Introduction

In this chapter we continue to study the dynamic behavior of the barotropic quasi-geostrophic equations in the absence of dissipation and external forcing, paying special attention to the non-linear interaction of the large-scale mean flow and the small-scale flow through topographic stress. Situations of obvious importance in atmosphere and ocean science occur when smaller-scale motions have a significant feedback and interaction with a larger-scale mean flow. One prototype situation of this sort occurs in the interaction of large-scale and small-scale components of barotropic flow over topography via topographic stress. In two influential papers, Charney and DeVore (1979) and Hart (1979) studied the multiple equilibrium states of this system with dissipation and single mode topography, and suggested their possible importance as model states for atmospheric blocking (see also Carnevale and Frederiksen, 1987; Vallis, 1985 for further developments).

In oceanography, in the special case of single mode topography as well as damping and driving, these equations have been used as a model for large-scale mean flow modification through topographic stress for flow along a continental shelf with smaller-scale topographic ridges (Allen etal., 1991; Samelson and Allen, 1987); also recently Holloway (Holloway, 1987; Edy and Holloway, 1994) has emphasized the possible dynamical significance of topographic stress in modifying coastal currents in many oceanographic contexts.