Transient Dynamics of Airflow near a Local Heat Source

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Abstract
The response of a stratified atmosphere to local heating is a common element in several problems in mesoscale dynamics. To investigate this response, a time-dependent linearized problem is solved analytically for an elevated, local heat source turned on as a pulse in a stratified, moving fluid. The thermally induced circulation in the vicinity of the drifting disturbance is qualitatively similar to that of a cumulus cloud in mean wind. The updraft at the center of this cloud is surrounded by the compensating downdrafts at early times even if that air has also been heated. Once the updraft at the drifting center weakens, upward motion begins in the adjacent regions. An integration of the pulse solution yields the response to steady heating, turned on at t = 0. As steady state is approached, this solution exhibits a region of positive displacement moving downstream while negative displacement develop near the stationary heat source. The solution offers an explanation to a curious negative phase relationship between heating and displacement and the lack of a true steady state noted by other authors. It is suggested that the nature of this response may help to explain three problems in mesoscale dynamics: cloud interaction, heat island/orographic rain, and the squall line.

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