Interacting Mountain Waves and Boundary Layers

Ronald B. Smith Department of Geology and Geophysics, Yale University, New Haven, Connecticut

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Abstract

Linear hydrostatic 3D mountain wave theory is extended to include a thin frictional boundary layer (BL), parameterized using two characteristic relaxation times for wind adjustment. The character of the BL is described using a “compliance coefficient,” defined as the ratio of BL thickness change to imposed pressure. In this formulation the simplest model that captures the two-way interaction between mountain waves and the boundary layer is sought. The slower BL wind speed amplifies the wind response and shifts it upstream so that the wind maxima occur in regions of favorable pressure gradient, not at points of minimum pressure. Variations in BL thickness reduce the mountain wave amplitude. The BL effect is sensitive to the wind profile convexity. The boundary layer improves the linear theory description of windy peaks. Low-level flow splitting is enhanced and wave breaking aloft is reduced. The BL also decreases the amount of upslope orographic precipitation. The wave momentum flux reduction by the BL is greater than the pressure drag reduction, indicating that part of the pressure drag is taken from BL momentum.

Corresponding author address: Ronald B. Smith, Department of Geology and Geophysics, Yale University, P.O. Box 208109, New Haven, CT 06520-8109. Email: ronald.smith@yale.edu

Abstract

Linear hydrostatic 3D mountain wave theory is extended to include a thin frictional boundary layer (BL), parameterized using two characteristic relaxation times for wind adjustment. The character of the BL is described using a “compliance coefficient,” defined as the ratio of BL thickness change to imposed pressure. In this formulation the simplest model that captures the two-way interaction between mountain waves and the boundary layer is sought. The slower BL wind speed amplifies the wind response and shifts it upstream so that the wind maxima occur in regions of favorable pressure gradient, not at points of minimum pressure. Variations in BL thickness reduce the mountain wave amplitude. The BL effect is sensitive to the wind profile convexity. The boundary layer improves the linear theory description of windy peaks. Low-level flow splitting is enhanced and wave breaking aloft is reduced. The BL also decreases the amount of upslope orographic precipitation. The wave momentum flux reduction by the BL is greater than the pressure drag reduction, indicating that part of the pressure drag is taken from BL momentum.

Corresponding author address: Ronald B. Smith, Department of Geology and Geophysics, Yale University, P.O. Box 208109, New Haven, CT 06520-8109. Email: ronald.smith@yale.edu

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