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This article is cited in 4 scientific papers (total in 4 papers)
Ordinary differential equations
Spectral analysis of small perturbations of geostrophic currents with a parabolic vertical profile of velocity as applied to the ocean
S. L. Skorokhodova, N. P. Kuzminab a Federal Research Center "Computer Science and Control", Russian Academy of Sciences, 119991, Moscow, Russia
b Shirshov Institute of Oceanology, Russian Academy of Sciences, 117997, Moscow, Russia
Abstract:
The paper presents an analysis of stable and unstable perturbations of ocean currents of a finite transverse scale with a parabolic vertical profiles of velocity (Poiseuille–Couette-type flow), based on the potential vorticity equation in the quasi-geostrophic approximation and taking into account both linear and constant flow velocity shear. The model takes into account the effect of vertical diffusion of buoyancy and vertical friction and assumes that the maximum mean current velocity takes place at the boundary of the layer. 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 the eigenfunctions and eigenvalues are constructed for small values of the wavenumber $k$. Using the method of continuation in the parameter $k$, the trajectories of the eigenvalues are calculated for different values of the problem's physical parameters. A detailed analysis of how the features of the vertical flow structure influence the characteristics of stable and unstable perturbations is presented. It is shown that the phase velocities of unstable perturbations can vary significantly depending on the linear vertical shear of the flow velocity.
Key words:
spectral non-self-adjoint problem, asymptotic expansions, parameter continuation method.
Received: 17.03.2021 Revised: 19.05.2021 Accepted: 20.06.2021
Citation:
S. L. Skorokhodov, N. P. Kuzmina, “Spectral analysis of small perturbations of geostrophic currents with a parabolic vertical profile of velocity as applied to the ocean”, Zh. Vychisl. Mat. Mat. Fiz., 61:12 (2021), 2010–2023; Comput. Math. Math. Phys., 61:12 (2021), 1966–1979
Linking options:
https://www.mathnet.ru/eng/zvmmf11327 https://www.mathnet.ru/eng/zvmmf/v61/i12/p2010
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