The effect of bottom sediment transport on wave set-up (original) (raw)
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Modelling the effect of bottom sediment transport on beach profiles and wave set-up
Ocean Modelling, 2012
In this paper we augment the wave-averaged mean field equations commonly used to describe wave setup and wave-induced mean currents in the near-shore zone, with an empirical sediment flux law depending only on the wave-induced mean current and mean total depth. This model allows the bottom to evolve slowly in time, and is used to examine how sediment transport affects the beach profile and wave setup in the surf zone. We show that the mean bottom depth in the surf zone evolves according to a simple wave equation, whose solution predicts that the mean bottom depth decreases and the beach is replenished. Further, we show that if the sediment flux law also allows for a diffusive dependence on the beach slope then the simple wave equation is replaced by a nonlinear diffusion equation which allows a steady-state solution, the equilibrium beach profile.
A phase-resolving cross shore sediment transport model for beach profile evolution
Coastal Engineering, 1997
A phase-resolving wave transformation module is combined with an intra-wave sediment transport module to calculate the on-/offshore sediment transport rates. The wave module is based on the Boussinesq equations extended into the surf zone. The vertical variation of the mean undertow and the intra-wave sediment concentrations are calculated. The net sediment transport rates are calculated, and the equation for conservation of sediment is solved to predict the beach profile evolution. The results of the present paper showed that the undertow contribution to the sediment transport rates is not dominating in all parts of the surf zone, even for eroding beaches, suggesting that other contributions should not be neglected. The present model also showed that for the same offshore wave energy the time series of the oscillatory motion is important and that the effect of wave groups cannot be disregarded.
A Simple Model of Sediment Transport in the Nearshore Zone
Asian Research Journal of Mathematics
In this paper we examine a simple model of sediment transport, induced by the breaking waves in the surf zone. Essentially the bottom is allowed to move in response to the divergence of a sediment flux, in turn determined by the breaking waves. The effect of this extra term on the previous solutions for setup , longshore currents and rip currents is then determined. It is found that the solutions for the mean flow are now unsteady on a slow timescale determined by a certain sediment transport parameter. There is a change in beach slope in the rip currents controlled by the sediment transport. The system of equations now forms a three-by-three nonlinear hyperbolic system of equations. These we solve approximately, using a simple wave solution based on the simple wave speed corresponding to the small sediment transport parameter. However, this solution will always breakdown after a long time, so we show that by adding another term proportional to the beach slope into the expression for the sediment flux, we can obtain a steady-state solution.
A Model of Beach Profile Evolution Including Wave-Undertow Interaction
Coastal Engineering Proceedings, 2012
A numerical model of beach profile evolution is developed to study the onshore and offshore sandbar migration under different wave conditions. The integrated model consists of wave model, roller model, flow model, sediment transport model and bed evolution model. In particular, the interaction between waves and wave-induced undertow current is considered in the flow model. This is achieved by adding a mean pressure gradient term into the firs-order momentum balance equation of flow. A simple empirical method is also introduced to describe the variation in eddy viscosity during one wave cycle. A preliminary application of the present model shows good agreements of both onshore and offshore sandbar migration phenomenon with the laboratory observation. It is found that the offshore sandbar migration is dominated by undertow while wave affects the transport rate. For the onshore sandbar migration, although sediment transport is mainly driven by wave and the undertow is weak, the transpo...
Modeling of surf zone processes on a natural beach using Reynolds-Averaged Navier-Stokes equations
Journal of Geophysical Research, 2007
The use of an advanced VOF-type model (COBRAS-UC), based 5 on the Reynolds-Averaged Navier-Stokes (RANS) equations, is proposed in 6 this work with the aim of improving the current state of understanding of 7 surf zone processes on natural beaches. Previous studies have suggested that 8 it is important to consider contributions from terms traditionally neglected 9 when assuming a uniform velocity and pressure distribution and a simple tur-10 bulence parameterization in surf zone hydrodynamics. In contrast with the 11 Boussinesq and Nonlinear Shallow Water (NSW) equations models, in the 12 RANS models none of the above mentioned limiting assumptions are required, 13 since no wave theory is imposed and the initiation of wave breaking is pre-14 dicted by using an advanced turbulence model. Although the model has been 15 widely validated in the laboratory, there is no previous study, to the best of 16 the authors' knowledge, which addresses the applicability of this model to 17 random waves on natural beaches. Free-surface elevation and wave-induced 18 velocity observations, from the SwashX field experiment, are used to vali-19 date this model. The model is able to satisfactorily predict the wave evolu-20 tion and flow characteristics across the surf zone. The model provides a means 21 to obtain high spatial and time resolution information of magnitudes which 22 are difficult or impossible to measure in the field and therefore may contribute 23 to improve our understanding on the physics of surf zone hydrodynamics.
