ON ROSSBY-WAVE PROPAGATION IN A MERIDIONALLY STRATIFIED CHANNEL

Rossby wave propagation in the presence of a nonseparable Brunt-Väisälä frequency, N(y,z), and the associated geostrophic zonal flow, U(y,z), is examined in this paper. The usual quasi-geostrophic potential vorticity equation only includes vertical variations in Brunt-Väisälä frequency (i.e. N(z)). We derive a linearised quasi-geostrophic potential vorticity equation which explicitly includes N(y, z), where variations in N may occur on the internal Rossby radius length scale. A mixed layer distribution that monotonically deepens in the poleward direction leads to a nonseparable N(y,z). The resulting meridional pressure gradient is balanced by an eastward zonal geostrophic flow. By assuming mixed layer depth changes occur slowly, relative to a typical horizontal wavelength of a Rossby wave, a local analysis is presented. The Rossby wave is found to have a strongly modulated meridional wavenumber, l, with amplitude proportional to |l|-1/2. To elucidate whether the modulations of the Rossby wave are caused by the horizontal variations in N or U we also consider the cases where either N or U vary horizontally. Mixed layer depth changes lead to largest l where the mixed layer is deepest, whereas l is reduced in magnitude where U is nonzero. When both U(y,z) and N(y,z) are present, the two effects compete with one another, the outcome determined by the size of |c|/Umax, where c is the Rossby wave phase speed. Finally, the slowly varying assumption required for the analytical approach is removed by employing a numerical model. The numerical model is suitable for studying Rossby wave propagation in a rectangular zonal channel with general N(y, z) and U(y, z). © 1990 Birkhäuser Verlag.