Resonance of Lee Waves of a Stratified Flow over Two Barriers

Abstract

Resonance of lee waves produced by two barriers in a two-dimensional channel is studied with special regard to relationship between the amplitude and the distance between the two barriers. This study deals with a two-dimensional, steady flow in a stably stratified, incompressible, and inviscid fluid. The governing equation is solved analytically under the approximate boundary conditions, and the results are compared with those solved numerically by finite-difference method under the accurate boundary conditions. When the distance between the two barriers increases, flow features periodically vary with the period which is equal to the characteristic wave length λ1 of the lee wave. The maximum amplitudes of lee waves are obtained when L=L0+nλ1 (n=0, 1, 2, ... ), where L0 is a constant which depends on the Froude number.