EGU2020-9872, updated on 12 Jun 2020
EGU General Assembly 2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Instability of surface quasigeostrophic spatially periodic flows

Maksim Kalashnik1, Michael Kurgansky1, and Sergey Kostrykin1,2
Maksim Kalashnik et al.
  • 1A.M. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Moscow, Russia, Moscow, Russian Federation (
  • 2G. I. Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia, Moscow, Russian Federation

The surface quasigeostrophic (SQG) model is developed to describe the dynamics of flows with zero potential vorticity in the presence of one or two horizontal boundaries (Earth surface and tropopause). Within the framework of this model, the problems of linear and nonlinear stability of zonal spatially periodic flows are considered. To study the linear stability of flows with one boundary, two approaches are used. In the first approach, the solution is sought by decomposing into a trigonometric series, and the growth rate of the perturbations is found from the characteristic equation containing an infinite continued fraction. In the second approach, few-mode Galerkin approximations of the solution are constructed. It is shown that both approaches lead to the same dependence of the growth increment on the wavenumber of perturbations. The existence of instability with a preferred horizontal scale on the order of the wavelength of the main flow follows from this dependence. A similar result is obtained within the framework of the SQG model with two horizontal boundaries. The Galerkin method with three basis trigonometric functions is also used to study the nonlinear dynamics of perturbations, described by a system of three nonlinear differential equations similar to that describing the motion of a symmetric top in classical mechanics. An analysis of the solutions of this system shows that the exponential growth of disturbances at the linear stage is replaced by a stage of stable nonlinear oscillations (vacillations). The results of numerical integration of full nonlinear SQG equations confirm this analysis.

The work was supported by the Russian Foundation for Basic Research (Project 18-05-00414) and the Russian Science Foundation (Project 19-17-00248).

How to cite: Kalashnik, M., Kurgansky, M., and Kostrykin, S.: Instability of surface quasigeostrophic spatially periodic flows, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-9872,, 2020

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