The above animation is described in the paper “Three-Dimensional Simulations of Deep-Water Breaking Waves.” The paper is available for download at http://tinyurl.com/y8eava8e. Videos associated with the paper are available at http://tinyurl.com/yc38hk5u.
The formulation of a canonical deep-water breaking wave problem is introduced, and the results of a set of three-dimensional numerical simulations for deep-water breaking waves are presented. In this paper fully non- linear progressive waves are generated by applying a normal stress to the free surface. Precise control of the forcing allows for a systematic study of four types of deep-water breaking waves, characterized herein as weak plunging, plunging, strong plunging, and very strong plunging.
The three-dimensional isocontours of vorticity exhibit intense streamwise vorticity shortly after the initial ovular cavity of air is entrained during the primary plunging event. An array of high resolution images are presented as a means to visually compare and contrast the major events in the breaking cycles of each case. The volume-integrated energy shows 50% or more of the peak energy is dissipated in strong and very strong plunging events. The volume of air entrained beneath the free surface is quantified. For breaking events characterized by plunging, strong plunging and very strong plunging, significant quantities of air remain beneath the free surface long after the initial breaking event. The rate at which the air beneath the free surface degasses is linear and the same in all cases. The use of volume-weighted (Reynolds) and mass-weighted (Favre) averages are compared, and it is found that statistics obtained by Favre averaging show better agreement with respect to the position of free surface than do those obtained by Reynolds averaging. The average volume fraction plotted on a log scale is used to visually elucidate small volumes of air entrained below the free surface. For the strong plunging and very strong plunging cases significant air is also entrained after the initial plunging event at the toe of spilling breaking region. Improvements to the Numerical Flow Analysis code, which expand the types of problems it can accurately simulate are discussed, along with the results of a feasibility study which shows that simulations with 5-10 billion unknowns are now tractable.