Large-wave simulation (LWS) of free-surface flows developing weak spillingbreaking waves

A methodology, called large-wave simulation (LWS), is presented for the num erical simulation of free-surface Hows past the appearance of spilling brea kers. LWS is designed to resolve only the large, energy-carrying scales of the How and model the effect of the subgrid, small-wavelength scales of the flow spectrum. This part of the spectrum includes the characteristic froth y 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 b y two sets of stresses. (i) the eddy SGS stresses, which are identical to t he ones arising in large-eddy-simulation of Hows without a foe surface, and (ii) the wave SGS stresses, which incorporate the free-surface effect. Bot h SGS stresses are modeled by eddy-viscosity models with constant coefficie nt. The methodology is applied on two free-surface flows: (i) the interacti on of a plane gravity wave with a surface wake layer, and (ii) the nonlinea r evolution of a surface shear layer instability. A priori and a posteriori tests show good agreement between the proposed model and actual SGS stress es, while LWS of both hows 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 observa tions. (C) 2000 Academic Press.