A parameter study of the mixed instability of idealized ocean currents

Abstract

We investigate the nature of linear instabilities that can arise on eastward-flowing baroclinic currents similar to those found to serve as sites of strong eddy-mean flow interaction in certain mesoscale-resolution ocean circulation studies. The intent is to deduce the dependence of the linear instability mechanism — thought to be operative in some form in these simulations — on the internal parameters characterizing them. Following conventional practice, we adopt as our physical model the two-level quasigeostrophic potential vorticity equations which, in their linearized form, are solved numerically to yield the properties of the most unstable linear waves under a variety of mean flow and environmental conditions. The kinematic and dynamic features of the growing perturbations — preferred wavelength, growth rate and frequency, eddy-mean field energy transfers and vertical distribution of wave amplitude — are shown to be sensitive functions of our nondimensional parameters: (i) α = (U3U1), the ratio of lower to upper level velocity scale amplitude; (ii) X = (RdL), the ratio of the first baroclinic deformation radius to the meridional width of the jet; (iii) δ = (H1H3), the resting layer depth ratio; and (iv) ϵ = (βL2U), an (inverse) Rossby number based on the northward gradient of the planetary vorticity (β). Viscous effects, although included in the analysis, are shown to be unimportant for values of frictional coefficients typical of recent eddy-resolving ocean model studies. Despite a strong dependence of the details of the linear instability mechanism on environmental factors, the associated unstable eigenmodes do have important structural similarities which are intimately connected with their ability to extract energy from the mean flow.