A Theoretical Study of Cold Air Damming

Abstract

The dynamics of cold air damming are examined analytically with a two-layer steady state model. The upper layer is a warm and saturated cross-mountain (easterly or southeasterly onshore) flow. The lower layer is a cold mountain-parallel (northerly) jet trapped on the windward (eastern) side of the mountain. The interface between the two layers represents a coastal front?a sloping inversion layer coupling the trapped cold dome with the warm onshore flow above through pressure continuity. An analytical expression is obtained for the inviscid upper-layer flow with hydrostatic and moist adiabatic approximations. Blackadar's PBL parameterization of eddy viscosity is used in the lower-layer equations. Solutions for the mountain-parallel jet and its associated secondary transverse circulation are obtained by expanding asymptotically upon a small parameter proportional to the square root of the inertial aspect ratio?the ratio between the mountain height and the radius of inertial oscillation. The geometric shape of the sloping interface is solved numerically from a differential-integral equation derived from the pressure continuity condition imposed at the interface. The observed flow structures and force balances of cold air damming events are produced qualitatively by the model. In the cold dome the mountain-parallel jet is controlled by the competition between the mountain-parallel pressure gradient and friction: the jet is stronger with smoother surfaces, higher mountains, and faster mountain-normal geostrophic winds. In the mountain-normal direction the vertically averaged force balance in the cold dome is nearly geostrophic and controls the geometric shape of the cold dome. The basic mountain-normal pressure gradient generated in the cold dome by the negative buoyancy distribution tends to flatten the sloping interface and expand the cold dome upstream against the mountain-normal pressure gradient (produced by the upper-layer onshore wind) and Coriolis force (induced by the lower-layer mountain-parallel jet). It is found that the interface slope increases and the cold dome shrinks as the Froude number and/or upstream mountain-parallel geostrophic wind increase, or as the Rossby number, upper-layer depth, and/or surface roughness length decrease, and vice versa. The cold dome will either vanish or not be in a steady state if the Froude number is large enough or the roughness length gets too small. The theoretical findings are explained physically based on detailed analyses of the force balance along the inversion interface.