TY - JOUR

T1 - Stability of gravity currents generated by finite-volume releases

AU - Mathunjwa, Jochonia S.

AU - Hogg, Andrew J.

PY - 2006/9/10

Y1 - 2006/9/10

N2 - We generalize the linear stability analysis of the axisymmetric self-similar solution of gravity currents from finite-volume releases to include perturbations that depend on both radial and azimuthal coordinates. We show that the similarity solution is stable to sufficiently small perturbations by proving that all perturbation eigenfunctions decay in time. Moreover, asymmetric perturbations are shown to decay more rapidly than axisymmetric perturbations in general. An asymptotic formula for the eigenvalues is derived, which indicates that asymptotic rates of decay of perturbations are given by t-σ where 0 < σ < 1/4 as the Froude number decreases from √2 to 0. We demonstrate that this formula agrees closely with numerically calculated eigenvalues and, in the absence of azimuthal dependence, it reduces to an expression that improves on the asymptotic formula obtained by Grundy & Rottman (1985). For two-dimensional (planar) currents, we further prove analytically that all perturbation eigenfunctions decay like t-1/2.

AB - We generalize the linear stability analysis of the axisymmetric self-similar solution of gravity currents from finite-volume releases to include perturbations that depend on both radial and azimuthal coordinates. We show that the similarity solution is stable to sufficiently small perturbations by proving that all perturbation eigenfunctions decay in time. Moreover, asymmetric perturbations are shown to decay more rapidly than axisymmetric perturbations in general. An asymptotic formula for the eigenvalues is derived, which indicates that asymptotic rates of decay of perturbations are given by t-σ where 0 < σ < 1/4 as the Froude number decreases from √2 to 0. We demonstrate that this formula agrees closely with numerically calculated eigenvalues and, in the absence of azimuthal dependence, it reduces to an expression that improves on the asymptotic formula obtained by Grundy & Rottman (1985). For two-dimensional (planar) currents, we further prove analytically that all perturbation eigenfunctions decay like t-1/2.

UR - http://www.scopus.com/inward/record.url?scp=33749001739&partnerID=8YFLogxK

U2 - 10.1017/S002211200600108X

DO - 10.1017/S002211200600108X

M3 - Article (Academic Journal)

AN - SCOPUS:33749001739

SN - 0022-1120

VL - 562

SP - 261

EP - 278

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

ER -