Abstract
An analytical-numerical method is developed for solving a problem for the potential vorticity equation in the quasi-geostrophic approximation with allowance for vertical diffusion of mass and momentum. The method is used to analyze small perturbations of ocean currents of finite transverse scale with a general parabolic vertical profile of velocity. For the arising spectral non-self-adjoint problem, asymptotic expansions of the eigenfunctions and eigenvalues are constructed for small values of the wave number \(k\). It is shown that, for small \(k\), there exist two bounded eigenvalues and a countable set of unboundedly growing eigenvalues. For a varying wave number \(k\), the trajectories of eigenvalues are calculated for various dimensionless parameters of the problem. As a result, it is shown that the growth rate of unstable perturbations depends significantly on the physical parameters of the model.
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Funding
N.P. Kuzmina’s research was supported by the Shirshov Institute of Oceanology of the Russian Academy of Sciences, subject FMWE -2021-0001.
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Translated by I. Ruzanova
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Skorokhodov, S.L., Kuzmina, N.P. Analytical-Numerical Method for Analyzing Small Perturbations of Geostrophic Ocean Currents with a General Parabolic Vertical Profile of Velocity. Comput. Math. and Math. Phys. 62, 2058–2068 (2022). https://doi.org/10.1134/S0965542522120120
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DOI: https://doi.org/10.1134/S0965542522120120