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

Gravity currents generated from an instantaneous buoyancy source propagating down a slope in the range of 0∘ ≤ θ < 90∘ have been investigated in the acceleration phase by means of high-resolution two-dimensional simulations of the incompressible Navier-Stokes equations with the Boussinesq approximation. Front velocity history shows that, after the heavy fluid is released from rest, the flow goes through the acceleration phase, reaching a maximum front velocity Uf,max, and followed by the deceleration phase. The existence of a maximum of Uf,max is found near θ = 40∘, which is supported by the improved theory. It is identified for the first time that the time of acceleration decreases as the slope angle increases, when the slope angle is approximately greater than 10∘, and the time of acceleration increases as the slope angle increases for gravity currents on lower slope angles. A fundamental difference in flow patterns, which helps explain the distinct characteristics of gravity currents on high and low slope angles using scaling arguments, is revealed. Energy budgets further show that, as the slope angle increases, the ambient fluid is more easily engaged in the gravitational convection and the potential energy loss is more efficiently converted into the kinetic energy associated with ambient fluid. The propagation of gravity currents on a slope is found to be qualitatively modified as the depth ratio, i.e., the lock height to channel height ratio, approaches unity. As the depth ratio increases, the conversion of potential energy loss into the kinetic energy associated with heavy fluid is inhibited and the conversion into the kinetic energy associated with ambient fluid is enhanced by the confinement of the top wall.