Gravity currents propagating into ambients with arbitrary shear and density stratification: vorticity‐based modelling

Abstract

We develop a vorticity-based approach for modelling quasi-steady, supercritical gravity currents propagating into a finite-height channel with arbitrary density and velocity stratification. The model enforces the conservation of mass, horizontal and vertical momentum. In contrast to previous approaches, it does not rely on empirical, energybased closure assumptions. Instead, the effective energy loss of the flow can be calculated a posteriori. The present model results in the formulation of a second-order, nonlinear ordinary differential equation (ODE) that can be solved in a straightforward fashion to determine the gravity-current velocity, along with the downstream ambient velocity and density profiles. Comparisons between model predictions and direct numerical simulations (DNS) show excellent agreement. Furthermore, they indicate that, for high Reynolds numbers, the gravity-current height adjusts itself so as to maximize the loss of energy.

Impact of ambient stable stratification on gravity currents propagating over a submerged canopy

“…Shin, Dalziel & Linden 2004;Cantero et al 2007;Ooi, Constantinescu & Weber 2009) or stably stratified (e.g. Birman & Meiburg 2007;Venayagamoorthy & Fringer 2007;Nicholson & Flynn 2015;Nasr-Azadani & Meiburg 2016). During the advancement of a gravity current, it may be subject to the influences of bottom roughness/submerged canopies consisting of distributed drag elements that occupy a portion of the flow depth.…”

An Analytical Solution to the Perturbation Analysis of the Interaction between Downburst Outflows and Atmospheric Boundary Layer Winds

“…A number of analytical models of downburst outflows has been proposed over the years. These models can be categorized into 1) gravity-current (von Kármán 1940;Benjamin 1968;Bryan and Rotunno 2008;Hogg et al 2016;Nasr-Azadani and Meiburg 2016), 2) semiempirical (e.g., impinging-jetlike) (Oseguera and Bowles 1988;Vicroy 1991;Chay et al 2006;Xhelaj et al 2020), and 3) ring-vortex models (Zhu and Etkin 1985;Ivan 1986;Schultz 1990). A recent review of the analytical formulations in the latter two categories is provided in Romanic and Hangan (2020).…”

Characteristics of colliding density currents: A numerical and theoretical study

“…s*() used the vorticity formulation to model the phenomenon of cold pools in shear flows. Xu and Moncrieff () also recognized the “importance of vorticity dynamics for the local flow in the vicinity of a density current.” Furthermore, Nasr‐Azadani and Meiburg () have developed a vorticity‐based model of quasi‐steady and supercritical ( Fr > 1) gravity currents.…”