Numerical investigation into the turbulence of an unsteady gravity current

Abstract

Unsteady gravity currents are flow processes developing after the intrusion of a fluid into a quiescent environment of lower density. The intense and complex turbulence dynamics developing at the interface between the two fluids contribute to a large range of interactions between the current and its surroundings; including entrainment and transport of large masses of fluid such as stagnant pollutants in coastal and urban areas, or damage to subaqueous infrastructure on its path due to the strain applied by both the current’s passage and the subsequent local turbulent strain. The study focuses on a two-dimensionally propagating gravity current over a mild slope. The local flow turbulence in the mixing layer of an unsteady channel gravity current is numerically investigated. The flow was modelled as a Boussinesq buoyant-driven flow using the inhouse Navier-Stokes solver SnS and a standard Smagorinsky large eddy simulation (LES) model. LES allows the investigation of fully turbulent flows that cannot otherwise be simulated due to computer limitations. The model is shown to predict well the bulk structure of the current as well as the local flow instabilities responsible for the growth of turbulence in the mixing layer, and recommendations are given for the choice of the grid resolution for a well-resolved- LES of gravity currents. Turbulence was statistically investigated by computing the averaged flow and turbulence statistics by ensemble- and spanwise-averaging 200 simulation results at two time instants, characteristic of two main propagation phases of the current, namely the slumping phase and the inertial phase. It is shown that the characteristic structure of a dense frontal head followed by a body akin to a stratified shear layer can be directly correlated to the growth, decay and changes in the isotropy of turbulence along the mixing layer. The stability of the mixing layer is found to be governed by the flux Richardson number at the limit of the head whereas the gradient Richardson number describes well the fading of the Kelvin-Helmholtz instabilities and the establishment of a region of dynamical quasi-stationarity in the body. In contrast with planar stratified shear layers where buoyancy is strictly dissipative, the motion is here shown to be partly supplied by buoyancy produced turbulence through energy backscatter at the front. This process is expected to extend farther inside the body with increasing bed slopes, and the mixing layer to develop substantially different turbulence and mixing dynamics than the ones implied here at sufficiently high bed slopes.