High-resolution simulations of non-Boussinesq downslope gravity currents in the acceleration phase

Abstract

Gravity currents generated from an instantaneous buoyancy source of density contrast in the density ratio range of 0.3 ≤ γ ≤ 0.998 propagating downslope in the slope angle range of 0° ≤ θ < 90° have been investigated in the acceleration phase by means of high-resolution two-dimensional simulations of the incompressible variable-density Navier-Stokes equations. For all density contrasts considered in this study, front velocity history shows that, after the heavy fluid is released from rest, the gravity currents go through the acceleration phase, reaching a maximum front velocity Uf,max, followed by the deceleration phase. It is found that Uf,max increases as the density contrast increases and such a relationship is, for the first time, quantitatively described by the improved thermal theory considering the non-Boussinesq effects. Energy budgets show that, as the density contrast increases, the heavy fluid retains more fraction of potential energy loss while the ambient fluid receives less fraction of potential energy loss in the process of energy transfer during the propagation of downslope gravity currents. Previously, it was reported that for the Boussinesq case, the downslope gravity currents have a maximum of Uf,max at θ ≈ 40°. It is found, as is also confirmed by the energy budgets in this study, that the slope angle at which the downslope gravity currents have a maximum of Uf,max may increase beyond 40° as the density contrast increases.