Nonlinear mountain waves with active precipitation

Abstract

Exact nonlinear mountain waves described using Lagrangian variables are considered with constant enthalpy of vapourisation in a moist atmosphere. It is shown that if a streamline in the flow with a given temperature is saturated, then the dynamics of the flow are sufficient to deduce the temperature at which any other streamline in the flow becomes saturated. The equation of state for vapour is then applied to deduce the saturation pressure for the water component of the atmospheric flow also. The first law of thermodynamics is then used to deduce the heat gain within a region due to precipitation from the flow. This heat loss is also used to obtain an estimate for the rate of hydrometeor fallout from this region of the flow.