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Shear Flow Instability over a Finite Time Interval

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Abstract

Within the framework of a discrete quasi-geostrophic model with two vertical levels, the problem of linear stability of the flow of a stratified rotating fluid with constant vertical and horizontal velocity shifts is solved. It is shown that taking into account the horizontal shear leads to a qualitative change in the dynamics of unstable wave disturbances. The main feature is related to the effect of temporary exponential growth of unstable perturbations, i.e., growth over a finite time period. This effect manifests itself in the alternation of stages of smooth oscillating behavior (in time) with stages of the exponential (explosive) growth of finite duration. A kinematic interpretation of the effect of temporal exponential growth is given, which is associated with the passage of a time-dependent perturbation wave vector through the region of exponential instability that exists in the absence of a horizontal shear. It is shown that mathematically this effect is described by solutions of a second-order differential equation containing turning points. Asymptotic solutions of the equation are given for weak horizontal shifts.

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Funding

This work was supported by the Russian Science Foundation, grant no. 22-27-00039.

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Authors and Affiliations

  1. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, 109017, Moscow, Russia

    M. V. Kalashnik

  2. Schmidt Institute of Physics of the Earth, 123242, Moscow, Russia

    M. V. Kalashnik

  3. Research and Production Association Typhoon, 249038, Obninsk, Russia

    M. V. Kalashnik

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Correspondence to M. V. Kalashnik.

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Kalashnik, M.V. Shear Flow Instability over a Finite Time Interval. Izv. Atmos. Ocean. Phys. 59, 144–149 (2023). https://doi.org/10.1134/S0001433823020032

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