Intrusive gravity currents propagating into two-layer stratified ambients: Vorticity modeling

Abstract

Intrusive gravity currents propagating into two-layer stratified ambients: Vorticity modeling M. A. Khodkar, M. M. Nasr-Azadani and E. Meiburg Department of Mechanical Engineering University of California at Santa Barbara Santa Barbara, CA 93106. Email: mkhodkar@umail.ucsb.edu Abstract A simplified model is developed for intrusive gravity currents propagating along the interface of a two- layer stratified ambient. The model is based on the conservation of mass and vorticity, and it does not require any empirical closure assumptions. A parametric study conducted with this model reproduces the correct behavior in various limits, and is consistent with previously reported experimental observations. Specifically, it predicts the formation of equilibrium intrusions when the intrusion density equals the depth-weighted mean density of the two ambient layers. It furthermore demonstrates the existence of non- smooth limits under certain conditions. An energy analysis shows that under non-equilibrium conditions the intrusion gains energy. The predictions by the parametric study are furthermore compared to two- dimensional DNS results, and very good agreement is observed with regard to all flow properties. 1. Introduction Intrusions represent a special class of gravity currents that propagate horizontally into a stratified ambient at intermediate depths. They occur in a variety of atmospheric and oceanic situations, where they can influence the dynamics of such flows as sea breeze fronts, river plumes and powder snow avalanches. Fig1. Schematic of an intrusion produced via a lock-release process: a) at the initial state, where all the fluids are at rest, b) when the gate is removed and a quasisteady, symmetric intrusion forms and c) when (𝜌 𝑙 𝑑 𝑙 + 𝜌 𝑢 𝑑 𝑢 )/𝐻 < 𝜌 𝑐 and a quasisteady, non-symmetric intrusion emerges.