A momentum-balance theory for the updraft structure in density currents analogous to squall lines

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Diego A. Alfaro
Fernando Lezana


A momentum-balance theory for the orientation of updrafts in density currents is developed for understanding squall-line–shear interactions. The motivation arises from studies showing the diagnostic limitations of the vorticity-balance theory by Rotunno et al. (1988) (RKW theory) under varying shear profiles, together with the flow-force balance constraint (FFB) which determines the shear-layer depth in optimal density currents. Considering that the FFB is derived from the horizontal momentum equation, momentum-balance concepts are explored as an alternative to RKW theory, by assuming that the updraft’s slope is determined by the balance between advective tendencies of inflowing air and the work done by pressure perturbations within the denser fluid. Density currents were simulated under diverse shear and buoyancy profiles. Results show that momentum-balance effectively diagnoses the updraft’s slope at low and mid-levels in experiments contemplating both “classic” cU variations, as well as changes to the shear and buoyancy vertical profiles. It is also found that cases with stronger system-relative inflow tend to produce deeper lifting of near-surface environmental air, notwithstanding the updraft’s slope. RKW theory’s quantitative criterion (cU) is not as effective at diagnosing the updraft’s slope nor the depth reached by near-surface parcels, although cU provides guidance for the updraft’s slope at upper levels. This result justifies a reinterpretation of cU as a measure of the impacts of wind velocities aloft on the updraft.


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