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1.
Characteristics of turbulent boundary layers over a rough bed under saw-tooth waves and its application to sediment transport 总被引：1，自引：0，他引：1
A large number of studies have been done dealing with sinusoidal wave boundary layers in the past. However, ocean waves often have a strong asymmetric shape especially in shallow water, and net of sediment movement occurs. It is envisaged that bottom shear stress and sediment transport behaviors influenced by the effect of asymmetry are different from those in sinusoidal waves. Characteristics of the turbulent boundary layer under breaking waves (saw-tooth) are investigated and described through both laboratory and numerical experiments. A new calculation method for bottom shear stress based on velocity and acceleration terms, theoretical phase difference, φ and the acceleration coefficient, ac expressing the wave skew-ness effect for saw-tooth waves is proposed. The acceleration coefficient was determined empirically from both experimental and baseline k–ω model results. The new calculation has shown better agreement with the experimental data along a wave cycle for all saw-tooth wave cases compared by other existing methods. It was further applied into sediment transport rate calculation induced by skew waves. Sediment transport rate was formulated by using the existing sheet flow sediment transport rate data under skew waves by Watanabe and Sato [Watanabe, A. and Sato, S., 2004. A sheet-flow transport rate formula for asymmetric, forward-leaning waves and currents. Proc. of 29th ICCE, ASCE, pp. 1703–1714.]. Moreover, the characteristics of the net sediment transport were also examined and a good agreement between the proposed method and experimental data has been found. 相似文献
2.
《Coastal Engineering》2005,52(9):745-770
New experiments were carried out in the Large Oscillating Water Tunnel of WL|Delft Hydraulics (scale 1:1) using asymmetric 2nd-order Stokes waves. The main aim was to gain a better understanding of size-selective sediment transport processes under oscillatory plane-bed/sheet-flow conditions. The new data show that for uniform sand sizes between 0.2 < D < 1.0 mm, measured net transport rates are hardly affected by the grain size and are proportional to the third-order velocity moment. However for finer grains (D = 0.13 mm) net sand transport rates change from the ‘onshore’ direction into the ‘offshore’ direction in the high velocity range. A new measuring technique for sediment concentrations, based on the measurement of electro-resistance (see [McLean, S.R., Ribberink, J.S., Dohmen-Janssen, C.M. and Hassan, W.N.M., 2001. Sediment transport measurements within the sheet flow layer under waves and currents. J. Waterw., Port, Coast., Ocean Eng., ISSN 0733-950X]), was developed further for the improved measurement of sediment dynamics inside the sheet-flow layer. This technique enabled the measurements of particle velocities during the complete wave cycle. It is observed that for long period waves (T = 12.0 s), time-dependent concentrations inside the sheet-flow layer are nearly in phase with the time-dependent flow velocities. As the wave period decreases, the sediment entrainment from the bed as well as the deposition process back to the bed lags behind the wave motion more and more. The new data show that size-gradation has almost no effect on the net total transport rates, provided the grain sizes of the sand mixture are in the range of 0.2 < D < 1.0 mm. However, if very fine grains (D = 0.13 mm) are present in the mixture, net total transport rates of graded sand are generally reduced in comparison with uniform sand with the same D50. The transport rates of individual size fractions of a mixture are strongly influenced by the presence of other fractions in a mixture. Fine particles in sand mixtures are relatively less transported than in that uniform sand case, while the opposite occurs for coarse fractions in a mixture. The relative contribution of the coarse grains to the net total transport is therefore larger than would be expected based on their volume proportion in the original sand mixture. This partial transport behaviour is opposite to what is generally observed in uni-directional (e.g. river) flows. This is caused by vertical sorting of grain sizes in the upper bed layer and in the sheet flow and suspension layers. Kinematic sorting is believed to be responsible for the development of a coarse surface layer on top of a relatively fine sub-layer, providing in this way a relatively large flow exposure for the coarser sizes. Furthermore fine grains are suspended more easily than coarse grains to higher elevations in the flow where they are subject to increasing phase-lag effects (settling lags). The latter also leads to reduced net transport rates of these finer sizes. 相似文献
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4.
