Effect of dissipation and dispersion on slowly varying wavetrains

Abstract

A kinematic model for disturbance wave motions slowly modulated in space and time is developed, which describes the effects of amplitude and frequency dispersion, modal dependence, flow inhomogeneities, dissipation, and high-order wave dispersion and diffusion. The results, based on general variational principles, apply to waves in arbitrary continuous media, but are discussed primarily in the fluid-dynamic context. The more complete theory presented here reduces to several known wave models in various limits and reconciles, within the framework of a broader unifying approach, a number of differences found among existing, although more specialized, formulations. These latter models are surveyed and, in particular, we emphasize how their domains of applicability may be limited by different kinds of dominant high-order dispersive or diffusive wave mechanisms. **;