A Theoretical Study of Cold Air Damming with Upstream Cold Air Inflow

Abstract

The previously developed two-layer model of cold air damming is extended to include upstream cold air inflow. The upper layer is an isentropic cross-mountain flow. The lower layer is a cold boundary layer flow partially blocked by a two-dimensional mountain with a cold dome formed on the windward side of the mountain. The interface represents a sloping inversion layer coupling the two layers. The shape of the interface can be approximated by a cubic polynomial, and the interfacial coupling condition yields a set of algebraic equations that quantify the scale and intensity of the dammed flow as functions of the external parameters characterizing the environmental conditions. It is found that the cold dome shrinks as the Froude number increases or, to a minor degree, as the Ekman number decreases or/and the upstream inflow veers from northeasterly to southeasterly (with respect to a longitudinal mountain to the west). The mountain-parallel jet speed increases as the Ekman number decreases or/and the upstream inflow veers from southeasterly to northeasterly or, to a minor degree, as the Froude number decreases. The theoretical results are qualitatively verified by numerical simulations with a full model and interpreted physically in comparison with the results of the previous two-layer model. It is also shown that our two-dimensional model may (or may not) be applied to a quasi-two-dimensional mountain ridge if the length scale of the ridge is (or is not) significantly larger than the Rossby radius of deformation multiplied by the inverse Froude number.