A comparison of two different types of shoreline boundary conditions (original) (raw)
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Open Ocean …, 2010
This paper deals with an analytical solution of the shoreline evolution due to random sea waves. The phenomenon of the shoreline change is modeled by means of a one-line theory. The solution is based on the hypotheses that the deviation of the shoreline planform from the general shoreline alignment (x-axis) approaches zero and that a particular relationship between higher order derivatives of the shoreline holds. It is proved that the shoreline evolution is described by a diffusion equation, in which the diffusivity G 1R is a function of the sea state and the sediment characteristics. Next, particular attention is dedicated to the longshore diffusivity. Its behaviour is analysed and effects of different spectral shapes and of different breaking depths are investigated. It is shown that the diffusivity assumes both positive and negative values.
A One-Line Numerical Model for Wind Wave Induced Shoreline Changes
A numerical model is developed to determine wind wave induced shoreline changes by solving sand continuity equation and taking one line theory as a base, in existence of Igroins and T-groins, whose dimensions and locations may be given arbitrarily. The model computes the transformation of deep water wave characteristics up to the surf zone and eventually gives the result of shoreline changes with user-friendly visual outputs. Herein, a modification to a readily accepted one-line model as sheltering effect of groins on wave breaking and diffraction is introduced together with representative wave input as annual average wave height. Compatibility of the currently developed tool is tested by a case study and it is shown that the results, obtained from the model, are in good agreement qualitatively with field measurements.
Improved coastal boundary condition for surface water waves
Ocean Engineering, 2001
Surface water waves in coastal waters are commonly modeled using the mild slope equation. One of the parameters in the coastal boundary condition for this equation is the direction at which waves approach a coast. Three published methods of estimating this direction are examined, and it is demonstrated that the wave fields obtained using these estimates deviate significantly from the corresponding analytic solution. A new method of estimating the direction of approaching waves is presented and it is shown that this method correctly reproduces the analytic solution. The ability of these methods to simulate waves in a rectangular harbor is examined.
Coastal Engineering, 2009
The note extends and completes the analysis carried out by . Shoreline motion in nonlinear shallow water coastal models. Coastal Eng. 56(5-6) (doi:101016/j. coastaleng.2008.10.008), 495-505.] on the performance of a state of the art Non-Linear Shallow Water Equations solver in common coastal engineering applications. The case of bore-generated overtopping of a truncated plane beach is considered and the performance of the model is assessed by comparing with the Peregrine and Williams [Peregrine, D., Williams, S.M., 2001. Swash overtopping a truncated beach. J. Fluid Mech. 440, 391-399.] analytical solution. In particular the influence of shoreline boundary conditions is investigated by considering the two best performing approaches discussed in Briganti and Dodd . Shoreline motion in nonlinear shallow water coastal models. Coastal Eng. 56(5-6) (doi:101016/j.coastaleng.2008.10.008), 495-505.]. Different distances of the edge of the beach from the bore collapse point are tested. For larger distances, the accuracy of the overtopping modelling decreases, as a consequence of the error in modelling the tip of the swash lens and, consequently, the run-up. A sensitivity analysis using the numerical resolution is carried out. This reveals that the approach in which cells shallower than a prescribed threshold are drained and wave propagation speeds for wet/dry Riemann problem are used at the interface between a wet and a dry cell (referred as Option 2ea in . Shoreline motion in nonlinear shallow water coastal models. Coastal Eng. 56(5-6) (doi:101016/j. coastaleng.2008.10.008), 495-505.]) performs consistently better than the other.
