Three-Dimensional Large Eddy Simulation of Breaking Waves

A three-dimensional large eddy simulation (LES) of wave breaking was carried out. A numerical method for LES is proposed in this paper. The following characteristics of vorticity and velocity field after wave breaking are discussed on the basis of results of the LES: (1) generation and evolution of the widthwise (shore direction) velocity component; (2) transition from a two-dimensional velocity field to a three-dimensional one after wave breaking; (3) evolution process of large-scale eddies comprised by horizontal, vertical and helical eddies; and (4) a coherent eddy structure involving a turbulent bottom and wall boundary layer.

[1]  S. Orszag,et al.  Renormalization group analysis of turbulence. I. Basic theory , 1986, Physical review letters.

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

[3]  Takashi Yabe,et al.  Unified Numerical Procedure for Compressible and Incompressible Fluid , 1991 .

[4]  U. Piomelli,et al.  Application of renormalization group theory to the large-eddy simulation of transitional boundary layers , 1990 .

[5]  D. Fritts,et al.  Gravity wave breaking in two and three dimensions: 1. Model description and comparison of two‐dimensional evolutions , 1994 .

[6]  Takashi Yabe,et al.  Cubic interpolated pseudo-particle method (CIP) for solving hyperbolic-type equations , 1985 .

[7]  S. Orszag,et al.  Development of turbulence models for shear flows by a double expansion technique , 1992 .

[8]  T. Sakai,et al.  VORTEX FORMATION IN PLUNGING BREAKER , 1986 .

[9]  Kazuo Nadaoka,et al.  Structure of the turbulent flow field under breaking waves in the surf zone , 1989, Journal of Fluid Mechanics.

[10]  Takashi Yabe,et al.  A universal solver for hyperbolic equations by cubic-polynomial interpolation I. One-dimensional solver , 1991 .

[11]  Ib A. Svendsen,et al.  A turbulent bore on a beach , 1984, Journal of Fluid Mechanics.

[12]  Koichiro Iwata,et al.  NUMERICAL ANALYSIS OF WAVE BREAKING DUE TO SUBMERGED BREAKEWATER IN THREE-DIMENSIONAL WAVE FIELD , 1999 .

[13]  S. Orszag,et al.  Renormalization group analysis of turbulence. I. Basic theory , 1986 .

[14]  P. Ø. Hvidsten,et al.  Vorticity dynamics in a breaking internal gravity wave. Part 1. Initial instability evolution , 1998, Journal of Fluid Mechanics.

[15]  A. Yoshizawa Derivation of a model Reynolds‐stress transport equation using the renormalization of the eddy‐viscosity‐type representation , 1993 .

[16]  David C. Fritts,et al.  Wave breaking and transition to turbulence in stratified shear flows , 1996 .

[17]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[18]  F. Feuillebois,et al.  Precise measurement of particle–wall hydrodynamic interactions at low Reynolds number using laser interferometry , 1993 .

[19]  M. Kac On the Partition Function of a One‐Dimensional Gas , 1959 .

[20]  D. H. Peregrine,et al.  Breaking Waves on Beaches , 1983 .

[21]  Fumihiko Yamada,et al.  Internal characteristics and numerical analysis of plunging breaker on a slope , 1997 .

[22]  Yoshizawa Bridging between eddy-viscosity-type and second-order turbulence models through a two-scale turbulence theory. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[23]  Takashi Yabe,et al.  A universal solver for hyperbolic equations by cubic-polynomial interpolation. II, Two- and three-dimensional solvers , 1991 .

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

[25]  D. Baker,et al.  Two substorm intensifications compared: Onset, expansion, and global consequences , 1998 .

[26]  The use of disks to approximate finite axisymmetric bodies in Stokes flow , 1992 .

[27]  H. Takewaki,et al.  The cubic-interpolated Pseudo particle (cip) method: application to nonlinear and multi-dimensional hyperbolic equations , 1987 .

[28]  Robert L. Street,et al.  A computer study of finite-amplitude water waves , 1970 .

[29]  H. Saeki,et al.  Numerical Analysis Of Breaking Waves , 1970 .

[30]  H. W. Iversen,et al.  WAVES AND BREAKERS IN SHOALING WATER , 2000 .

[31]  J. Battjes Surf-Zone Dynamics , 1988 .

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