Front propagation of gravity currents on inclined bottoms in linearly stratified fluids

Abstract

Gravity currents propagating on an inclined bottom into stratified environment can be frequently encountered in nature or engineering fields. However, theoretical analysis and simulations on the evolution process of lock-exchange gravity currents in such environments are still in lack of investigations. In this work, we derive a set of semi-empirical formulae to determine the frontal propagation speed in homogenous and linearly stratified ambient fluids. Two phases can be clearly observed in the propagation process, a relatively short acceleration phase followed by a deceleration phase. In the acceleration phase, the formula considers the influence of initial position and ambient stratification by introducing mass centroid coefficient (αp) and effective stratification coefficient (αs), respectively. In the deceleration phase, the formula is derived by adding the effective buoyancy parameter Bm′ and entrainment coefficient km, where km is eventually a function of the fraction of heavy fluid in the dense current head (χ) as it propagating down the ramp. We propose a simplified and efficient method to estimate the value of χ in various conditions, which has been previously assumed as a constant. A series of lock-exchange gravity current experiments were conducted in the tank with linear stratifications to validate the propagation theory. The comparisons between the calculated and measured front propagation speed show good agreement, which reveal that the front velocity exhibits a rapid acceleration stage followed by a deceleration stage in the linearly stratified ambience. The good agreement between measured and calculated data indicates that semi-empirical formulae are capable to predict the whole process of gravity current propagation using only measurable information prior to initiate gravity current experiments.