Viscous Spreading of Non-Newtonian Gravity Currents on a Plane |
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Authors: | Vittorio Di Federico Stefano Malavasi Stefano Cintoli |
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Institution: | (1) D.I.S.T.A.R.T, Idraulica Università di Bologna, V. Risorgimento 2, 40136 Bologna, Italy;(2) D.I.A.A.R., Politecnico di Milano, P.zza Leonardo da Vinci 32, 20133 Milano, Italy |
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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 special 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. |
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Keywords: | Non-Newtonian fluids Gravity current Viscous flow Self-similar solution Fluid mechanics |
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