Fully nonlinear solitary waves in continuously stratified incompressible Boussinesq fluids

This study is concerned with a fully nonlinear theoretical treatment of internal solitary waves in continuously stratified, incompressible, inviscid, shear-free Boussinesq fluids. Results are presented for wave propagation in both deep and shallow fluids with four different ambient stability profiles. Only the dominant mode with the greatest wave speed is considered. The morphology of finite-amplitude internal solitary waves in Boussinesq fluids is shown to be very sensitive to the precise form of the stability profile. The calculations :indicate that a wave of maximum amplitude, which is less than the total fluid depth, exists for all internal solitary waves in continuously stratified Boussinesq fluids of finite depth. There is apparently no upper limit on the amplitude of internal solitary waves in many physically realistic unbounded fluids. Large amplitude waves of this type are mutually similar in form and the morphology of these waves appears to be independent of the ambient stability profile in the waveguide layer. It is shown that the properties of highly nonlinear waves with recirculating flow depend on the density distribution and vorticity of the trapped fluid inside the closed circulation cell. Fluid velocity components associated with the wave motion are evaluated and used to calculate the surface perturbation pressure. The surface perturbation pressure signature for internal solitary waves is found to change with the onset of recirculation from a single-crested profile at small wave amplitudes to a bimodal profile at large wave amplitudes. Results for solitary waves in finite-depth fluids differ from those found for deep fluids in that the surface perturbation pressure at the center of the wave eventually changes sign as wave amplitude increases. (C) 1998 American Institute of Physics.