On the role of the Chezy frictional term near the shoreline

The behavior of the Chezy frictional term near the shoreline has been studied in detail. An asymptotic analysis valid for water depths going to zero clearly shows that the use of such a term implies a non-receding motion of the shoreline. This phenomenon is induced by a thin layer of water which, because of frictional forces, remains on the beach and keeps it wet seaward of the largest run-up. However, the influence of such a frictional layer of water on the global wave motion is very weak and practically negligible for most of the swash zone flow dynamics. The existence of a non-receding shoreline has led to some clarifications on the role of some ad-hoc tools used in numerical models for the prediction of the wet/dry interface.

[1]  A. Balzano,et al.  Evaluation of methods for numerical simulation of wetting and drying in shallow water flow models , 1998 .

[2]  E. Toro.  Riemann Solvers and Numerical Methods for Fluid Dynamics , 1997 .

[3]  Maurizio Brocchini,et al.  An integral swash zone model with friction: an experimental and numerical investigation , 2002 .

[4]  Evolution of solitary waves and undular bores in shallow-water flows over a gradual slope with bottom friction , 2007, Journal of Fluid Mechanics.

[5]  O. Bühler,et al.  Wave-driven currents and vortex dynamics on barred beaches , 2001, Journal of Fluid Mechanics.

[6]  Maurizio Brocchini,et al.  Integral flow properties of the swash zone and averaging , 1996, Journal of Fluid Mechanics.

[7]  Alfredo Bermúdez,et al.  Upwind methods for hyperbolic conservation laws with source terms , 1994 .

[8]  H. P. Greenspan,et al.  Water waves of finite amplitude on a sloping beach , 1958, Journal of Fluid Mechanics.

[9]  D. Pritchard,et al.  The near-shore behaviour of shallow-water waves with localized initial conditions , 2007, Journal of Fluid Mechanics.

[10]  K. Holland,et al.  Estimating swash zone friction coefficients on a sandy beach , 2001 .

[11]  M. Brocchini.  Eulerian and Lagrangian aspects of the longshore drift in the surf and swash zones , 1997 .

[12]  Vimal Singh,et al.  Perturbation methods , 1991 .

[13]  Maximum run-up, breaking conditions and dynamical forces in the swash zone: a boundary value approach , 2008 .

[14]  A. Hogg,et al.  On fine sediment transport by long waves in the swash zone of a plane beach , 2003, Journal of Fluid Mechanics.

[15]  Maurizio Brocchini,et al.  Recent advances in modeling swash zone dynamics: Influence of surf‐swash interaction on nearshore hydrodynamics and morphodynamics , 2008 .

[16]  Maurizio Brocchini,et al.  An efficient solver for nearshore flows based on the WAF method , 2001 .

[17]  W. N. Houston,et al.  The motion of cobbles in the swash zone on an impermeable slope , 1998 .

[18]  A. Hogg,et al.  On the transport of suspended sediment by a swash event on a plane beach , 2005 .

[19]  T. Baldock,et al.  Hydrodynamics and sediment transport in the swash zone: a review and perspectives , 2002 .

[20]  R. E. Meyer,et al.  Climb of a bore on a beach Part 3. Run-up , 1963, Journal of Fluid Mechanics.

[21]  J. Ribberink.  Bed-load transport for steady flows and unsteady oscillatory flows , 1998 .

[22]  A. Hogg,et al.  The effects of hydraulic resistance on dam-break and other shallow inertial flows , 2004, Journal of Fluid Mechanics.

[23]  D. Peregrine,et al.  The propagation of solitary waves and bores over a porous bed , 1979 .

[24]  G. Whitham,et al.  The effects of hydraulic resistance in the dam-break problem , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[25]  D. H. Peregrine,et al.  Swash overtopping a truncated plane beach , 2001, Journal of Fluid Mechanics.

[26]  Eleuterio F. Toro,et al.  The weighted average flux method applied to the Euler equations , 1992, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.