Hydrodynamic Instability of Spatially Periodic Flows of Homogeneous and Stratified Fluid with Regard for Friction. Formation of Steady-State Vortex Disturbances

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The stability of spatially periodic flows of homogeneous and stratified fluid is investigated with regard for bottom friction. The Galerkin method with three basis Fourier harmonics is used to solve the stability problem. A system of ordinary differential equations for the amplitudes of the Fourier harmonics is formulated. A solution to the linearized version of the system is obtained and an expression for the increment of disturbance growth is found. It is established that at the nonlinear stage of development the exponential growth of linear disturbances is replaced by the regime of establishing steady-state periodic disturbances in form of closed cells. These disturbances reduce the averaged horizontal velocity of the flow. Analytical expressions for the spatial period and amplitude of steady-state disturbances are obtained.

Sobre autores

M. Kalashnik

Obukhov Institute of Atmospheric Physics of the Russian Academy of Sciences; Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences

Email: kalashnik-obn@mail.ru
Moscow, Russia

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