Amplification of Forced Rossby Waves in the Presence of a Nonlinear Critical Layer

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  • 1 Department of Meteorology, McGill University, Montreal, Quebec, Canada H3A 2K6
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Abstract

The nondivergent barotropic vorticity equation is integrated numerically in order to investigate a potential resonance mechanism for Rossby waves on a shear flow in the presence of a nonlinear critical layer. lie numerical model, which uses a mixture of spectral and finite element techniques, simulates the propagation of a weakly forced Rossby wave on a semi-infinite beta plane. It is found that a large amplitude response can be obtained by “tuning” the geometry of the flow and that there is an associated increase in the thickness of the critical layer, showing that this mechanism gives a low latitude response to a midlatitude forcing. Nonlinear critical layers may thus have an important impact on large-scale atmospheric motions. The logarithmic phase shift is also investigated. It appears to develop an imaginary part as the nonlinearities come into force.

Abstract

The nondivergent barotropic vorticity equation is integrated numerically in order to investigate a potential resonance mechanism for Rossby waves on a shear flow in the presence of a nonlinear critical layer. lie numerical model, which uses a mixture of spectral and finite element techniques, simulates the propagation of a weakly forced Rossby wave on a semi-infinite beta plane. It is found that a large amplitude response can be obtained by “tuning” the geometry of the flow and that there is an associated increase in the thickness of the critical layer, showing that this mechanism gives a low latitude response to a midlatitude forcing. Nonlinear critical layers may thus have an important impact on large-scale atmospheric motions. The logarithmic phase shift is also investigated. It appears to develop an imaginary part as the nonlinearities come into force.

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