The numerical simulation of atmospheric gravity currents. Part II. Environments with stable layers

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Abstract
The two-dimensional numerical model for an atmospheric gravity current described in Part I is used to study the effect of an ambient low-level stable layer on the evolution of a gravity current. This is a common situation in the atmosphere, but appears to have received little attention in the literature. Simulations are presented for stable layers of various static stabilities and depths. Two important parameters characterizing the evolution of the gravity current are the Froude number Fr, defined in Part I, and the quantity μ=c o/c gr, where c o is the phase speed for the propagation of infinitesimal amplitude long waves on the stable layer and c gr, is the speed of the equivalent gravity current in the absence of the stable layer. We have identified two broad parameter regimes: when μ is less than about 0.7, the gravity current head separates from the feeder flow to form a solitary-type disturbance preceding the former and for the larger values of μ in this range, a second head may form and break away so that the disturbance takes the form of an undular-type bore; when μ is greater than about 0.7, the gravity current spawns a solitary wave, or, for larger values of μ an undular bore, moving ahead of it on the stable layer. These findings are consistent with the results of laboratory experiments and appear to provide a basis for interpreting observations of certain wave and bore-like phenomena in the lower atmosphere. Whatever the nature of the leading disturbance, its propagation speed exceeds c grby an amount that is linearly proportional to c o.