The influence of a Critical latitude on Topographically Forced Stationery Waves in a Barotropic Model

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  • 1 Geophysical Fluid Dynamics Program, Princeton University, Princeton, NJ 08540
  • | 2 Goophysics Fluid Dynamics Laboratory/N0AA, Princeton University, Princeton, NJ 08540
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Abstract

A nondivergent barotropic model on a sphere is used to study the effects of a critical latitude on stationary atmospheric waves forced by topography. Linear and “quasi-linear” calculations are performed with an idealized wavenumber 3 mountain and with realistic topography. Quasi-linear dynamics, where mean flow changes are due to momentum flux convergence, “form drag” and relation to a prescribed climatological mean flow, produces an S-shaped kink in the zonal mean absolute vorticity gradient near the critical latitude, resulting in enhanced reflection. The component of the quasi-linear solution resulting from enhanced reflection at the critical latitude is computed by taking the difference between the linear and the quasi-linear solutions. In a calculation with realistic topography and zonal flow, this reflected component is found to be dominated by a wave train emanating from the western tropical Pacific and propagating northward and then eastward across the Pacific 0cean and the North American continent. This wave train results from the reflection of the Himalayan wave train at the zero-wind latitude in the tropical winter troposphere.

The vorticity gradients in the monthly mean statistics of Oort (1983) show structure near the critical latitude similar to that produced in our quasi-linear model, suggesting that some reflection of incident Rossby waves is likely in the atmosphere, at least in the western Pacific, and that the wind structure responsible for this reflection may be created in part by the stationary Rossby waves themselves.

Abstract

A nondivergent barotropic model on a sphere is used to study the effects of a critical latitude on stationary atmospheric waves forced by topography. Linear and “quasi-linear” calculations are performed with an idealized wavenumber 3 mountain and with realistic topography. Quasi-linear dynamics, where mean flow changes are due to momentum flux convergence, “form drag” and relation to a prescribed climatological mean flow, produces an S-shaped kink in the zonal mean absolute vorticity gradient near the critical latitude, resulting in enhanced reflection. The component of the quasi-linear solution resulting from enhanced reflection at the critical latitude is computed by taking the difference between the linear and the quasi-linear solutions. In a calculation with realistic topography and zonal flow, this reflected component is found to be dominated by a wave train emanating from the western tropical Pacific and propagating northward and then eastward across the Pacific 0cean and the North American continent. This wave train results from the reflection of the Himalayan wave train at the zero-wind latitude in the tropical winter troposphere.

The vorticity gradients in the monthly mean statistics of Oort (1983) show structure near the critical latitude similar to that produced in our quasi-linear model, suggesting that some reflection of incident Rossby waves is likely in the atmosphere, at least in the western Pacific, and that the wind structure responsible for this reflection may be created in part by the stationary Rossby waves themselves.

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