Symmetric instability of geostrophic currents with a finite transverse lengthscale
https://doi.org/10.7868/S2073667321040018
Abstract
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.
About the Authors
N. P. Kuzmina
Shirshov Institute of Oceanology, Russian Academy of Sciences
Russian Federation
Russian Federation
117997, Nahimovskiy prospekt, 36, Moscow
N. V. Zhurbas
Shirshov Institute of Oceanology, Russian Academy of Sciences
Russian Federation
Russian Federation
117997, Nahimovskiy prospekt, 36, Moscow
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Review
For citations:
Kuzmina N.P., Zhurbas N.V. Symmetric instability of geostrophic currents with a finite transverse lengthscale. Fundamental and Applied Hydrophysics. 2021;14(4):3-13. https://doi.org/10.7868/S2073667321040018
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