Viscous Spreading Of Non-Newtonian Gravity Currents In Radial Geometry
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V. Di Federico, S. Cintoli & G. Bizzarri
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 selfsimilar 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. Keywords: non-Newtonian fluid, density current, gravity current, viscous flow, self-similar solution. 1 Introduction Gravity currents, also termed density or buoyancy currents, are usually defined as flow of one fluid into another, driven by a density difference. These currents are mainly horizontal and are a common feature in many natural and artificial phenomena. Spreading of a gravity current along a rigid horizontal surface is governed by an interplay between buoyancy, inertial, and viscous forces. In the process, a gravity current passes through several distinct flow regimes which are characterized by the relative balance of forces. Immediately after its release, a gravity current usually experiences an adjustment phase that is strongly influenced by the release conditions. Subsequently, the balance between the buoyancy and inertial forces governs flow (this phase being thus termed the inertial regime) and holds until the current becomes so thin that viscous effects
non-Newtonian fluid, density current, gravity current, viscous flow, self-similar solution.