RANS Model for Spilling Breaking Waves

A RANS model for spilling breaking waves is developed, which can be implemented with ship hydrodynamics RANS CFD codes. The model is based on the Cointe & Tulin theory of steady breakers. The breaker cross section is assumed triangular with maximum height determined by the theoretical/experimental linear relationship with following wave height. Pressure and velocity boundary conditions are imposed on the dividing streamline between the breaker and underlying flow based on the hydrostatic and mixing layer models. An iterative solution procedure provides a unique solution for specified breaking criteria and simulation conditions. The model is implemented using CFDSHIP-IOWA and validated using spilling breaking wave benchmark data for two-dimensional submerged hydrofoils. As with other current RANS codes, wave elevations are under-predicted. However, for the first time in literature, the breaking wave wake is predicted

[1]  W. Melville,et al.  The velocity field under breaking waves: coherent structures and turbulence , 2002, Journal of Fluid Mechanics.

[2]  C. S. Weller,et al.  Electromagnetic scattering from large steady breaking waves , 2001 .

[3]  Fabián J. Bonetto,et al.  The interaction of background ocean air bubbles with a surface ship , 1998 .

[4]  P. Liu,et al.  Velocity, acceleration and vorticity under a breaking wave , 1998 .

[5]  Frederick Stern,et al.  Prediction of Solid/Free-Surface Juncture Boundary Layer and Wake of a Surface-Piercing Flat Plate at Low Froude Number , 1998 .

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

[7]  Takanori Hino,et al.  An unstructued grid method for incompressible viscous flows with a free surface , 1997 .

[8]  David T. Walker,et al.  Radar backscatter and surface roughness measurements for stationary breaking waves , 1996, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[9]  Akihiro Kanai,et al.  Numerical simulation of three-dimensional breaking waves , 1996 .

[10]  Stéphane Zaleski,et al.  TWO-DIMENSIONAL NAVIER-STOKES SIMULATION OF BREAKING WAVES , 1996, comp-gas/9605002.

[11]  D. Rockwell,et al.  Evolution of a quasi-steady breaking wave , 1995, Journal of Fluid Mechanics.

[12]  M. Banner,et al.  Modeling Wave-Enhanced Turbulence in the Ocean Surface Layer , 1994 .

[13]  M. Tulin,et al.  A theory of steady breakers , 1994, Journal of Fluid Mechanics.

[14]  M. Longuet-Higgins.  Shear instability in spilling breakers , 1994, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[15]  F. Menter.  Two-equation eddy-viscosity turbulence models for engineering applications , 1994 .

[16]  James H. Duncan,et al.  The formation of spilling breaking water waves , 1994 .

[17]  C. Lemos,et al.  Wave Breaking: A Numerical Study , 1992 .

[18]  T. Hino.  NUMERICAL COMPUTATION OF A FREE SURFACE FLOW AROUND A SUBMERGED HYDROFOIL BY THE EULER/NAVIER-STOKES EQUATIONS , 1988 .

[19]  Frederick Stern,et al.  Effects of Waves on the Boundary Layer of a Surface-Piercing Flat Plate: Experiment and Theory , 1987 .

[20]  K. Mori.  Sub-breaking waves and critical condition for their appearance , 1986 .

[21]  James H. Duncan,et al.  The breaking and non-breaking wave resistance of a two-dimensional hydrofoil , 1983, Journal of Fluid Mechanics.

[22]  Jurjen A. Battjes,et al.  Velocity field in a steady breaker , 1981, Journal of Fluid Mechanics.

[23]  J. Duncan,et al.  An experimental investigation of breaking waves produced by a towed hydrofoil , 1981, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[24]  Michael Selwyn Longuet-Higgins,et al.  The deformation of steep surface waves on water - I. A numerical method of computation , 1976, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[25]  Eiichi Baba,et al.  A NEW COMPONENT OF VISCOUS RESISTANCE OF SHIPS , 1969 .

[26]  Marshall P. Tulin,et al.  Breaking Waves in the Ocean and around Ships , 2001 .

[27]  A. Olivieri,et al.  Numerical and Experimental Study of the Wave Breaking Generated by a Submerged Hydrofoil , 2001 .

[28]  Lars Larsson,et al.  Level Set Methods for Predicting Viscous Free Surface Flows , 1999 .

[29]  Luigi Martinelli,et al.  Calculation of Plunging Breakers with A Fully-Implicit Adaptive-Grid Method , 1998 .

[30]  W. K. Melville,et al.  The Role of Surface-Wave Breaking in Air-Sea Interaction , 1996 .

[31]  D. Peregrine,et al.  Wave Breaking in Deep Water , 1993 .