Gravity currents produced by lock-release: Theory and experiments concerning the effect of a free top in non-Boussinesq systems

Abstract

We present an experimental and theoretical analysis of non-Boussinesq inertial (large Reynolds number flow) gravity currents (GCs) flowing in rectangular cross-sections. Attention is focused on the effects of the open upper boundary, which become pronounced when the density contrast between the current and the ambient is significant (non-Boussinesq case). The study is conducted deriving first a two-layer shallow-water (SW) model for the release of a constant fluid volume into an ambient of given height with a free-surface boundary condition, with an arbitrary density ratio r between the ambient and the intruding fluid. The jump conditions at the front are provided by the novel extension of Benjamin (1968) analysis , subject to energy-dissipation and sub-critical speed requests, as detailed in Ungarish (2017). The resulting SW lock-release problem is solved via a finite difference approach. Lock-release experiments are then conducted in this configuration with r=0.837−0.950, full-depth and part-depth locks, and two different lock lengths. Experimental results obtained for the front position and speed of the intruding current, its thickness, and the free-surface depression of the ambient fluid (a signature of these experiments marking the position of the intruding front) agree, to various degrees, with their theoretical counterparts, with a better agreement for the front position and depression than for the other quantities, but demonstrating in all cases the consistency of the trend. Some of the experiments were repeated with a top-lid boundary condition, to discern its effect on the current propagation. These effects turn out to be relatively minor except for the obvious absence of interface-height depression. The range of density ratio r examined is further extended by conducting a numerical simulations with r=0.7 using a numerical commercial Computational Fluid Dynamics code (CFD) based on Reynolds Averaged Navier-Stokes equations (RANS). A comparison among SW theory, experiments, and the numerical simulations is conducted in terms of the trough behind the current nose, leading to an overestimation of theoretical results with respect to experiments. The length of the through adequately scales with the lock-length.