Numerical modelling of short- and long-wave transformation on a barred beach

Abstract This work aims to demonstrate an advancement towards the integrated modelling of surf zone hydrodynamics by means of a VOF-type numerical model (COBRAS-UC) based on the Reynolds-Averaged Navier–Stokes equations. In this paper, the numerical model is adapted and validated for the study of nearshore processes on a mildly-sloping beach. The model prediction of wave energy transformation and higher order statistics (skewness and asymmetry) are in good agreement with detailed laboratory observations from a barred beach [Boers, M. (1996). “Simulation of a surf zone with a barred beach; Report 1: Wave heights and wave breaking”. Tech. Rep.96-5, Comm. on Hydrol. and Geol. Eng., Dept. of Civil Engineering, Delft University of Technology]. Moreover, the numerical model allows us to study the low-frequency motions inside the surf zone. It is found that in order to achieve a satisfactory simulation of both short- and long-wave transformation, the numerical model must achieve: (i) the simultaneous second-order wave generation and absorption, (ii) the energy transfer between triad of components, (iii) the short- and long-wave energy dissipation inside the surf zone, and (iv) the wave reflection at the shoreline. Comparisons between numerical and experimental results demonstrate the model capability to satisfactorily simulate all the aforementioned processes.

[1]  Javier L. Lara,et al.  Wave interaction with low-mound breakwaters using a RANS model , 2008 .

[2]  A. Chadwick,et al.  Numerical experiments of swash oscillations on steep and gentle beaches , 2005 .

[3]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

[4]  Javier L. Lara,et al.  Modelling of velocity and turbulence fields around and within low-crested rubble-mound breakwaters , 2005 .

[5]  T. Aagaard,et al.  Infragravity wave contribution to surf zone sediment transport — The role of advection , 2008 .

[6]  M. Longuet-Higgins,et al.  Radiation stress and mass transport in gravity waves, with application to ‘surf beats’ , 1962, Journal of Fluid Mechanics.

[7]  Nonlinear surface waves over topography , 2006 .

[8]  P. Lynett.  Wave breaking velocity effects in depth-integrated models , 2006 .

[9]  I. A. Svendsen,et al.  Wave Breaking in Wave Groups , 2001 .

[10]  Tom E. Baldock,et al.  A laboratory study of nonlinear surface waves on water , 1996, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[11]  Pengzhi Lin,et al.  Turbulence transport, vorticity dynamics, and solute mixing under plunging breaking waves in surf zone , 1998 .

[12]  Robert A. Dalrymple,et al.  Boussinesq modeling of longshore currents , 2003 .

[13]  Javier L. Lara,et al.  RANS modelling applied to random wave interaction with submerged permeable structures , 2006 .

[14]  Tsutomu Sakakiyama,et al.  A numerical model for wave motions and turbulence flows in front of a composite breakwater , 2002 .

[15]  J. Kirby,et al.  BOUSSINESQ MODELING OF WAVE TRANSFORMATION, BREAKING, AND RUNUP. II: 2D , 2000 .

[16]  Hemming A. Schäffer,et al.  Infragravity waves induced by short-wave groups , 1993, Journal of Fluid Mechanics.

[17]  J. A. Battjes,et al.  Long waves induced by short-wave groups over a sloping bottom , 2003 .

[18]  Javier L. Lara,et al.  Numerical analysis of wave overtopping of rubble mound breakwaters , 2008 .

[19]  P. Bradshaw,et al.  Turbulence Models and Their Application in Hydraulics. By W. RODI. International Association for Hydraulic Research, Delft, 1980. Paperback US $15. , 1983, Journal of Fluid Mechanics.

[20]  Stig E. Sand,et al.  Long waves in directional seas , 1982 .

[21]  M. Boers.  Surf Zone Turbulence , 2005 .

[22]  A. R. van Dongeren,et al.  Absorbing-Generating Boundary Condition for Shallow Water Models , 1997 .

[23]  J. A. Battjes,et al.  Shoaling of subharmonic gravity waves , 2004 .

[24]  Alexandre J. Chorin,et al.  On the Convergence of Discrete Approximations to the Navier-Stokes Equations , 1969 .

[25]  Marcel Zijlema,et al.  Efficient computation of surf zone waves using the nonlinear shallow water equations with non-hydrostatic pressure , 2008 .

[26]  Javier L. Lara,et al.  Breaking waves over a mild gravel slope: Experimental and numerical analysis , 2006 .

[27]  A. Chorin.  Numerical solution of the Navier-Stokes equations , 1968 .

[28]  M. Longuet-Higgins,et al.  Changes in the form of short gravity waves on long waves and tidal currents , 1960, Journal of Fluid Mechanics.

