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Interpreting Stationary Wave Nonlinearity in Barotropic Dynamics

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  • 1 Department of Physics, University of Toronto, Toronto, Ontario, Canada
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Abstract

Stationary wave nonlinearity describes the self-interaction of stationary waves and is important in maintaining the zonally asymmetric atmospheric general circulation. However, the dynamics of stationary wave nonlinearity, which is often calculated explicitly in stationary wave models, is not well understood. Stationary wave nonlinearity is examined here in the simplified setting of the response to localized topographic forcing in quasigeostrophic barotropic dynamics in the presence and absence of transient eddies. It is shown that stationary wave nonlinearity accounts for most of the difference between the linear and full nonlinear response, particularly if the adjustment of the zonal-mean flow to the stationary waves is taken into account. The separate impact of transient eddy forcing is also quantified. Wave activity analysis shows that stationary wave nonlinearity in this setting is associated with Rossby wave critical layer reflection. A nonlinear stationary wave model, similar to those used in baroclinic stationary wave model studies, is also tested and is shown to capture the basic features of the full nonlinear stationary wave solution.

Corresponding author address: Lei Wang, Department of Physics, University of Toronto, 60 St. George St., Toronto, ON M5S 1A7, Canada. Email: lei@atmosp.physics.utoronto.ca

Abstract

Stationary wave nonlinearity describes the self-interaction of stationary waves and is important in maintaining the zonally asymmetric atmospheric general circulation. However, the dynamics of stationary wave nonlinearity, which is often calculated explicitly in stationary wave models, is not well understood. Stationary wave nonlinearity is examined here in the simplified setting of the response to localized topographic forcing in quasigeostrophic barotropic dynamics in the presence and absence of transient eddies. It is shown that stationary wave nonlinearity accounts for most of the difference between the linear and full nonlinear response, particularly if the adjustment of the zonal-mean flow to the stationary waves is taken into account. The separate impact of transient eddy forcing is also quantified. Wave activity analysis shows that stationary wave nonlinearity in this setting is associated with Rossby wave critical layer reflection. A nonlinear stationary wave model, similar to those used in baroclinic stationary wave model studies, is also tested and is shown to capture the basic features of the full nonlinear stationary wave solution.

Corresponding author address: Lei Wang, Department of Physics, University of Toronto, 60 St. George St., Toronto, ON M5S 1A7, Canada. Email: lei@atmosp.physics.utoronto.ca

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