Waves of large amplitudes in geophysical and technical applications

Abstract

The paper addresses the asymptotic models that explicitly describe the structure of solitary waves with recirculation zones for some special but important incident stream configurations, which occur in geophysical and industrial applications . The key feature that allows building a theoretical model is that shear and/or stratification of the media in geophysical applications or axisymmetric swirling incoming flows in technical applications have an almost linear equation for vorticity. It happens when the upstream flow is almost linearly stratified in the case of geophysical applications and a swirling flow has almost solid body rotation if industrial applications are considered. It is shown that the resulting equation for the stationary amplitude function of the solitary waves is described by a generalized Korteweg-de Vries equation in the outer zone, consistenty matched with a new complicated equation in the inner zone, which contains the recirculation core. This recirculation zone exists for wave amplitudes that are slightly greater than a certain critical amplitude, for which a wave breaking initially occurs. The recirculation zones have a universal structure, so that their width increases up to the semi-infinite bore as the amplitude of the wave increases from a critical amplitude to a certain maximum amplitude. This amplitude may be sensitive to the actual configuration of the incident flow. Regardless of the physical nature, solitary waves are described by two types of equations with different non-linearities. The type of nonlinearity in the inner zone where the vortex core is located is then caused by the position of the vortex core at the outer boundary or in the middle of the flow.