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 Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 11, Pages 1962–1974 (Mi zvmmf11164)

Mathematical physics

On the influence of the beta effect on the spectral characteristics of unstable perturbations of ocean currents

S. L. Skorokhodova, N. P. Kuzminab

a Dorodnicyn Computing Center, Federal Research Center "Computer Science and Control", Russian Academy of Sciences, Moscow, 119991 Russia
b Shirshov Institute of Oceanology, Russian Academy of Sciences, Moscow, 117997 Russia

Abstract: Based on the equation for potential vorticity in the quasi-geostrophic approximation, an analysis of stable and unstable perturbations of ocean currents of a finite transverse scale with a vertical linear velocity profile (Couette-type flows) is presented. The model takes into account the influence of vertical diffusion of buoyancy, friction, and the beta effect (the change in the Coriolis parameter with latitude). The analysis is based on the small perturbation method. The problem depends on several physical parameters and reduces to solving a spectral non-self-adjoint problem for a fourth-order equation with a small parameter at the highest derivative. Asymptotic expansions of eigenfunctions and eigenvalues are constructed for small values of the wavenumber $k$. Using the continuation in the parameter $k$, trajectories of the eigenvalues are calculated, which made it possible to compare the influence of the beta effect on unstable perturbations of the first and higher order modes. It is shown that the flow instability depends in a complex way on the physical parameters of the flow.

Key words: spectral non-self-adjoint problem, parameter continuation method, Newton's method, asymptotic expansions.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 0149-2019-0003 The participation of N.P. Kuzmina in this study was supported by the budgetary funding of the Shirshov Institute of Oceanology of the Russian Academy of Sciences (project no. 0149-2019-0003).

DOI: https://doi.org/10.31857/S0044466920110137

English version:
Computational Mathematics and Mathematical Physics, 2020, 60:11, 1900–1912

Bibliographic databases:

UDC: 517.63
Revised: 21.05.2020
Accepted:07.07.2020

Citation: S. L. Skorokhodov, N. P. Kuzmina, “On the influence of the beta effect on the spectral characteristics of unstable perturbations of ocean currents”, Zh. Vychisl. Mat. Mat. Fiz., 60:11 (2020), 1962–1974; Comput. Math. Math. Phys., 60:11 (2020), 1900–1912

Citation in format AMSBIB
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