Propagation of water waves through shearing currents in general bathymetry

Abstract

A coupled-mode model is presented for wave-current-seabed interaction, with application to the problem of wave scattering by steady shearing currents in variable bathymetry regions. We consider obliquely incident waves on a horizontally non-homogeneous current in a variable-depth strip, which is characterized by straight and parallel bottom contours. The flow associated with the current is assumed to be parallel to the bottom contours and it is considered to be known. In a finite subregion containing the bottom irregularity, we assume an arbitrary horizontal current structure. Outside this region, the current is assumed to be uniform (or zero). Based on a variational principle, in conjunction with a rapidly-convergent local-mode series expansion of the wave pressure field in a finite subregion containing the current variation and the bottom irregularity, a coupled-mode system is obtained. The present model can be considered as an extension of the works by Smith (1983Smith ( , 1987 and McKee (1987McKee ( ,1996, and it can be further elaborated to treat more general current profiles with vertical structure and cross-jet component, and to include the effects of weak nonlinearity.

Shear Current Effects on Monochromatic Water Waves Crossing Trenches

“…where is the shear current velocity, is the gravity acceleration, and ℎ is the water depth. By dividing the domain into several steps and assuming that the shear current Journal of Applied Mathematics 3 is small enough so that there would be no possibility of turbulence flow, we could extend the scope of analysis to various topographies with nonhomogeneous shear current [15,31].…”

The Calculation of Reflection Coefficients of Water Waves over Various Shear Currents with a Uniform Depth Topography

“…만약 구간 간격을 조밀하게 나누어 수심과 외부흐름을 변화시키면 다양한 형상의 지형과 외부흐름 으로 해석 범위를 확장시킬 수 있다. 단, 본 연구에서는 기 존의 연구 (Liu et al, 1992;Simons and Maciver,1998;Belibassakis, 2005) (Lee and Cho, 2002).…”