The instantaneous Froude number and depth of unsteady gravity currents

We have studied two-dimensional and three-dimensional gravity currents with Reynolds number 22,600. We present a definition for h c , a spatially varying characteristic depth of an unsteady current which can be used to determine an appropriate current head height h H . We also propose a robust method for the determination of the front speed u c and a characteristic measure of the available buoyancy in the head g′ c . The proposed definitions and methods are robust in the sense that the quantities (h c , u c and g′ c ) computed from the instantaneous flow fields show a largely continuous behaviour in time despite the unsteady nature of the flow. We show that the Froude number calculated from these variables, , remains constant throughout the constant-velocity and the self-similar regimes. We also investigate the dependence of the Froude number on the ratio of the current depth to the channel depth and compare our results with the theories of Nokes et al. [(2008). The front condition for intrusive gravity currents. J. Hydraulic Res. 46(6), 788–801] and Shin et al. [(2004). Gravity currents produced by lock exchange. J. Fluid Mech. 521, 1–34].