Gravity current propagating against constant and pulsating counter flows

Abstract

This paper describes the evolution of two-dimensional (2D) gravity currents that flow against a horizontally uniform laminar pulsating flow. We study the effect of opposing mean flow amplitude and the oscillatory velocity amplitude on the evolution of the gravity current, the emergence of instabilities due to shear at the interface of heavy and light fluid and unstable density stratification near the bottom wall, and the associated density redistributions. The velocity amplitudes and the oscillation frequency are reminiscent of tidal estuarine flows. This study revealed two key processes affecting the horizontal density transport of the heavy fluid, in addition to the buoyancy-driven propagation of the gravity current. The first process concerns the presence of shear-driven Kelvin-Helmholtz (KH) billows, depending on the strength of the opposing mean flow and the thickness of the gravity current. These KH billows are generated in the inertial phase of gravity current propagation and are responsible for coherent advective transport of heavy-fluid patches away from the gravity current head. The second process is related to the lifting of the gravity current head due to differential advection near the bottom wall when the propagation direction of the gravity current and the oscillating externally imposed flow are in the same direction. It generates a layer of light fluid below the heavy fluid of the gravity current head and becomes unstable when the ambient flow opposes the gravity current propagation, generating Rayleigh-Taylor-like (RT-like) instabilities. This results in a strong vertical redistribution of light and heavy fluid. Non-hydrostatic effects, such as the presence of KH billows and RT-like instabilities, with associated vertical density transport, have significant implications for large-scale horizontal density transport and modeling of salt intrusions in rivers and estuaries.