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Viscous Spreading of Non-Newtonian Gravity Currents on a Plane

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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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Authors and Affiliations

  1. D.I.S.T.A.R.T, Idraulica Università di Bologna, V. Risorgimento 2, 40136, Bologna, Italy

    Vittorio Di Federico & Stefano Cintoli

  2. D.I.A.A.R., Politecnico di Milano, P.zza Leonardo da Vinci 32, 20133, Milano, Italy

    Stefano Malavasi

Authors
  1. Vittorio Di Federico
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  2. Stefano Malavasi
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  3. Stefano Cintoli
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Correspondence to Vittorio Di Federico.

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Federico, V.D., Malavasi, S. & Cintoli, S. Viscous Spreading of Non-Newtonian Gravity Currents on a Plane. Meccanica 41, 207–217 (2006). https://doi.org/10.1007/s11012-005-3354-9

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  • DOI: https://doi.org/10.1007/s11012-005-3354-9

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