Analytical Solutions of One-Line Model for Shoreline Change near Coastal Structures
Journal of Waterway, Port, Coastal, and Ocean Engineering, 1997
Shoreline evolution in the vicinity of a groin for variable sand transport rate conditions (two solution areas; 6 = 0.5 , a. =-0.1 rad , a " =-0.4 rad) ol o2 43 Shoreline evolution behind a jetty with linear variation in breaking wave angle in the shadow zone (a =-0.1 rad , a" = 0.4 rad) Y rl 44 Shoreline evolution behind a jetty with exponential variation in breaking wave angle (a = 0.4 rad , yL = 1) ANALYTICAL SOLUTIONS OF THE ONE-LINE MODEL OF SHORELINE CHANGE
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
A hydrodynamic model of nearshore waves and wave-induced currents
2011
In This study develops a quasi-three dimensional numerical model of wave driven coastal currents with accounting the effects of the wave-current interaction and the surface rollers. In the wave model, the current effects on wave breaking and energy dissipation are taken into account as well as the wave diffraction effect. The surface roller associated with wave breaking was modeled based on a modification of the equations by Dally and Brown (1995) and Larson and Kraus (2002). Furthermore, the quasi-three dimensional model, which based on Navier-Stokes equations, was modified in association with the surface roller effect, and solved using frictional step method. The model was validated by data sets obtained during experiments on the Large Scale Sediment Transport Facility (LSTF) basin and the Hazaki Oceanographical Research Station (HORS). Then, a model test against detached breakwater was carried out to investigate the performance of the model around coastal structures. Finally, the model was applied to Akasaki port to verify the hydrodynamics around coastal structures. Good agreements between computations and measurements were obtained with regard to the cross-shore variation in waves and currents in nearshore and surf zone.
Journal of Fluid Mechanics, 2007
The aim of the present work, final of a three-part series, is to analyse in detail flow motions within the swash zone and define suitable shoreline boundary conditions for the longshore flow for wave-averaged circulation models. The analyses of Parts 1 and 2 are extended to cover horizontally two-dimensional flows. An analytical solution for the longshore motion representing the drift velocity of the whole swash zone water mass is found. This is seen to be approximated well by the ratio between the time integral of the longshore momentum flux crossing the swash lower boundary and the swash zone net water volume. Further, a complete set of shoreline boundary conditions, taking into account wave-wave interactions, is obtained on the basis of fully numerical solutions of the nonlinear shallow-water equations. The main focus of the work is to clarify the structure of the shoreline boundary conditions for the longshore flow, but attention has also been paid to their derivation and assessment from the numerical solutions. The latter have been obtained on the basis of a fairly broad range of input wave conditions which, though biased towards those typical of reflective beaches, are believed to cover conditions also typical of moderate dissipative beaches. Two main terms are found to contribute to the longshore drift velocity: (i) a term, proportional to the shallow-water velocity, accounting for short-wave interactions, frictional swash zone forces and continuous forcing due to non-breaking wave nonlinearities and (ii) a drift-type term representing the momentum transfer due to wave breaking.
Shoreline motion in nonlinear shallow water coastal models
Coastal Engineering, 2009
Different shoreline boundary conditions for numerical models of the Non-Linear Shallow Water Equations based on Godunov-type schemes are compared. The study focuses on the Peregrine and Williams [Peregrine, D.H., Williams, S.M., 2001. Swash overtopping a truncated plane beach. Journal of Fluid Mechanics 440, 391–399.] problem of a single bore collapsing on a slope. This is considered the best test to
А Finite Element Method in the Study of Nearshore Wave Processes
2023
The paper suggests that the only feasible method for implementing adequate nearshore wave dynamics models under conditions of extreme complexity is numerical methods with computational experiments on powerful computers. When the fundamental laws of continuum mechanics are roughly written for a finite element (FE) with an emphasis on the ensuing numerical solution, the finite element method (FEM) offers great opportunities in this regard. The FEM has the benefit of allowing for the well-approximation of coastal water areas by a collection of irregular triangles, and their boundaries can typically be curvilinear. The FEM has the advantage that its grid equations typically are independent of the type of grid and its topology, setting it apart from other grid methods. The generalized solutions to the original problems are divided into grid-like equations for the FEM, which are derived on the basis of integral relations. The fundamental integral laws are thus automatically maintained for grid equations. For the study of the coastal wave regime in a non-stationary three-dimensional formulation, grid equations of the FEM are constructed in this work. The generalized solutions to the original problems are divided into grid-like equations for the FEM, which are derived on the basis of integral relations. The fundamental integral laws are thus automatically maintained for grid equations. For the study of the coastal wave regime in a non-stationary three-dimensional formulation, grid equations of the FEM are constructed in this work.