Evolution of waves and currents over a submerged laboratory shoal

Abstract The vertically-integrated effect of interaction between waves and wave-induced currents on wave transformation over a submerged elliptic shoal was investigated based on numerical simulations of the Vincent and Briggs experiment [Vincent, C.L., Briggs, M.J., 1989. Refraction- diffraction of irregular waves over a mound. Journal of Waterway, Port, Coastal and Ocean Engineering, 115(2), pp. 269–284.]. The numerical simulations were performed using two numerical wave-current model systems: one, a combination of the wave model SWAN and the current model SHORECIRC, and the other, a combination of the wave model REF/DIF and the same current model. A time-dependent, phase-resolving wave and current model, FUNWAVE, was also utilized to simulate the experiment. In the simulations, the developed wave-induced currents defocused waves behind the shoal and brought on a wave shadow zone that showed relatively low wave height distributions. For the breaking case of monochromatic waves, the wave heights computed using FUNWAVE showed good agreement with the measurements and the resulting wave-induced currents showed a jet-like velocity distribution in transverse direction. And the computed results of the two model combinations agreed better with the measurements than the computed results obtained by neglecting wave-current interaction. However, it was found that for the case in which transverse interference pattern caused by refracted waves was strong, REF/DIF-SHORECIRC did not correctly evaluate radiation stresses, the gradients of which generate wave-induced currents. SWAN-SHORECIRC, which cannot deal with the interference patterns, predicted a jet-like wave-induced current. For breaking random wave cases, the computed results of the two model combinations and FUNWAVE agreed well with the measurements. The agreements indicate that it is necessary to take into account the effect of wave-induced current on wave refraction when wave breaking occurs over a submerged shoal.

[1]  G. Wei,et al.  A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves , 1995, Journal of Fluid Mechanics.

[2]  J. Kirby,et al.  Evolution of Breaking Directional Spectral Waves in the Nearshore Zone , 1994 .

[3]  W. Rosenthal,et al.  Similarity of the wind wave spectrum in finite depth water: 1. Spectral form , 1985 .

[4]  J. A. Battjes,et al.  Calibration and Verification of a Dissipation Model for Random Breaking Waves , 1985 .

[5]  C. Vincent,et al.  REFRACTION-DIFFRACTION OF IRREGULAR WAVES OVER A MOUND , 1989 .

[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]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[8]  C. Mei.  The applied dynamics of ocean surface waves , 1983 .

[9]  Ib A. Svendsen,et al.  Three-dimensional dispersion of momentum in wave-induced nearshore currents , 1999 .

[10]  Yoshimi Goda.  A 2-D Random Wave Transformation Model with Gradational Breaker Index , 2004 .

[11]  Nico Booij,et al.  Phase-decoupled refraction¿diffraction for spectral wave models , 2003 .

[12]  APPLICATION OF ANGULAR SPECTRUM MODEL TO SIMULATION OF IRREGULAR WAVE PROPAGATION , 1993 .

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

[14]  Sung Bum Yoon,et al.  Numerical simulation of irregular wave transformation due to wave-induced current , 2007 .

[15]  Edward B. Thornton,et al.  Transformation of wave height distribution , 1983 .

[16]  M. Longuet-Higgins,et al.  Radiation stresses in water waves; a physical discussion, with applications , 1964 .

[17]  J. Larsen,et al.  Open boundaries in short wave simulations — A new approach , 1983 .

[18]  J. Kirby.  Rational approximations in the parabolic equation method for water waves , 1986 .

[19]  I. A. Svendsen.  Mass flux and undertow in a surf zone , 1984 .

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

[21]  Yong-Sik Cho,et al.  Effects of breaking-induced currents on refraction-diffraction of irregular waves over submerged shoal , 2004 .

[22]  Hocine Oumeraci,et al.  The SWAN model used to study wave evolution in a flume , 2001 .

[23]  N. Booij,et al.  A third-generation wave model for coastal regions-1 , 1999 .

[24]  Ge Wei,et al.  Generation of waves in Boussinesq models using a source function method , 1999 .

[25]  J. A. Battjes,et al.  ENERGY LOSS AND SET-UP DUE TO BREAKING OF RANDOM WAVES , 1978 .