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

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 ( t R ), and find that t R ∼ 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 t R by an amount roughly proportional to 1/ Fr . For some Fr , stratification effects overwhelm the deformative effect, and complete reconnection results.