How well does the classical density current model represent realistic unsteady sea breeze fronts?

Past studies of idealized gravity currents relevant to sea-breeze and cold-air outflow phenomena are extended here, via 2-D numerical simulations, to examine individually the effects of more realistic initial stratification and continuous solar heating. A stratified current flowing into a neutral boundary layer with a stable layer above is considered, characterizing the daytime situation over land surfaces.

Results reveal that in the traditionally studied case where a density contrast is imposed as initial conditions (here termed ``impulse heating''), the current's propagation speed quickly approaches a constant values that} is well predicted by the available potential energy of the initial state. This holds through a range of imposed initial stratifications spanning several octaves, over which the horizontal density contrast and depth of the current vary substantially but, for a given available potential energy, in inverse proportion so as to produce a nearly invariant propagation speed (correctly diagnosed by the classical Benjamin formula).

No relations tested, however, proved accurate for predicting or even diagnosing the current speed in the more realistic case where heat is put in steadily through the land surface as by diurnal solar heating. The density current shape appeared similar to those in the previous case, but accelerated sharply with time because of steady increases in both the depth and density contrast of the boundary current. The increasing contrast was maintained, in part, by the replenishment of cold air in the current head via a recirculation within the current, while the increasing thickness resulted from the boundary layer growth. Even accounting for these factors however the Benjamin formula falls far short of diagnosing the acceleration, likely because the entire current cannot accelerate as dictated by the force balance at the current head alone. We conclude that existing theories are inadequate to explain the behavior of time-dependent density currents in realistic situations, even when the currents qualitatively resemble their steady counterparts.