Quadtree grid numerical model of nearshore wave–current interaction

This paper describes an adaptive quadtree-based 2DH wave-current interaction model for evaluating nearly horizontal wave-induced currents in the surf-zone. The model accounts for wave breaking, shoaling, refraction, diffraction, wave-current interaction, set-up and set-down, mixing processes (turbulent diffusion), bottom frictional effects, and movement of the land-water interface at the shoreline. The wave period- and depth-averaged governing equations, which conserve mass, momentum, energy and wave action, are discretised explicitly by means of an Adams-Bashforth second-order finite difference technique on adaptive hierarchical staggered quadtree grids. Grid adaptation is achieved through seeding points distributed according to flow criteria (e.g. local current gradients). The model is verified for nearshore circulation at a sinusoidal beach and nearshore currents at a multi-cusped beach. Reasonable agreement is obtained with experimental data from da Silva Lima [da Silva Lima, S.S.L., 1981. Wave-induced Nearshore Currents. PhD Thesis, Department of Civil Engineering, University of Liverpool] and Borthwick et al. [Borthwick, A.G.L., Foote, Y.L.M., Ridehalgh, A., 1997. Nearshore measurements at a cusped beach in the UK Coastal Research Facility, Coastal Dynamics '97, Plymouth, 953-962]. The modelling approach presented herein should be useful in simulating nearshore processes in complicated natural coastal domains. Of particular value is the local grid enrichment capability, which permits refined modelling of important localised flow behaviour such as rip currents and surf-zone circulation systems.

[1]  H. G. Wind,et al.  Cross-shore mean flow in the surf zone , 1986 .

[2]  J. A. Battjes Refraction of Water Waves , 1968 .

[3]  P. Dong,et al.  A numerical model of the vertical distribution of longshore currents on a plane beach , 1991 .

[4]  Gengsheng Wei,et al.  A WDM method on a generalized curvilinear grid for calculation of storm surge flooding , 1997 .

[5]  Robert A. Dalrymple,et al.  Rip Channels and Nearshore Circulation , 1998 .

[6]  Qin Chen,et al.  Wave-current interaction based on an enhanced Boussinesq approach , 1998 .

[7]  A. Sánchez-Arcilla,et al.  VERTICALLY VARYING VELOCITY FIELD IN Q-3D NEARSHORE CIRCULATION , 1993 .

[8]  I. A. Svendsen,et al.  Cross-shore currents in surf-zone modelling , 1988 .

[9]  John M'Cowan On the highest wave of permanent type , 1893 .

[10]  Paul D. Komar,et al.  Beach Processes and Sedimentation , 1976 .

[11]  E. Noda Wave‐induced nearshore circulation , 1974 .

[12]  Charles Teisson,et al.  NUMERICAL MODELLING OF THREE-DIMENSIONAL WAVE-DRIVEN CURRENTS IN SURF-ZON , 1995 .

[13]  Ib A. Svendsen,et al.  Nearshore mixing and dispersion , 1994, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[14]  Robert G. Dean,et al.  A MODEL FOR BREAKER DECAY ON BEACHES , 1984 .

[15]  Elke A. Rundensteiner,et al.  Fast, adaptive summation of point forces in the two-dimensional Poisson equation , 1989 .

[16]  J. Kamphuis,et al.  Waves and currents on natural beaches: A quasi 3-D numerical model , 1993 .

[17]  D. Yoo Mathematical modelling of wave-current interacted flow in shallow waters , 1986 .

[18]  Deborah Greaves,et al.  Quadtree grid generation: Information handling, boundary fitting and CFD applications , 1996 .

[19]  R. Dalrymple,et al.  NEARSHORE WATER CIRCULATION INDUCED BY WIND AND WAVES. , 1975 .

[20]  SHORECIRC: A QUASI 3-D NEARSHORE MODEL , 1995 .

[21]  Bharat K. Soni,et al.  Handbook of Grid Generation , 1998 .

[22]  Deborah Greaves,et al.  On the use of adaptive hierarchical meshes for numerical simulation of separated flows , 1998 .

[23]  M. Stive,et al.  Quasi-3D Modelling of Nearshore Currents , 1987 .

[24]  R. Dalrymple,et al.  Numerical Modelling of Nearshore Circulation , 1980 .

[25]  I. A. Svendsen,et al.  Velocities in combined undertow and longshore currents , 1989 .

[26]  Deborah Greaves,et al.  Hierarchical tree-based finite element mesh generation , 1999 .

[27]  P. J. Visser,et al.  UNIFORM LONGSHORE CURRENT MEASUREMENTS AND CALCULATIONS , 1984 .

[28]  Brian A. O'Connor,et al.  MATHEMATICAL MODELLING OF WAVE-INDUCED NEARSHORE CIRCULATIONS , 1986 .

[29]  I. A. Svendsen,et al.  The interaction between the undertow and the boundary layer flow on a beach , 1987 .

[30]  Da Silva Limia Wave-induced nearshore currents , 1981 .

[31]  E. Thornton VARIATION OP LONGSHORE CURRENT ACROSS THE SURF ZONE , 1970 .

[32]  Shallow Lake Modelling Using Quadtree-Based Grids , 1994 .