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Direct numerical simulations of the Crow instability and subsequent vortex reconnection in a stratified fluid

Published online by Cambridge University Press:  12 January 2001

J. F. GARTEN ,
J. WERNE ,
D. C. FRITTS  and
S. ARENDT
J. F. GARTEN
Affiliation:
Colorado Research Associates, 3380 Mitchell Lane, Boulder, CO 80301, USA Program in Atmospheric and Oceanic Sciences, University of Colorado, Boulder, CO 80309-0311, USA Current address: Space Physics Research Laboratory, 2455 Hayward St., University of Michigan, Ann Arbor, MI 48109, USA.
J. WERNE
Affiliation:
Colorado Research Associates, 3380 Mitchell Lane, Boulder, CO 80301, USA
D. C. FRITTS
Affiliation:
Colorado Research Associates, 3380 Mitchell Lane, Boulder, CO 80301, USA Program in Atmospheric and Oceanic Sciences, University of Colorado, Boulder, CO 80309-0311, USA
S. ARENDT
Affiliation:
Colorado Research Associates, 3380 Mitchell Lane, Boulder, CO 80301, USA
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Abstract

The evolution of a vertically propagating three-dimensional vortex pair in ambient stratification is studied with a three-dimensional numerical model. We consider a range of Reynolds (Re) and Froude (Fr) numbers, and initialize the vortex pair in a configuration that promotes growth of the Crow instability (Crow 1970). The growth rate of the instability is Re dependent, and we present a method for extending Crow's model to predict this dependence. We also find that relatively strong ambient stratification (Fr [les ] 2) further alters the growth of the instability via advection by baroclinically produced vorticity. For all of our cases with Fr [ges ] 1 (including our unstratified cases where Fr → ∞), the instability leads to vortex reconnection and formation of a vortex ring. A larger Re delays the commencement of the reconnection, but it proceeds more rapidly once it does commence. We compute a reconnection time scale (tR), and find that tR ∼ 1/Re, in agreement with a model formulated by Shelley et al. (1993). We also discuss a deformative/diffusive effect (related to yet distinct from the curvature reversal effect discussed by Melander & Hussain 1989) which prevents complete reconnection. Ambient stratification (in the range Fr [ges ] 1) accelerates the reconnection and reduces tR by an amount roughly proportional to 1/Fr. For some Fr, stratification effects overwhelm the deformative effect, and complete reconnection results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 426 , 10 January 2001 , pp. 1 - 45
Copyright
© 2001 Cambridge University Press

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