The Effect of Nonuniform Wind Shear on the Intensification and Reflection of Mountain Waves

Abstract

Following the analysis of Klemp and Lilly, a study is made of the intensification and reflection of mountain waves when the shear of the basic wind profile is nonuniform. A two-layer atmospheric model is treated, and the wind profile in the troposphere is assumed to be parabolic. The Scorer parameter includes the wind profile curvature term, ūzz/ū, which may not be neglected if the Richardson number Ri is finite. When Ri is finite, the optimal phase difference across the troposphere for maximum surface velocity intensifications is found to be slightly greater than ϕ. As Ri increases, the optimal phase difference decreases with Ri and approaches the limiting value 7ϕ. This implies that waves approximately reverse phase between the surface and the tropopause for maximum wave intensifications in most physically realistic atmospheric situations. The concept of Eliassen and Palm concerning the additivity of the vertical wave energy fluxes is expanded (valid at least up to the parabolic wind profile), by which the upward and downward energy transporting modes are identified. The reflection coefficient r decays rapidly with Ri when Rimin is smaller than about unity, but the dependence of r on Ri is quite mild when Rimin ≥ 3, attaining the limiting behavior describable by the static stability ratio alone.