We analyse the linear stability of self-similar shallow two-dimensional and axisymmetric gravity currents of a viscous power-law non-Newtonian fluid in a porous medium. The flow domain is initially saturated by a fluid lighter than the intruding fluid, whose volume varies with time as .The transition between decelerated and accelerated currents occurs at = 2 for two-dimensional and at = 3 for axisymmetric geometry. Stability is investigated analytically for special values of and numerically in the remaining cases; axisymmetric currents are analysed only for radially varying perturbations.The two-dimensional currents are linearly stable for < 2 (decelerated currents) with a continuum spectrum of eigenvalues and unstable for = 2, with a growth rate proportional to the square of the fluid behavior index. The axisymmetric currents are linearly stable for any < 3 (decelerated currents) with a continuum spectrum of eigenvalues, while for = 3 no firm conclusion can be drawn. For > 2 (two-dimensional accelerated currents) and > 3 (axisymmetric accelerated currents) the linear stability analysis is of limited value since the hypotheses of the model will be violated.

Stability Analysis of Gravity Currents of a Power-Law Fluid in a Porous Medium / Longo, Sandro Giovanni; Di Federico, Vittorio. - In: MATHEMATICAL PROBLEMS IN ENGINEERING. - ISSN 1024-123X. - 2015:(2015), pp. 1-11. [10.1155/2015/286487]

Stability Analysis of Gravity Currents of a Power-Law Fluid in a Porous Medium

LONGO, Sandro Giovanni;
2015

Abstract

We analyse the linear stability of self-similar shallow two-dimensional and axisymmetric gravity currents of a viscous power-law non-Newtonian fluid in a porous medium. The flow domain is initially saturated by a fluid lighter than the intruding fluid, whose volume varies with time as .The transition between decelerated and accelerated currents occurs at = 2 for two-dimensional and at = 3 for axisymmetric geometry. Stability is investigated analytically for special values of and numerically in the remaining cases; axisymmetric currents are analysed only for radially varying perturbations.The two-dimensional currents are linearly stable for < 2 (decelerated currents) with a continuum spectrum of eigenvalues and unstable for = 2, with a growth rate proportional to the square of the fluid behavior index. The axisymmetric currents are linearly stable for any < 3 (decelerated currents) with a continuum spectrum of eigenvalues, while for = 3 no firm conclusion can be drawn. For > 2 (two-dimensional accelerated currents) and > 3 (axisymmetric accelerated currents) the linear stability analysis is of limited value since the hypotheses of the model will be violated.
Stability Analysis of Gravity Currents of a Power-Law Fluid in a Porous Medium / Longo, Sandro Giovanni; Di Federico, Vittorio. - In: MATHEMATICAL PROBLEMS IN ENGINEERING. - ISSN 1024-123X. - 2015:(2015), pp. 1-11. [10.1155/2015/286487]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2789132
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