 Stability Analysis of Gravity Currents of a Power-Law Fluid in a Porous MediumSandro Longo and Vittorio Di Federico Mathematical Problems in Engineering, 2015, vol. 2015, 1-11 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 α = 2 for two-dimensional and at α = 3 for axisymmetric geometry. Stability is investigated analytically for special values of α and numerically in the remaining cases; axisymmetric currents are analysed only for radially varying perturbations. The two-dimensional currents are linearly stable for α < 2 (decelerated currents) with a continuum spectrum of eigenvalues and unstable for α = 2, with a growth rate proportional to the square of the fluid behavior index. The axisymmetric currents are linearly stable for any α < 3 (decelerated currents) with a continuum spectrum of eigenvalues, while for α = 3 no firm conclusion can be drawn. For α > 2 (two-dimensional accelerated currents) and α > 3 (axisymmetric accelerated currents) the linear stability analysis is of limited value since the hypotheses of the model will be violated. Date: 2015 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:286487 DOI: 10.1155/2015/286487 Access Statistics for this article More articles in Mathematical Problems in Engineering from Hindawi |
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