Many existing practical sand transport formulae for the coastal marine environment are restricted to a limited range of hydrodynamic and sand conditions. This paper presents a new practical formula for net sand transport induced by non-breaking waves and currents. The formula is especially developed for cross-shore sand transport under wave-dominated conditions and is based on the semi-unsteady, half wave-cycle concept, with bed shear stress as the main forcing parameter. Unsteady phase-lag effects between velocities and concentrations, which are especially important for rippled bed and fine sand sheet-flow conditions, are accounted for through parameterisations. Recently-recognised effects on the net transport rate related to flow acceleration skewness and progressive surface waves are also included. To account for the latter, the formula includes the effects of boundary layer streaming and advection effects which occur under real waves, but not in oscillatory tunnel flows. The formula is developed using a database of 226 net transport rate measurements from large-scale oscillatory flow tunnels and a large wave flume, covering a wide range of full-scale flow conditions and uniform and graded sands with median diameter ranging from 0.13 mm to 0.54 mm. Good overall agreement is obtained between observed and predicted net transport rates with 78% of the predictions falling within a factor 2 of the measurements. For several distinctly different conditions, the behaviour of the net transport with increasing flow strength agrees well with observations, indicating that the most important transport processes in both the rippled bed and sheet flow regime are well captured by the formula. However, for some flow conditions good quantitative agreement could only be obtained by introducing separate calibration parameters. The new formula has been validated against independent net transport rate data for oscillatory flow conditions and steady flow conditions. 相似文献
5.
Field measurements of cross-shore currents 0.25 m from the bed were made on two natural beaches under a range of incident wave conditions. The results indicated the presence of a relatively strong, offshore-directed mean current, both within and seaward of the surf zone. Typical velocities within the surf zone were of the order of 0.2–0.3 m/s. This bed return flow, or “undertow”, represents a mass conservation response, returning water seaward that was initially transported onshore in the upper water column, primarily above the trough of the incident waves. The measurements demonstrated that the bed return flow velocity increases with the incident wave height. In addition, the crossshore distribution of the bed return flow is characterised by a mid-surf zone maximum, which exhibits a strong decrease in velocity towards the shoreline and a more gradual decay in the offshore direction. Several bed return flow models based on mass continuity were formulated to predict the cross-shore distribution of the bed return flow under an irregular wave field and were compared with the field data. Best agreement was obtained using shallow water linear wave theory, after including the mass transport associated with unbroken waves. The contribution of the unbroken waves enables net offshore-directed bottom currents to persist outside the region of breaking waves, providing a mechanism, other than rip currents, to transport sediment offshore beyond the surf zone. 相似文献
6.
A simple conceptual formulation to compute seabed shear stress due to asymmetric and skewed waves is presented. This formulation generalizes the sinusoidal wave case and uses a variable friction factor to describe the physics of the boundary layer and to parameterize the effects of wave shape. Predictions of bed shear stresses agree with numerical computations using a standard boundary layer model with a k–ε turbulence closure. The bed shear stress formulation is combined with a Meyer-Peter and Müller-type formula to predict sheet flow bedload transport under asymmetric and skewed waves for a horizontal or sloping bed. The predictions agree with oscillatory water tunnel measurements from the literature. 相似文献
7.
《Coastal Engineering》2001,42(2):173-197
Intra-wave sediment suspension is examined using high-resolution field measurements and numerical hydrodynamic and sediment models within 120 mm of a plane seabed under natural asymmetric waves. The detailed measurements of suspended sediment concentration (at 5 mm vertical resolution and at 4 Hz) showed two or three entrainment bursts around peak flow under the wave crest and another at flow reversal during the decelerating phase. At flow reversal, the mixing length was found to be approximately double the value attained at peak flow under the crest. To examine the cause of multiple suspension peaks and increased diffusion at flow reversal, a numerical “side-view” hydrodynamic model was developed to reproduce near-bed wave-induced orbital currents. Predicted currents at the bed and above the wave boundary layer were oppositely directed around flow reversal and this effect became more pronounced with increasing wave asymmetry. When the predicted orbital currents and an enhanced eddy diffusivity during periods of oppositely directed flows were applied in a Lagrangian numerical sediment transport model, unprecedented and extremely close predictions of the measured instantaneous concentrations were obtained. The numerical models were simplified to incorporate only the essential parameters and, by simulating at short time scales, empirical time-averaged parameterisations were not required. Key factors in the sediment model were fall velocities of the full grain size distribution, diffusion, separation of entrainment from settlement, and non-constant, but vertically uniform, eddy diffusivity. Over the plane bed, sediment convection by wave orbital vertical currents was found to have no significant influence on the results. 相似文献
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9.
