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Asymptotic Analysis of Nonlinear Generation Mechanisms of Unstable Normal Modes in Horizontally Sheared Zonal Flows

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This study explores the nonlinear development of the barotropic instability in weakly supercritical horizontally sheared zonal currents on a beta-plane in the presence of vertical stratification. The energy exchange between unstable normal modes and the flow is shown to be confined to the common critical layer-region where the modal wave speed matches the flow velocity. A closed system of equations governing the evolution of instability wave amplitudes and critical layer vorticity distributions is derived with the aid of an asymptotic procedure. The dependence of the evolutionary scenarios of the flow on the values of the supercriticality and dissipation parameters is examined within the framework of qualitative and numerical analysis of the obtained equations.

Author(s):

Sergei Shagalov    
Institute of Applied Physics of the Russian Academy of Sciences
Russian Federation

Galina Rybushkina    
Institute of Applied Physics of the Russian Academy of Sciences
Russian Federation