The development of rolls is attributed to the existence of moist absolutely unstable layers (MAULs) that form above the squall line cold pool. It is believed that the thermal (or convective) instability mechanism is primarily responsible for generation of the rolls (as opposed to the inflection-point instability or parallel instability processes identified in theoretical studies of boundary layer rolls). If the theory is applicable to moist absolutely unstable layers, it suggests that the spacing between the rolls (and, therefore, the spacing between deep deep convective cells) is proportional to the depth of the MAUL and to the magnitude of instability (i.e., lapse rate) within the MAUL.
Although the overall structure of deep convective rolls in squall lines is qualitatively similar to shallow convective rolls in the PBL, several differing aspects are noted. For example, the shallow PBL rolls are basically horizontal, and can extend for hundreds of km. In contrast, the squall line rolls are tilted, with the axis of rotation about 30-45 degrees from the horizontal. Consequently, the squall line rolls extend only about 10-20 km behind the surface gust front. Another difference concerns the aspect ratio of the rolls. For PBL rolls, a representative aspect ratio can be determined based on the depth of the PBL and the spacing between cells. In contrast, since the deep convective rolls have no capping inversion, the plumes that form in the ascending branch of the counter-rotating vortex tubes can grow vertically. Hence, the aspect ratio of the rolls decreases with distance behind the surface gust front.
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