An Analysis of Three-Dimensional Mountain Lee Waves in a Stratified Shear Flow

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  • 1 Department of Astro-Geophysics, University of Colorado, Boulder 80309
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Abstract

A three-dimensional, linear, hydrostatic model of stationary mountain waves in a stably stratified airstream is considered. A general solution is presented for the case of a cross-wind variation of the basic current represented by the hyperbolic secant profile; both the current and the Brunt-Väisälä frequency are independent of height. Particular solutions are presented for a variety of hill shapes.

The pressure pattern and distribution of velocity at ground level are similar in many respects to the fields obtained by Smith (1980) for constant flow over a circular hill. High pressure occurs on the windward side with relatively low pressure in the lee, and the oncoming airstream tends to partially circumvent the hill resulting in a permanent streamline deflection in the lee. The flow field aloft is characterized by an upstream tilt of the phase lines, associated with outward vertical propagation of wave energy. Wave energy also is directed downstream but is totally reflected in the cross-stream direction as a consequence of the cross-stream variation of the basic current. Thus, the wave disturbance is primarily contained within a horizontal strip, at each level, that is somewhat larger than the characteristic breadth of each hill shape. This latter response is significantly different than the typical “ship wave” pattern that occurs when a constant flow passes over a hill.

Some prominent features of the wave response aloft, as a function of the characteristic hill shape used to represent orography, are examined by means of an asymptotic representation of the solution.

Abstract

A three-dimensional, linear, hydrostatic model of stationary mountain waves in a stably stratified airstream is considered. A general solution is presented for the case of a cross-wind variation of the basic current represented by the hyperbolic secant profile; both the current and the Brunt-Väisälä frequency are independent of height. Particular solutions are presented for a variety of hill shapes.

The pressure pattern and distribution of velocity at ground level are similar in many respects to the fields obtained by Smith (1980) for constant flow over a circular hill. High pressure occurs on the windward side with relatively low pressure in the lee, and the oncoming airstream tends to partially circumvent the hill resulting in a permanent streamline deflection in the lee. The flow field aloft is characterized by an upstream tilt of the phase lines, associated with outward vertical propagation of wave energy. Wave energy also is directed downstream but is totally reflected in the cross-stream direction as a consequence of the cross-stream variation of the basic current. Thus, the wave disturbance is primarily contained within a horizontal strip, at each level, that is somewhat larger than the characteristic breadth of each hill shape. This latter response is significantly different than the typical “ship wave” pattern that occurs when a constant flow passes over a hill.

Some prominent features of the wave response aloft, as a function of the characteristic hill shape used to represent orography, are examined by means of an asymptotic representation of the solution.

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