On the role of the stratosphere in the process of overflow of mesoscale mountains

Abstract. A 2-D, two- and three-layer stratified airflow over a mountain of arbitrary shape is considered on the assumptions that upstream wind velocity and static stability within each layer are constant (Long's model). The stratosphere is simulated by an infinitely deep upper layer with enhanced static stability.

The analytical solution for the stream function, as well as first (linear) and second order approximations to the wave drag, are obtained in hydrostatic limit N₁L/U₀→∞, where N₁ is the Brunt-Väsälä frequency in the troposphere, L is a characteristic length of the obstacle, and U₀ is upstream velocity. The results of numerical computations show the principal role of long waves in the process of interaction between the model layers for a typical mesoscale mountains for which the hydrostatic approximation proves valid in a wide range of flow parameters, in accordance with the earlier conclusions of Klemp and Lilly (1975). Partial reflection of wave energy from the tropopause produces strong influence on the value of wave drag for typical middle and upper tropospheric lapse rates, leading to a quasi-periodic dependance of wave drag on a reduced frequency ( is tropopause height) in the troposphere. The flow seems to be statically unstable for k≥2 for sufficiently large obstacles (whose height exceeds 1 km). In this case, vast regions of rotor motions and strong turbulence are predicted from model calculations in the middle troposphere and the lower stratosphere. The model calculations also point to a testify for possible important role of nonlinear effects associated with finite height of the mountain on the conditions of wave drag amplification in the process of overflow of real mountains.