Inertial and Frictional Effects on Stratified Hydrostatic Airflow past an Isolated Heat Source

Abstract

Inertial and frictional effects on stratified hydrostatic airflow past an isolated warm region are investigated by linear theories. For an inviscid quasi-geostrophic flow, there exists in the lower layer upward motion upstream and downward motion downstream of the warm region. The vertical velocity field is in phase with the diabatic heating and cooling. As expected, regions of high buoyancy, low pressure and positive vorticity are produced in the vicinity of the warm region. Strong vortex stretching occurs near the center of the warm region, accompanied by two regions of weak vortex compression upstream and downstream. With the inertial effects included, the vertical motion and the vorticity are strengthened. The horizontal wind experiences a much stronger cyclonic circulation near the diabatic source. For a flow with a larger Rossby number O(1), the advection effect of the basic flow is dominant. U-shaped patterns of disturbance are pronounced, which are associated with the upward propagating inertia-gravity waves. The wind is deflected cyclonically around the region of positive relative vorticity and is advected downstream of the center of the warm region, rather than around the region of the low pressure. The frictional effects are investigated by the addition of an Ekman friction layer to a quasi-geostrophic flow. There are three significant features of the disturbance: (i) an upstream-downstream asymmetry, (ii) an upstream phase tilt in the lower layer, and (iii) weakening of the positive relative vorticity and low pressure. Items (i) and (ii) are explained by the upward motion and vorticity and the advection of the basic flow on the disturbance induced by the Ekman friction. The weakening of the positive relative vorticity and the low pressure can be explained as the spindown process of the interior flow to the Ekman friction.