On an eddy viscosity model for energetic deep-water surface gravity wave breaking

Abstract

We present an investigation of the fundamental physical processes involved in deep-water gravity wave breaking. Our motivation is to identify the underlying reason causing the deficiency of the eddy viscosity breaking model (EVBM) in predicting surface elevation for strongly nonlinear waves. Owing to the limitation of experimental methods in the provision of high-resolution flow information, we propose a numerical methodology by developing an EVBM enclosed standalone fully nonlinear quasi-potential (FNP) flow model and a coupled FNP plus Navier–Stokes flow model. The numerical models were firstly verified with a wave train subject to modulational instability, then used to simulate a series of broad-banded focusing wave trains under non-, moderate- and strong-breaking conditions. A systematic analysis was carried out to investigate the discrepancies of numerical solutions produced by the two models in surface elevation and other important physical properties. It is found that EVBM predicts accurately the energy dissipated by breaking and the amplitude spectrum of free waves in terms of magnitude, but fails to capture accurately breaking induced phase shifting. The shift of phase grows with breaking intensity and is especially strong for high-wavenumber components. This is identified as a cause of the upshift of the wave dispersion relation, which increases the frequencies of large-wavenumber components. Such a variation drives large-wavenumber components to propagate at nearly the same speed, which is significantly higher than the linear dispersion levels. This suppresses the instant dispersive spreading of harmonics after the focal point, prolonging the lifespan of focused waves and expanding their propagation space.