[29]  Steve Elgar,et al.  Tidal modulation of infragravity waves via nonlinear energy losses in the surfzone , 2006 .

[30]  Y. Goda.  Irregular Wave Deformation in the Surf Zone , 1975 .

[31]  Nobuhisa Kobayashi,et al.  Numerical simulation of swash zone fluid accelerations , 2007 .

[32]  Steve Elgar,et al.  Observations of bispectra of shoaling surface gravity waves , 1985, Journal of Fluid Mechanics.

[33]  John E. Richardson,et al.  Field Verification of a Computational Fluid Dynamics Model for Wave Transformation and Breaking in the Surf Zone , 2008 .

[34]  M. Merrifield,et al.  Forcing of resonant modes on a fringing reef during tropical storm Man‐Yi , 2009 .

[35]  M. J. Tucker,et al.  Surf beats: sea waves of 1 to 5 min. period , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[36]  Julien De Rouck,et al.  An active wave generating–absorbing boundary condition for VOF type numerical model , 1999 .

[37]  Javier L. Lara,et al.  Numerical analysis of wave loads for coastal structure stability , 2009 .

[38]  A. Bayram,et al.  Wave transformation in the nearshore zone: comparison between a Boussinesq model and field data , 2000 .

[39]  I. A. Svendsen,et al.  The flow in surf-zone waves , 2000 .

[40]  M. Boers,et al.  Simulation of a surf zone with a barred beach. Report 1. Wave heights and wave breaking , 1996 .

[41]  Tian-Jian Hsu,et al.  Toward modeling turbulent suspension of sand in the nearshore , 2004 .

[42]  Nobuhisa Kobayashi,et al.  WAVE REFLECTION AND RUN-UP ON ROUGH SLOPES , 1987 .

[43]  Rolf Deigaard,et al.  A Boussinesq model for waves breaking in shallow water , 1993 .

[44]  P. Liu,et al.  A two-layer approach to wave modelling , 2004, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[45]  S. Elgar,et al.  Wave transformation across the inner surf zone , 1996 .

[46]  D. Howell Peregrine,et al.  Low frequency waves in the surf zone , 1993 .

[47]  T. Hsu,et al.  Effects of wave shape on sheet flow sediment transport , 2004 .

[48]  Javier L. Lara,et al.  2-D numerical analysis of near-field flow at low-crested permeable breakwaters , 2004 .

[49]  Pengzhi Lin,et al.  A numerical study of breaking waves in the surf zone , 1998, Journal of Fluid Mechanics.

[50]  D. Huntley,et al.  Long Wave Generation by a Time-Varying Breakpoint , 1982 .

[51]  Steve Elgar,et al.  Nonlinear generation and loss of infragravity wave energy , 2006 .

[52]  B. Raubenheimer.  Observations and predictions of fluid velocities in the surf and swash zones , 2002 .

[53]  Steve Elgar,et al.  Swash on a gently sloping beach , 1995 .

[54]  T. Baldock.  Long wave generation by the shoaling and breaking of transient wave groups on a beach , 2006, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[55]  Britt Raubenheimer,et al.  Observations and predictions of run‐up , 1996 .

[56]  Hajime Mase,et al.  Hybrid frequency-domain KdV equa-tion for random wave transformation , 1992 .

[57]  Javier L. Lara,et al.  Modeling of surf zone processes on a natural beach using Reynolds‐Averaged Navier‐Stokes equations , 2007 .

[58]  Steve Elgar,et al.  Spectral Energy Balance of Breaking Waves within the Surf Zone , 2000 .

[59]  R. Holman,et al.  Bars, bumps, and holes: Models for the generation of complex beach topography , 1982 .

[60]  James M. Kaihatu,et al.  Nonlinear transformation of waves in finite water depth , 1995 .

[61]  Steve Elgar,et al.  Wave-Induced Sediment Transport and Sandbar Migration , 2003, Science.

[62]  Nobuhisa Kobayashi,et al.  IRREGULAR WAVE SETUP AND RUN-UP ON BEACHES , 1992 .

[63]  Per A. Madsen,et al.  Surf zone dynamics simulated by a Boussinesq type model. Part I. Model description and cross-shore motion of regular waves , 1997 .

[64]  J. A. Battjes,et al.  Shoaling and shoreline dissipation of low?frequency waves , 2007 .

[65]  Steve Elgar,et al.  Spectral evolution of shoaling and breaking waves on a barred beach , 1997 .

[66]  Patrick J. Lynett,et al.  Nearshore Wave Modeling with High-Order Boussinesq-Type Equations , 2006 .

[67]  Felice D'Alessandro,et al.  The BCI criterion for the initiation of breaking process in Boussinesq-type equations wave models , 2008 .