Mean flow generation by topographic Rossby waves

Abstract

This paper makes use of the ease of modelling topographic Rossby waves in a laboratory context to investigate the ability of these waves to generate strong zonal mean flows when the geostrophic (f/H) contours are closed. A zonally travelling wave is forced in a narrow latitude band of a ‘polar beta plane’. Stronger signals occur when the motion of the driving is retrograde and at the phase speed of the gravest free modes. An important zonal westward mean flow occurs in the free interior while a compensating eastward jet is found at forced latitudes. The dependence of the mean flow strength upon the wave steepness indicates that genuine rectification processes are indeed taking place when the fluid is stirred by purely oscillating devices. This general tendency for topographic Rossby waves to transfer energy to zonal components is first analysed theoretically by investigating a side-band instability mechanism within an unforced fluid. Among the products of the interactions between a primary wave of wavenumber k and its side bands of wavenumber k± δ k, the zonal flow is prominent. Wave steepnesses of order (|δ k|/|k|)½ only are required for zonal energy to grow whereas non-zonal components of scale longer or shorter than the primary wave need huge steepnesses [of order (|δ k|/|k|−3/2] for amplification. This supplements the earlier notion that ‘nearly zonal’ waves may be generated by weak resonant interaction. For gentle driving certain classical aspects of Rossby wave propagation can be checked against the experiments. The linear theory provides also a convenient framework to discuss the meridional structure of the wave-induced Reynolds stress. For more energetic driving, a test of the potential vorticity mixing theory can be carried out and sheds further light upon the rectification mechanisms.