A numerical model of nearshore waves, currents, and sediment transport
Coastal Engineering, 2009
A two-dimensional numerical model of nearshore waves, currents, and sediment transport was developed. The multi-directional random wave transformation model formulated by Mase [Mase, H., 2001. Multi-directional random wave transformation model based on energy balance equation. Coastal Engineering Journal 43 (4) (2001) 317] based on an energy balance equation was employed with an improved description of the energy dissipation due to breaking. In order to describe surface roller effects on the momentum transport, an energy balance equation for the roller was included following Dally-Brown [Dally, W. R., Brown, C. A., 1995. A modeling investigation of the breaking wave roller with application to cross-shore currents. Journal of Geophysical Research 100(C12), 24873]. Nearshore currents and mean water elevation were modeled using the continuity equation together with the depth-averaged momentum equations. Sediment transport rates in the offshore and surf zone were computed using the sediment transport formulation proposed by Camenen-Larson
Cross-shore suspended sediment transport in the surf zone: a field-based parameterization
Marine Geology, 2002
Existing cross-shore sediment transport models for two-dimensional surf zone bathymetries almost invariably predict offshore-directed sand transports and bar migrations during storm conditions. However, onshore-directed suspended sediment fluxes and associated nearshore bar migration were observed during recent field experiments on a gently sloping beach on the Danish North Sea coast. Field measurements of suspended sediment flux obtained during three experiments on two different beaches are used to parameterize the observed fluxes. This parameterization predicts suspended sediment transport due to incident waves and undertow across bars in two-dimensional surf zones. First, a non-dimensional sediment flux index is formulated which describes the tendency towards net onshore or offshore transport and the strength of that tendency. The non-dimensional formulation circumvents the problem of measurement inconsistencies due to varying elevations of sediment concentration sensors relative to the bed. The index is found to depend upon the undertow velocity, the incident wave skewness and the cross-correlation between orbital velocity and sediment concentration. However, some of these parameters are difficult to predict, particularly in barred surf zones and therefore, the independent variables are recast in terms of a set of more easily obtainable parameters. The sediment flux index depends on a combination of the following: non-dimensional bed shear stress (the Shields parameter), relative water depth, wave orbital velocity, relative wave height and bed slope. Finally, a formulation of suspended sediment transport across bars is obtained by linking the flux index with a parameterization of the sediment concentration/distribution in the water column. These concentrations are found to depend on nondimensional bed shear stress, relative wave height and water depth. The formulation predicts a tendency for onshoredirected sediment transport due to incident waves on gently sloping beaches and/or with large bed shear stresses. On steeply sloping beaches and/or in the inner part of the surf zone there is a tendency towards offshore sediment transports due to the undertow.
Wave-induced setup of the mean surface over a sloping beach
Continental Shelf Research, 2009
A new theoretical approach for the wave-induced setup over a sloping beach is presented that takes into consideration the explicit variations of the surface waves due to bottom slope and viscosity. In this way, the wave forcing of the mean Lagrangian volume fluxes is calculated without assuming that the local depth is constant. The analysis is valid in the region outside the surf zone and is based on the shallowwater assumption. A novel approach for separating the viscous damping of the waves from the frictional damping of the mean flow is introduced, where the mean Eulerian velocity is applied in the bottom stress for the mean fluxes. In the case where the onshore Lagrangian mean transport is zero, a new formula is derived for the Eulerian mean free surface slope, in which the effects of bottom slope, viscous wave damping and frictional bottom drag on the mean flow are clearly identified. The analysis suggests that viscous damping of the waves and frictional dissipation of the Eulerian near-bed return flow could lead to setup outside the surf zone.
Fuel and Energy Abstracts, 2011
In this study, new large scale experimental data are presented showing evidences of a link between the swash zone dynamics and the surf zone morphodynamics. Two sets of large scale experiments are presented. The first set of experiments investigates the swash and surf dynamics under the same hydrodynamic forcing but with two different swash zone morphological conditions, one of which was created by manual reshaping of the sub-aerial beach-face. It is shown that more dissipative swash zone conditions (a more mildly sloping beach-face) significantly reduce the rate of seaward
Coastal Engineering Proceedings, 2018
A practical numerical model was developed to simulate cross-shore profile evolution at two coastal sites in Iran. The model consists of three sub-models for calculating wave and current, sediment transport, and bed level changes. Validation and calibration of the model was carried out using the measured field data on the north and south coasts of Iran, where historic measurements of cross-shore beach profiles and wave conditions have been recorded. The model is formulated for calculating cross-shore sediment transports in and outside the surf zone by the product of time-averaged suspended sediment concentration under three different mechanisms and undertow velocity. The comparisons between the model results and field data show reasonable agreement for both coastal sites and will be capable of applying it to other coastal sites with modifications to the free parameters.