Viscous gravity currents over flat inclined surfaces

Previous analyses of the flow of low-Reynolds-number, viscous gravity currents down inclined planes are investigated further and extended. Particular emphasis is on the motion of the fluid front and tail, which previous analyses treated somewhat cavalierly. We obtain reliable, approximate, analytic solutions in these regions, the accuracies of which are satisfactorily tested against our numerical evaluations. The solutions show that the flow has several time scales determined by the inclination angle, a. At short times, the influence of initial and boundary conditions is important and the flow is governed by both the pressure gradient and the direct action of gravity due to inclination. Later on, the areas where the boundary conditions are important shrink. This fact explains why previous solutions, being inaccurate near the front and the tail, described experimental data with high accuracy. At larger times, of the order of alpha(-5)(/2), the influence of the pressure gradient may be neglected and the fluid profile converges to the square-root shape predicted in previous works. Important extensions of our approach are also outlined.