Intrusive gravity currents from finite-length locks in a uniformly stratified fluid

Abstract

Gravity currents intruding into a uniformly stratified ambient are examined in a series of finite-volume full-depth lock-release laboratory experiments and in numerical simulations. Previous studies have focused on gravity currents which are denser than fluid at the bottom of the ambient or on symmetric cases in which the intrusion is the average of the ambient density. Here, we vary the density of the intrusion between these two extremes. After an initial adjustment, the intrusions and the internal waves they generate travel at a constant speed. For small departures from symmetry, the intrusion speed depends weakly upon density relative to the ambient fluid density. However, the internal wave speed approximately doubles as the waves change from having a mode-2 structure when generated by symmetric intrusions to having a mode-1 structure when generated by intrusions propagating near the bottom. In the latter circumstance, the interactions between the intrusion and internal waves reflected from the lock-end of the tank are sufficiently strong and so the intrusion stops propagating before reaching the end of the tank. These observations are corroborated by the analysis of two-dimensional numerical simulations of the experimental conditions. These reveal a significant transfer of available potential energy to the ambient in asymmetric circumstances.

A general description of a gravity current front propagating in a two-layer stratified fluid

“…A possible explanation for this distinction is that a Boussinesq fluid with uniform stratification does not support internal solitary waves of the classic KdV type; however, nonlinear internal waves governed by a related equation are possible (Grimshaw & Yi 1991). This seems consistent with Munroe et al (2009), who found significant energy transfers (up to 22 %) to upstream disturbances in a linearly stratified system.…”

A steady-state model for asymmetric intrusive gravity currents in a linearly stratified ambient

“…This creates a non-trivial gap between the present results and the available experimental data and "intuition", derived mostly from lock-release flows. Moreover, the available data are typically for a full-depth, not-small height/length lock, and are subject to oscillations produced at release (see Bolster et al [4]; Munroe et al [8]); the resulting strong return oscillatory flow in the ambient and nose-waves interactions, are clearly very different from the present problem. A sharper evaluation of the reliability of the insights provided by the present theory require new experiments and numerical simulations.…”

“…In this setup the intrusion can be solved rigorously as a superposition of two mirror-image boundary currents above and below the neutralbuoyancy level. Various related experimental and numerical investigation have been presented, e.g., Cheong et al [5], Bolster et al [4], and Munroe et al [8]. We must stress that these studies were concerned with the lock-release time-dependent problem.…”

On the performance of high resolution non-oscillating advection schemes in the context of the flow generated by a mixed region in a stratified fluid

“…From Eq. (21), one can see that if Ψ = 0 we find the upwind scheme, and if Ψ = 1 the scheme is reduced to the central one. The following limiter functions are used in this study [15]: The Minmod and Superbee limiters were introduced by Roe [23] and Roe and Sidilkover [24].…”

“…The interest in this problem stems from the study of a number of geophysical phenomena and a number of technical problems [7,16,18,19,26,21]. For example, because the turbulent wake behind a body traveling through stratified fluid is very slender in the direction of body motion, the flow field and internal waves induced by the wake can be adequately described by studying the collapse of a non-turbulent mixed region in stratified medium [9,16,20,29,30].…”