Revisiting gravity currents and free shear flows
ABSTRACT: The rate at which free shear flows widen along their path can be specified by invoking the concept of entrainment. A different approach was proposed by Prandtl, who considered the widening of jets as being due to a diffusion process. His diffusion relation in terms of the half-width has since been successfully modified for models of free shear flows averaged over the width. In the present contribution we apply it to gravity currents. A further topic we address here is that the structure of the conventional shallow water equations for gravity currents is consistent with the Bresse equations for open channel flows, but that the underlying depth and velocity scales of the two flows are different. For gravity currents the scales are derived from the velocity distribution in analogy to previous work on free shear flows, whereas they are based on the vertical extent, and flux, of the dense liquid phase in open channel flows. To avoid this disparity, we defined a set of scales for both flows which is based on the distribution and flux of excess mass. To compare entrainment and diffusion rates for gravity driven flows in terms of velocity-and mass-based scales, we reanalyze field data on katabatic winds, which are similar to gravity currents.