Front Velocity and Front Location of Lock-exchange Gravity Currents Descending a Slope in a Linearly Stratified Environment

TL;DR

This paper develops analytical formulas to predict the front velocity and location of lock-exchange gravity currents descending slopes in linearly stratified environments, validated by experimental data.

Contribution

It introduces new formulas incorporating stratification effects and density distribution, advancing understanding of gravity current dynamics in stratified settings.

Findings

Formulas accurately predict front velocity and location.

Gravity currents exhibit rapid acceleration followed by deceleration.

Experimental data validate the theoretical predictions.

Abstract

Gravity currents descending a slope in a linearly stratified environment can be frequently encountered in nature. However, few studies have quantitatively investigated the evolution process of lock-exchange gravity currents in such environments. A new set of analytical formulae is proposed by integrating both mass conservation and linear momentum equations to determine the front velocity and the front location of a downslope current. Based on the thermal theory, the formula considers the influence of ambient stratification by introducing a newly defined stratification coefficient in the acceleration stage. As for the deceleration stage, the formula is derived by adding a parameter that takes into account the density distribution of the ambient water. The transition point between the acceleration and deceleration stages and the maximum front velocity are also determined by the proposed formulae. Lock-exchange gravity current experiments are conducted in the flume with linear stratifications to provide data for the validation of the formulae. The comparisons between the calculated and measured data in terms of front location and front velocity show satisfactory agreements, which reveal that front velocity presents a rapid acceleration stage and then a deceleration stage in a linearly stratified ambient.