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

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 less than or equal to 2) further alters the growth of the instability via advection by baroclinically produced vorticity. For all of our cases with Fr greater than or equal to 1 (including our unstratified cases where Fr --> infinity), 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) similar to 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 greater than or equal to 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.