science Fund for Creative Research Groups of the National Natural Science Foundation of China, China (No. 51621092). We appreciate Chenfei Xue and Yu Zhao for their help to the experiment. Comments from the editor and the anonymous reviewers are sincerely thanked.
Appendix A. Schedule Calculation results of Run 1–5
Run
T (min)
1 1 1 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 5 5 5 5 5 5 5
240 360 480 600 840 1080 1380 1620 120 240 360 540 780 60 180 300 480 720 1080 1140 1560 1740 240 420 540 660 780 900 1020 180 420 780 1020 1140 1320 1500
h (cm)
B (cm)
p (cm)
0.2958 0.2237 0.2502 0.3096 0.2425 0.2723 0.1942 0.1667 0.2503 0.2493 0.2108 0.2374 0.2263 0.5743 0.1823 0.2562 0.2195 0.2157 0.1197 0.1969 0.0717 0.1833 0.3457 0.1465 0.1486 0.1169 0.1373 0.1181 0.1816 0.3955 0.3296 0.2289 0.0685 0.0924 0.0825 0.1398
39.9549 62.3476 36.7523 49.1131 51.1002 67.9209 68.0584 74.1039 70.3620 76.8474 88.0646 97.655 103.7543 23.0516 58.8874 46.2839 52.5590 69.0794 78.9048 85.4360 90.8102 90.3656 42.8986 69.4080 77.0381 74.7147 77.0061 81.8889 83.3672 68.0520 77.5503 85.8645 104.3972 116.4751 122.3610 117.1275
65.0451 95.2601 114.0744 114.9506 114.9049 113.4576 114.1011 122.8454 91.4031 106.3328 148.1207 142.3953 144.6134 52.9854 56.6059 86.7035 99.8296 102.7728 107.7557 120.7531 125.9180 128.7131 84.9728 85.7466 91.6286 90.0102 93.2906 99.2147 98.7701 60.7935 94.7280 119.6551 123.0315 122.3340 122.9100 131.6432
8
Qs (cm3/s)
ΔTp (h)
ΔT (h)
0.098 0.098 0.098 0.098 0.098 0.098 0.098 0.098 0.196 0.196 0.196 0.196 0.196 0.074 0.074 0.074 0.074 0.074 0.074 0.074 0.074 0.074 0.098 0.098 0.098 0.098 0.098 0.098 0.098 0.098 0.098 0.098 0.098 0.098 0.098 0.098
2.1790 3.7659 2.9733 4.9543 4.0359 5.3073 4.2746 4.3091 2.2814 2.8871 3.8970 4.6786 4.8122 2.6331 2.2811 3.8593 4.3232 4.9808 3.8204 7.6252 3.0432 8.0030 3.5719 2.4714 2.9732 2.7278 2.7958 2.7197 4.2385 4.6378 6.8631 5.7137 2.4938 3.7318 3.5169 6.1099
2–3 3–4 2–3 4–5 4–5 5–6 4–5 – 2–3 2–3 3–4 4–5 – 2–3 2–3 3–4 4–5 4–5 3–4 7–8 3–4 – 3–4 2–3 2–3 2–3 2–3 2–3 – 4–5 6–7 5–6 2–3 3–4 3–4 –
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Appendix B
B.1
B.2
B.3
B.4
B.5
Fig. B. 1. Delta morphology at 4 h of Run1. 2. Delta morphology at 9 h of Run1. 3. Delta morphology at 14 h of Run 1. 4. Delta morphology at 25 h of Run1. 5. Delta morphology at 30 h in Run1.
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