Direct numerical simulations of the Crow instability and subsequent vortexreconnection 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 initiali ze the vortex pair in a configuration that promotes growth of the Crow inst ability (Crow 1970). The growth rate of the instability is Re dependent, an d 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 b y baroclinically produced vorticity. For all of our cases with Fr greater t han or equal to 1 (including our unstratified cases where Fr --> infinity), the instability leads to vortex reconnection and formation of a vortex rin g. 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 formul ated by Shelley et al. (1993). We also discuss a deformative/diffusive effe ct (related to yet distinct from the curvature reversal effect discussed by Melander & Hussain 1989) which prevents complete reconnection. Ambient str atification (in the range Fr greater than or equal to 1) accelerates the re connection and reduces t(R) by an amount roughly proportional to 1/Fr. For some Fr, stratification effects overwhelm the deformative effect, and compl ete reconnection results.