本文用了一个可考虑相位差作用和波浪边界层非对称性的瞬态理论模型和一个两相紊流模型共同研究非对称歪斜波引起的片流输沙现象。为了解速度偏度和加速度偏度对输沙通量和输沙率的贡献，两相流模型为理论模型提供了必要的相位超前、瞬时侵蚀深度和边界层的发展过程。理论模型研究显示了由速度偏度和加速度偏度引起的向岸阶段和离岸阶段的泥沙运动非对称性，解释了净输沙的产生原因。在以往的非对称歪斜波片流输沙研究中，净输沙的产生主要被归结于相位差作用。本文的研究则表明了非对称的边界层发展所产生的净流量和动床面效应在净输沙产生过程中的比相位差作用更为重要。 相似文献
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11.
《Coastal Engineering》2006,53(10):825-843
A newly developed two-phase flow model was applied to simulate the sediment movement under 2nd-order Stokes wave sheetflow conditions with different sediment sizes and wave periods. As for the distribution of eddy viscosity and sediment diffusion coefficient, the difference between onshore and offshore phases was considered by using an equivalent sinusoidal velocity amplitude for the asymmetric velocity profile. Sophisticated comparisons between laboratory measurements [O'Donoghue, T., Wright, S., 2004b. Flow tunnel measurements of velocities and sand flux in oscillatory sheetflow for well-sorted and graded sands. Coast. Eng., 51 (11–12), 1163–1184.] and the present numerical simulation were performed for sediment concentration, sediment velocity, sand flux and net transport rate. Four existing engineering models, together with the present two-phase flow model, were introduced for net transport rate prediction. Taking both the net sand transport rate magnitude and direction into account, the present process-based two-phase flow model provided the best estimations, which can simulate both the onshore net transport for medium/coarse sand cases and offshore net transport for fine sand cases with the agreement by a factor of 2 for almost all the considered cases. 相似文献
12.
Modelling of sand transport under wave-generated sheet flows with a RANS diffusion model 总被引：1，自引：0，他引：1
A 1DV-RANS diffusion model is used to study sand transport processes in oscillatory flat-bed/sheet flow conditions. The central aim is the verification of the model with laboratory data and to identify processes controlling the magnitude and direction (‘onshore’/‘offshore’) of the net time-averaged sand transport. The model is verified with a large series of measured net sand transport rates, as collected in different wave tunnels for a range of wave-current conditions and grain sizes. Although not all sheet flow details are represented in the 1DV-model, it is shown that the model is able to give a correct representation of the observed trends in the data with respect to the influence of the velocity, wave period and grain diameter. Also detailed mean sediment flux profiles in the sheet flow layer are well reproduced by the model, including the direction change from ‘onshore’ to ‘offshore’ due to a difference in grain size from 0.34 mm (medium sand) to 0.13 mm (fine sand). A model sensitivity study with a selected series of net transport data shows that the stirring height of the suspended sediment εs/ws strongly controls the magnitude and direction of the net sediment transport. Inclusion of both hindered settling and density stratification appears to be necessary to correctly represent the sand fluxes for waves alone and for waves + a superimposed current. The best agreement with a large dataset of net transport measurements is obtained with the 1DV-RANS model in its original settings using a Prandtl–Schmidt number σρ = 0.5. 相似文献
13.
《Coastal Engineering》2006,53(11):897-913
For the general purposes of morphodynamic computations in coastal zones, simple formula-based models are usually employed to evaluate sediment transport. Sediment transport rates are computed as a function of the bottom shear stress or the near bed flow velocity and it is generally assumed that the sediment particles react immediately to changes in flow conditions. It has been recognized, through recent laboratory experiments in both rippled and plane bed sheet flow conditions that sediment reacts to the flow in a complex manner, involving non-steady processes resulting from memory and settling/entrainment delay effects. These processes may be important in the cross-shore direction, where sediment transport is mainly caused by the oscillatory motions induced by surface short gravity waves.The aim of the present work is to develop a semi-unsteady, practical model, to predict the total (bed load and suspended load) sediment transport rates in wave or combined wave-current flow conditions that are characteristic of the coastal zone. The unsteady effects are reproduced indirectly by taking into account the delayed settling of sediment particles. The net sediment transport rates are computed from the total bottom shear stress and the model takes into account the velocity and acceleration asymmetries of the waves as they propagate towards the shore.A comparison has been carried out between the computed net sediment transport rates with a large data set of experimental results for different flow conditions (wave-current flows, purely oscillatory flow, skewed waves and steady currents) in different regimes (plane bed and rippled bed) with fine, medium and coarse uniform sand. The numerical results obtained are reasonably accurate within a factor of 2. Based on this analysis, the limits and validity of the present formulation are discussed. 相似文献
14.
