Nonlinear wind wave model under effects of wind and dissipation: Establishment and validation

Abstract

Nonlinear model for the long-time evolution of two-dimensional water waves under wind forcing effect and energy dissipation effect is established. The wind forcing terms constitute the Miles’ shear flow theory and the Jeffreys’ sheltering theory with a wind model criterion to determine when and which model to use. The dissipation terms consist of non-breaking dissipation parts and breaking dissipation parts. A wave-breaking onset criterion based on the ratio of local energy flux velocity to the local crest velocity is used for the determining wave breaking. Numerical evolutions of focusing wave trains solved by the wind wave model are compared with previous works to validate the non-breaking and breaking dissipation terms. Non-breaking focusing wave groups under different wind conditions are resolved and the results are compared with previous experimental studies to validate the wind forcing terms. After the validation, the long-time evolutions of the modulational instability wave trains under wind action and wind forcing conditions are investigated by the wind wave model. The variations of surface profiles, wave energy, and spectrum with the effects of wind forcing and energy dissipation are analyzed.