Kuzmina N.P., Zhurbas N.V.
A comparative analysis of unstable symmetric perturbations of the geostrophic current with a constant vertical and horizontal velocity shear in an unbounded region and a region with lateral boundaries is performed accounting for vertical diffusion of buoyancy and momentum. Calculations of the growth rate of unstable perturbations are presented as a function of the vertical wavenumber for various dimensionless parameters of the problem. It is found that in the case of the geostrophic current with lateral boundaries, the maximum-growing mode of symmetric instability arising when condition Ri · (1 + Ro) < 1 (Ri is the geostrophic Richardson number, Ro is the Rossby number) is satisfied has a finite vertical length scale, while in the case of the unbounded region, the vertical wavenumber of the maximum-growing mode is asymptotically vanishing. A combined effect of lateral boundaries and diffusion of buoyancy and momentum at Pr ≥ 1 (Pr is the Prandtl number), depending on the values of the dimensionless parameters of the problem, can significantly affect the dynamics of symmetric perturbations, namely, lead to a narrowing of the spectrum of unstable perturbations and a decrease in their growth rates, and even prevent the development of instability.
