Publication Date:
2015-01-01
Description:
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 astα. The transition between decelerated and accelerated currents occurs atα= 2 for two-dimensional and atα= 3 for axisymmetric geometry. Stability is investigated analytically for special values ofαand numerically in the remaining cases; axisymmetric currents are analysed only for radially varying perturbations. The two-dimensional currents are linearly stable forα〈 2 (decelerated currents) with a continuum spectrum of eigenvalues and unstable forα= 2, with a growth rate proportional to the square of the fluid behavior index. The axisymmetric currents are linearly stable for anyα〈 3 (decelerated currents) with a continuum spectrum of eigenvalues, while forα= 3 no firm conclusion can be drawn. Forα〉 2 (two-dimensional accelerated currents) andα〉 3 (axisymmetric accelerated currents) the linear stability analysis is of limited value since the hypotheses of the model will be violated.
Print ISSN:
1024-123X
Electronic ISSN:
1563-5147
Topics:
Mathematics
,
Technology
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