The Eliassen transverse circulation equation is derived from the set of f-plane, semigeostrophic, slab-symmetric equations with the inclusion of both diabatic hearing and ambient shear effects. Numerical integrations of this model in geostrophic coordinates are performed in the context of a typical midlatitude squall line characterized by a leading convective line and a trailing stratiform rain region. Some dynamical insights are provided by these integrations in conjunction with the theoretical framework, which seem to be unavailable by primitive-equation model simulations. A more complete dynamical picture of a squall line circulation system is revealed from this study: a balanced midlevel horizontal vortex coupled with an ageostrophic transverse circulation in the normal-line plane. This configuration suggests an interaction between two distinct dynamical scales, that is, the scales with geostrophic and ageostrophic-like motions, both of which play important roles in mesoscale convective systems. The internal and external physical processes that affect the ageostrophic transverse circulation are further discussed.
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