Alternative depth-averaged models for gravity currents and free shear flows

Abstract

Two approaches have traditionally been used to describe the widening rate of jets and plumes: the diffusion concept of Prandtl, and the entrainment principle of Morton, Taylor and Turner. The entrainment concept is based on depth-averaged flow scales, and was later applied to plane gravity currents on an incline by Ellison and Turner [ET]. The two parameterizations are compared here for free shear flows, and gravity currents. It is shown that the diffusion concept is suitable for supercritical gravity currents, and that both approaches agree for subcritical ones. Depth-averaged models are also used for open channel flows, but the depth and velocity scales for the two flows are different. Those of ET are derived from the velocity distribution, whereas the depth of an open channel flow is the vertical extent of the dense liquid phase, and the velocity is derived from its flux. To reconcile the two descriptions, we extended the mass-based flow scales of open channel flows to gravity currents in an earlier contribution. In the present study these scales are outlined, and extended further to axisymmetric and non-buoyant free shear flows. Ratios of the diffusion rates in terms of mass- and velocity-based flow scales, are obtained from available experimental data for free shear flows.