Precipitation in nonlinear mountain waves with temperature-dependent enthalpy

Mountains play a crucial role in shaping regional climates. For example, precipitation may occur when a moist air mass is forced over a mountain range, where the associated cooling as it rises results in the air becoming saturated.

In this talk, we will consider an exact solution to the nonlinear governing equations for mountain waves, in the Lagrangian framework. The waves propagate in a moist atmosphere, and we incorporate a temperature dependence in the enthalpy of condensation of water vapour.

We show that if a streamline in the atmospheric flow at a given temperature is saturated, then the explicit specification of the dynamics of the flow is sufficient to deduce the temperature and vapour pressure profiles for any other saturated streamline in the flow.

We further deduce a restriction on the domain for which precipitation is admissible, enforced by the second-law of thermodynamics.

(Joint work with Dr. Tony Lyons)