Viscous propagation of two-dimensional non-Newtonian gravity currents

Abstract

This paper presents the results of a detailed experimental and theoretical investigation on the viscous propagation of non-Newtonian gravity currents. Laboratory gravity currents are generated in a horizontal rectangular tank by releasing a constant flux of high-concentration fluid mud suspensions that exhibit profound non-Newtonian (shear thinning) behavior. Experimental observations on the propagation of fluid mud gravity currents revealed that viscous propagation of these currents was typically preceded by two phases as expected: an initial momentum-driven horizontal buoyant wall jet and a buoyancy-driven inertial phase. The experimental transition times, t**, and positions, x**, at which fluid mud gravity currents transition into viscous propagation phase were determined. The experimental data that correspond to the viscous propagation of fluid mud gravity currents (i.e. experimental time, t ⩾ t**, and front position, xN ⩾ x**) were used to evaluate the predictive capabilities of two well-known mathematical modeling approaches: the lubrication theory approximation and the box-model approaches. Regarding the lubrication theory approximation, a recently developed self-similarity solution for viscous propagation of power-law gravity currents that has not been experimentally evaluated was used. Regarding the box-model approach, a viscous box-model solution for two-dimensional (2D) non-Newtonian gravity currents was developed. The evaluation of these models using experimental data revealed that both models were in good agreement with the experimental observations, despite several simplifying assumptions embedded in each. Given its more advanced mathematical development, the lubrication theory approximation model provides a more complete description of a gravity current (i.e. shape and velocity variation along the gravity current) than the box model at the expense of a relatively simple computational effort.