Nonlinear Characteristics of Internal Waves in a Deep-Water Region or near a Wave-Breaking Point

Abstract

A set of nonlinear internal-wave equations, which have been derived on the basis of the variational principle without any assumptions concerning wave nonlinearity and dispersion, is applied to compare numerical results with experimental data of internal waves propagating in a deep-water region. Internal waves propagating over a uniformly sloping beach are also simulated. Internal progressive waves show remarkable shoaling after the interface reaches the critical level, after which the physical variables change discontinuously near the wave-breaking point. In the wave-breaking case of internal waves reflecting at a vertical wall, the vertical velocity of the particles in the vicinity of the interface is different from that of the moving interface on the wall, which means that the kinematic boundary condition on the interface is not satisfied.