J.S.M. van Thiel de Vries M.R.A. van Gent D.J.R. Walstra A.J.H.M. Reniers 《Coastal Engineering》2008,55(12):1028-1040
Large-scale physical model tests were conducted with different wave periods to examine the physical processes driving dune erosion. The model tests have been carried out in a flume (2DV) with a sandy dune exposed to extreme surge and wave conditions [Van Gent, M.R.A., Van Thiel de Vries, J.S.M., Coeveld, E.M., De Vroeg, J.H. and Van de Graaff, J., 2008. Large-scale dune erosion tests to study the effect of wave periods. Coastal Engineering. doi:10.1016/j.coastaleng.2008.04.003.]. Detailed measurements in time and space of water pressure, flow velocities and sediment concentrations were performed in the near shore area. The data revealed that both short- and long waves are important to inner surf hydrodynamics. Depth averaged flows are directed offshore and increase towards the shore line. The corresponding mean sediment concentrations rise sharply towards the dune face (up to 50 g/l near the bed). The strong increase in the mean sediment concentration towards the dune face correlates well with the maximum wave surface slope which in turn is coupled to both the pressure gradient and the near-bed wave-breaking induced turbulence. Analysis shows that the pressure gradient is only partially coupled to the flow acceleration suggesting that the latter cannot always be used as a proxy for the first. Weak correlation is obtained with the near-bed flows related to the bed shear stress. Tests with a larger wave period resulted in a larger dune erosion volume. During these tests more wave energy (combined incident and infragravity waves) reached the dune face, but more importantly, this wave energy is dissipated by fewer waves resulting in more intense wave breakers and steeper wave fronts. It is therefore expected that the wave-breaking induced near-bed turbulence increases resulting in significantly higher (O(100%)) mean sediment concentrations. In addition the mean flow velocities are comparable, yielding a substantially larger offshore directed sediment transport capacity. This increase in offshore directed transport is only partially compensated by a concurrent increase in the wave related onshore transport capacity associated with intrawave processes, resulting in a net increase in the dune erosion rate. 相似文献
15.
Tide-driven bed load transport is an important portion of the net annual sediment transport rate in many shoreface and shelf environments. However, bed load transport under waves cannot be measured in the field and bed load transport by currents without waves is barely measurable, even in spring tidal conditions. There is, consequently, a strong lack of field data and validated models. The present field site was on the shoreface and inner shelf at 2 to 8.5 km offshore the central Dutch coast (far outside the surfzone), where tidal currents flow parallel to the coast. Bed load transports were carefully measured with a calibrated sampler in spring tidal conditions without waves at a water depth of 13–18 m with fine and medium sands. The near-bed flow was measured over nearly a year and used for integration to annual transport rates. An empirical bed load model was derived, which predicts bed load transports that are a factor of > 5 smaller than predicted by existing models. However, they agree with laboratory data of sand and gravel transport in currents near incipient motion. The damped transport rates may have been caused by cohesion of sediment or turbulence damping due to mud or biological activity. The annual bed load transport rate was calculated using a probability density function (pdf) derived from the near-bed current and orbital velocity data which represented the current and wave climate well when compared to 30 years of data from a nearby wave station. The effect of wave stirring was included in the transport calculations. The net bed load transport rate is a few m2/year. This is much less than predicted in an earlier model study, which is partly due to different bed load models but also due to the difference in velocity pdf. The annual transport rate is very sensitive to the probability of the largest current velocities. 相似文献
16.
