DOI 10.1007/s11012-005-3354-9 Meccanica (2006) 41:207–217 © Springer 2006 Viscous Spreading of Non-Newtonian Gravity Currents on a Plane VITTORIO DI FEDERICO ∗ , STEFANO MALAVASI 1 and STEFANO CINTOLI D.I.S.T.A.R.T. - Idraulica, Universit` a di Bologna, V. Risorgimento 2, 40136 Bologna, Italy; 1 D.I.A.A.R., Politecnico di Milano, P.zza Leonardo da Vinci 32, 20133 Milano, Italy (Received: 13 October 2003; accepted in revised form: 29 August 2005) Abstract. A gravity current originated by a power-law viscous fluid propagating on a horizontal rigid plane below a fluid of lower density is examined. The intruding fluid is considered to have a pure Ostwald 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 time-variable volume of fluid, the shape of the gravity current is determined numerically using an approximate analytical solution derived close to the current front as a starting condition. A closed-form analytical expression is derived for the spe- cial case of the release of a fixed volume of fluid. The space-time development of the gravity current is discussed for different flow behavior indexes. Key words: Non-Newtonian fluids, Gravity current, Viscous flow, Self-similar solution, Fluid mechanics. 1. Introduction Gravity current, also termed density or buoyancy current, is 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 cur- rent passes through several distinct flow regimes that are characterized by the relative balance of forces. Typically, immediately after its release a gravity current enters an adjustment phase that is strongly influenced by the release conditions. Subsequently, the balance between the buoyancy and inertial forces governs flow (this phase is termed the inertial regime) and lasts until the current becomes so thin that viscous effects become comparable with the inertia of the current, if this ever happens. In this later stage (the viscous regime), flow is governed by the buoyancy and viscous forces. Typical currents, that eventually evolve into the viscous regime, include mud- flows, lava flows, and those originating by discharge of effluents into rivers or lakes. A large body of literature exists on gravity currents in different geophysical [1], environmental and industrial applications (for a review see Simpson [2, 3]). Hori- zontal gravity currents were studied by Hoult [4], Huppert and Simpson [5], and Didden and Maxworthy [6] among others. Huppert [7] derived, under a lubrication ∗ Author for correspondence: e-mail: vittorio.difederico@mail.ing.unibo.it