On oscillatory flow over topography in a rotating fluid

Abstract

Quasi-geostrophic β-plane motion of a homogeneous liquid over topography is considered for situations in which there is a time-periodic forcing of a zonal current. Such an oscillatory current generates a topographic Rossby wave response that has a complicated, but periodic, temporal structure. The linear solution shows resonances at all integer values of the β-parameter. The nonlinear analysis demonstrates that for weak friction and forcing, the resonances are bent and multiple equilibria of the time-dependent Rossby wave states are possible in certain parameter ranges. While the basic forced flow in the absence of topography has no time-mean, the nonlinear amplitude equations show that a mean retrograde (westward) Eulerian zonal flow is generated in the interactions of the forced flow with the topography. This result is in agreement with a previous theory of Samelson & Allen, constructed for strongly nonlinear flow over a series of asymptotically long ridges. However, in contrast to the behaviour of their amplitude equations for certain parameter settings, the nearresonant weakly nonlinear model for more or less isotropic bottom topography appears non-chaotic for all accessible parameter values.