Instabilities and transient growth of trailing vortices in stratified fluid

The wake, which forms behind an aircraft due to its lift, is a pair of horizontal counter-rotating vortices propagating downwards. Depending on the atmospheric conditions, such dipole can persist over a long time or be rapidely destroyed. This vortex pair, in homogeneous fluids, is unstable with respect to three-dimensional perturbations. Crow [1] has discovered a long-wavelength instability, symmetric with respect to the plane separating the two vortices. The existence of a short-wavelength elliptic instability has been revealed by Tsai & Widnall [2], Moore & Saffman [3] and numerous articles ever since for both symmetric and antisymmetric modes. Recently Donnadieu et al. [4] observed a novel oscillatory instability, less unstable than Crow and elliptic odes, for large Reynolds numbers. However, in many atmospheric situations, as such dipoles propagate downwards, they evolve under the influence of the stable stratification of the atmosphere. The three-dimensional dynamics of this vortex pair in stratified flow, has received much less attention: still Robins & Delisi [5] and Garten et al. [6] have discussed persistance of the Crow instability and Nomura et al. [7] of the short-wavelength instability.