A two-phase numerical model for sediment transport prediction under oscillatory sheet flows 总被引：1，自引：0，他引：1
To predict sediment transport under oscillatory sheet flow condition, especially for fine sand, is still a challenging research subject in coastal engineering. This paper describes a newly-developed numerical model based on two-phase theory with the use of a one-equation turbulence closure, and its applications in predicting fine sediment suspension in near-prototype oscillatory sheet flow conditions. Model results were compared with comprehensive laboratory measurements of flow velocity and sediment concentration under both symmetrical and asymmetrical oscillatory sheet flows from a large-scale water tunnel. Good agreements between the model results and measurements were achieved and the results demonstrated that the model is capable of reproducing detailed characteristics of sediment entrainment process in the sheet flow regime. The comparisons also revealed the fact that the concentration peaks at flow reversal is associated with the strong vertical sediment transport flux in the pickup layer, which has been widely observed in many laboratory experiments. The effects of flow reversal events on total sediment transport were also discussed. 相似文献
17.
A shore-normal array of seven, bi-directional electromagnetic flowmeters and nine surface piercing, continuous resistance wave staffs were deployed across a multiple barred nearshore at Wendake Beach, Georgian Bay, Canada, and monitored for a complete storm cycle. Time-integrated estimates of total (ITVF) and net (INVF) sediment volume flux together with bed elevation changes were determined using depth-of-activity rods.
The three bars, ranging in height from 0.10 to 0.40 m accreted during the storm (0.03 m), and the troughs were scoured (0.05 m). Sediment reactivation depths reached 0.14 m and 12% of the nearshore control volume was mobilized. However, the INVF value for the storm was less than 1% of the control volume revealing a near balance in sediment volume in the bar system. Landward migration of the inner, crescentic and second, sinuous bars occurred in association with an alongshore migration of the bar form itself; the outermost, straight, shore-parallel bar remained fixed in location.
The surf zone was highly dissipative throughout the storm (ε = 3.8 × 102–192 × 102) and the wave spectrum was dominated by energy at the incident frequency. Spectral peaks at frequencies of the first harmonic and at one quarter that of the incident wave were associated with secondary wave generation just prior to breaking and a standing edge wave, respectively. The former spectral peak was within the 95% confidence band for the spectrum while the latter contributed not more than 10% to the total energy in the surface elevation spectrum even near the shoreline.
During the storm wave height exceeded 2 m (Hs) and periods reached 5 s (Tp k): orbital velocities exceeded 0.5 m s−1 (urm s) and were above the threshold of motion for the medium-to-fine sands throughout the storm. Shore-parallel flows in excess of 0.4 m s−1 were recorded with maxima in the troughs and minima just landward of the bar crest.
The rate and direction of sediment flux is best explained by the interaction of antecedent bed slopes with spatial gradients in the mean and asymmetry of the shore-normal velocity field. These hydrodynamic parameters represent “steady” flows superimposed on the dominantly oscillatory motion and assumed a characteristic spatial pattern from the storm peak through the decay period. Increases spatially in the magnitudes of both the mean flows and flow asymmetries cause an increasing net transport potential (erosion); decreases in these values spatially cause a decreasing net transport potential and thus deposition. These transport potentials are increased or decreased through the gravity potential induced by the local bed slope. Shore-parallel flow was important in explaining sediment flux and morphological change where orbital velocities, mean flows and flow asymmetries were at a minimum. 相似文献
18.
Predictability of wave-induced net sediment transport using the conventional 1DV RANS diffusion model 总被引：1，自引：0，他引：1
Based on a large database of laboratory experiments, the predictability of the conventional one-dimensional vertical Reynolds-averaged Navier–Stokes (RANS) diffusion model is systematically investigated with respect to wave-induced net sediment transport. The predicted net sediment transport rates are compared with the measured data of 176 physical experiments in wave flumes and oscillating water tunnels, covering a wide range of wave conditions (surface, skewed, and asymmetric waves with and without currents), sediment conditions (fine, medium, and coarse sands with median grain diameters ranging from 0.13 to 0.97 mm) and bed forms (flat beds and rippled beds), corresponding to various sediment dynamic regions in the near-shore area. Comparisons show that the majority (73 %) of predictions on a flat bed are within a factor 2 of the measurements. The model behaves much better for medium/coarse sand than for fine sand. The model generally underpredicts the transport rates beneath asymmetric waves and overpredicts the fine sand transport beneath skewed waves. Nevertheless, the model behaves well in reproducing the transport rates under surface waves. A detailed discussion and a quantitative measure of the overall model performance are made. The poor model predictability for fine sand cases is mainly due to the underestimation of unsteady phase-lag effect. It is revealed that the model predictability can be significantly improved by implementing alternative bedload formulas and incorporating more physical processes (mobile-bed roughness, hindered settling, and turbulence damping). 相似文献
19.
