Analysis of the Momentum Transfer Operated by the Breaking in Modulated Wave Trains in Wind and No-Wind Conditions

Abstract

An analysis of the flow and of the vertical transfer of the horizontal momentum induced by the breaking of modulated wave trains in wind and no-wind conditions is presented. The study is based on the results of two-dimensional numerical simulation of the Navier-Stokes equations for two-phase flow. The open source Gerris flow solver has been used, which employs a Volume of Fluid technique to capture the air-water interface. The breaking is induced through the Benjamin-Feir instability mechanism. The numerical simulations cover the entire range from the initial development of the instability, the breaking phase and the post-breaking evolution. In order to investigate the role played by the wind, a uniform wind profile, twice the phase speed, is initialized in the air phase and it is left to evolve while interacting with the wave system. Results in terms of averaged horizontal velocity and vertical flux of horizontal momentum are presented. It is shown that in the wind case the backward stresses induced at the wave troughs as a consequence of the flow separation at the crest influence significantly the flow in the upper water layer, particularly in the pre-breaking phase. No substantial differences are found between the wind and no-wind solutions in terms of the vertical transfer of horizontal momentum in the lower water layer. The vertical flux of horizontal momentum in air is consistent with the velocity reduction occurring in the wind case in the early stage.