Optimal Perturbations of a Counter-rotating Vortex Pair in Stratified Flows

Abstract eng:
This paper investigates the three dimensional perturbations developping on a pair of horizontal counter-rotating vortices in stably stratified flow. The 2D flow is unsteady and the stability is reformulated by searching transient energy growth of perturbations around a time varying flow. For weak and moderate stratifications (large Froude numbers), the stratification acts on a long timescale compared to the advection time of the dipole, when 3D instabilities are added, transient analysis at different instant retrieves the instability peaks corresponding to the Crow instability for the long wavelengths and to the elliptic instability. This shows the validity of the quasi-steady approximation and that stratification destabilizes the flow by bringing vortices closer. For strong stratifications (Froude numbers smaller than 2), the quasi-steady approximation is not valid. Optimal perturbations depart from their homogeneous counterpart with large perturbation in the wake of the dipole associated with density effects.

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