Shejun Fan Donald J. P. Swift Peter Traykovski Samuel Bentley Jeffry C. Borgeld Christopher W. Reed Alan W. Niedoroda 《Marine Geology》2004,210(1-4):17-41
Coast-hugging surface flood plumes occur on the inner shelf of northern California during the winter season, generating dense, near-bottom suspensions which may attain fluid mud concentrations as particles settle. The period of storm-heightened waves may continue into the flood period, leading to gravity-driven seaward displacement of the bottom suspension; or the wave regime may ameliorate, leaving the suspension to consolidate as a short-lived, inner-shelf flood bed. Such beds tend to be resuspended within days or weeks by subsequent storm events that may recreate the original high concentrations. The sediment is thus dispersed seaward by gravity flows, to be deposited as a muddy flood bed on the central shelf. The locus of deposition of these “high-concentration regimes” is a function of the relative intensities of river discharge and storm wave height. Greater discharge piles thicker storm beds nearer shore, while intense wave regimes allow deposition of the fluid mud further seaward. During events with high values of both parameters, large amount of fluid mud may bypass over the shelf edge. In contrast, “low-concentration regimes” occur during storm periods when there has been no recent flood deposition on the inner shelf. The shelf floor is better consolidated than in the previous case, and the resulting suspended sediment concentrations are lower. As a consequence, low-concentration regimes are winnowing and bypassing regimes, and the beds deposited are thinner and sandier. Algorithms describing deposition by high and low-concentration regimes have been embedded in a probabilistic model. A simulation of a 400-year sequence of beds deposited by winter storms and floods suggests that on the Eel shelf, the Holocene transgressive systems tract consists of back-stepping, seaward-fining event beds, whose timelines (bedding planes) dip more gently than do their gradational facies boundaries. At these longer time scales, flood beds dominate over storm beds. 相似文献
20.
Alan M. Davies Jiuxing Xing John M. Huthnance Philip Hall Laurenz Thomsen 《Progress in Oceanography》2002,52(2-4)
A three dimensional time-dependent baroclinic hydrodynamic model, including sediment transport and incorporating a turbulence energy sub-model, is used in cross sectional form to examine sediment movement at the shelf edge off North West Iberia at 42°40.5’N where measurements were made as part of the OMEX-II programme. These calculations are complemented by a simpler, in essence time-independent model, which is used to examine the sensitivity of the sediment distribution over the slope (from a shelf-break source) to changes in the specified values of horizontal and vertical diffusion coefficients. The philosophy of the paper is to use idealized tidal, wind and wind wave forcing to examine changes in sediment distribution resulting from these processes. Calculations with the time-dependent and steady state models give insight into both the role of events and long-term effects. The steady state model focuses on the off-shelf region, whilst the time-dependent model considers on-shelf events.Tidal calculations showed that for the stratification used here the internal tide in the OMEX region was primarily confined to the shelf edge and ocean. A mean on-shelf sediment transport in the surface layer and off-shelf transport at the bed was found. Across-shelf circulations produced by up-welling/down-welling favourable winds gave rise to on-shelf/off-shelf currents in the bottom boundary layer with an opposite flow in the surface layer. In the case of an up-welling favourable wind, sediment suspension was at a maximum in the near coastal region, with sediment being advected off shore in the surface layer. With a down-welling favourable wind, surface sediment was advected towards the shore, but there was offshore transport at the bed. Near the shelf edge any upwelling flow had the tendency to return this sediment to the surface layer from whence it was transported on-shore. So in essence the sediment was trapped within an on-shelf circulation cell. Wind waves effects increased the total bed stress and hence the sediment concentration and its transport, although its pattern was determined by tidal and wind forcing.The time independent model with increased/decreased lateral diffusivity gave an enhanced/reduced horizontal sediment distribution for a given settling velocity. As the settling velocity increases, the down-slope movement of sediment is increased, with a reduction in the thickness of the near-bed sediment layer, but with little change in its horizontal extent. 相似文献