Large-Wave Simulation (LWS) of Free-Surface Flows Developing Weak Spilling Breaking Waves

Abstract

A methodology, called large-wave simulation (LWS), is presented for the numerical simulation of free-surface flows past the appearance of spilling breakers. LWS is designed to resolve only the large, energy-carrying scales of the flow and model the effect of the subgrid, small-wavelength scales of the flow spectrum. This part of the spectrum includes the characteristic frothy whitecaps associated with spilling breakers. Modeling in LWS is based on the consistent application of spatial filtering on both the velocity field and the free-surface elevation. The subgrid scale (SGS) effect is modeled by two sets of stresses: (i) the eddy SGS stresses, which are identical to the ones arising in large-eddy-simulation of flows without a free surface, and (ii) the wave SGS stresses, which incorporate the free-surface effect. Both SGS stresses are modeled by eddy-viscosity models with constant coefficients. The methodology is applied on two free-surface flows: (i) the interaction of a plane gravity wave with a surface wake layer, and (ii) the nonlinear evolution of a surface shear layer instability. A priori and a posteriori tests show good agreement between the proposed model and actual SGS stresses, while LWS of both flows successfully continue past the breaking point as opposed to corresponding direct numerical simulations. For the first flow, LWS predicts the postbreaking appearance of a recirculating flow region in the wake of the breaker in qualitative agreement with experimental observations.