Viscous spreading of non-Newtonian gravity currents in radial geometry

A gravity current originated by a power-law viscous fluid propagating in axisymmetric geometry on a horizontal rigid plane below a fluid of lesser density is examined. The intruding fluid is considered to have a pure power-law constitutive equation. The set of equations governing the flow is presented, under the assumption of buoyancy-viscous balance and negligible inertial forces. The conditions under which the above assumptions are valid are examined and a self-similar solution in terms of a nonlinear ordinary differential equation is derived for the release of a fixed volume of fluid. The space-time development of the gravity current is discussed for different flow behavior indexes.