The transverse circulation implied by the observations cannot be explained solely on the basis of geostropic deformation acting upon the cross-frontal horizontal temperature gradient field, since the observed circulation is characterized by spatial and temporal scales much smaller than those predicted by semigeostrophic theory. The observed scales can be explained by considering a superposition of the cross-frontal variation in surface sensible heat flux upon the deformation field. The possible relevance of other mesoscale processes as explanations for these satellite-observed features is also examined. -from Author
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Koch, S. E. (1984). The role of an apparent mesoscale frontogenetic circulation in squall line initiation. Monthly Weather Review, 112(10), 2090–2111. https://doi.org/10.1175/1520-0493(1984)112<2090:TROAAM>2.0.CO;2