Abstract
When a Squall line propagates through the atmosphere, it not only excite transient gravity–inertia wave motion but also produces more permanent modifications to the large-scale balanced flow. Here we calculate this balanced response using the is isentropic/geostrophic coordinate version of semigeostrophic theory. This approach results in a simple mathematical form in which the horizontal ageostrophic velocities am completely implicit and the entire dynamics reduces to a predictive equation for the potential pseudodensity and an invertibility relation. For a two-dimemional squall line, the potential pseudoderisity equation is simple enough to be solved analytically. The solutions illustrate how the squall line leaves in its wake a region of low potential pseudodensity in the lower troposphere and a region of potential pseudodensity in the upper troposphere. The solutions also show that the character of the potential pseudodensity modification by the squall line depends on the ratio of the convective overturning time to the squall line leaves passage time. This allows us to dynamically distinguish intensely mining, wide. slowly moving squau lines from weakly raining, narrow, fast-moving squall lines. After the potential pseudensity is determined, it can be used in the invertibility relation to yield balanced wind and mass fields which capture some of the observed large-scale features associated with squall lines.
