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, x N 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.

Propagation of viscous gravity currents inside confining boundaries: the effects of fluid rheology and channel geometry

“…These studies were mainly aimed at obtaining the rate of propagation over time of a current generated by the release of a constant or time variable volume of fluid. Their results were substantiated by the experiments conducted by various researchers [24][25][26]. The accumulated body of knowledge allows, in principle, using controlled experiments as rheometers to determine the fluid parameters [26,27].…”

Anatomy and propagation dynamics of continuous-flux release bottom gravity currents through emergent aquatic vegetation

“…5, exhibited a similar trend as the viscous propagation trend, the data were more closely correlated to the wall jet propagation. 7,45 The phase transition times and distances are tabulated in Table III. Table II indicates that the total viscous force (including both the bottom shear and vegetation drag forces) dominated over the inertia force at the instant when the current transitioned into the drag-dominated phase for all of our experimental runs.…”

“…(8) is proposed for C D by correlating our experimental C D values and the dimensionless parameters listed in Eq. (7). The experimental C D values were estimated from Eq.…”

“…Nevertheless, if the viscous forces dominate over the inertia force before the jet phase terminates, the gravity current may by-pass the inertia-buoyancy phase and undergo the viscous-buoyancy phase. 7 The propagation characteristics of the inertial and viscous currents are distinct. For example, for constant-flux currents mathematical models predict the current front position (x f )-time (t) dependency as: x f ∝ t for inertia-buoyancy propagation phase and x f ∝ t 2n+2/2n+3 for the viscous-buoyancy propagation phase.…”

“…For example, for constant-flux currents mathematical models predict the current front position (x f )-time (t) dependency as: x f ∝ t for inertia-buoyancy propagation phase and x f ∝ t 2n+2/2n+3 for the viscous-buoyancy propagation phase. 8,9,2,7,10 Here, n is the flow behavior index from the Ostwald power-law model with n = 1 for Newtonian fluids. These theoretical predictions, supported by experimental observations (e.g., Refs.…”