Time-dependent Stratified Flow over Topography: Waves and Rotating Hydraulics

Abstract

Abstract : My long-term goals for this research project are to understand the interaction of stratified flow with topography with an emphasis on those flows relevant to coastal oceans and marginal seas. The specific objectives of the last year have been a study of two related problems in the general area of time-dependent rotating hydraulics and nonlinear waves. The first is a study of the fully nonlinear dam break problem in a rotating channel. One focus of this work has been to study the characteristics and dynamics of the shocks and bores. The second project is an extension of Long's (1954, 1970) classic problem of upstream influence and the establishment of hydraulically controlled flows in rotating channels. Both of these projects have been on single-layer flows, though the long-term goal is to extend the work to two-layer systems. The work on the hydraulics of rotating flows adds to the understanding of the role of straits and sills in regulating flow within and between abyssal basins, marginal seas, etc. The work on the dynamics of shocks and bores in rotating flows is applicable not only the issue of time-dependence in rotating hydraulic flows, but also to nonlinear wave dynamics in straits and coastal zones, including the dynamics of the marine boundary layer along the California coast. Though the focus to date has been on single layer flows, the results gained so far should help in the interpretation of stratified flows. It is also worth pointing out that the fully nonlinear shocks and bores are the hydrostatic limit of the (typically) weakly nonlinear solitary wave and undular bore solutions. As such they may provide information on the initial, or boundary, conditions which result in solitary waves in the far field.