Three-dimensional stability of vortices in a stratified fluid
Résumé
The three-dimensional linear stabilities of vertically uniform shear flows and vortex configurations (dipole, couple, von Karman street and double symmetric row) are investigated through experiments, theoretical and numerical analysis when the fluid is stratified. For strong stratification, all the vortex configurations are unstable to the zigzag instability associated to vertically sheared horizontal translations that develop spontaneously. The most unstable wavelength decreases with the strength of the stratification, whereas the maximum growthrate is independent of the stratification and solely proportional to the strain felt by the vortex core. Experiments and direct numerical simulation show that the zigzag instability eventually decorrelates the flow on the vertical. The zigzag instability is therefore a generic instability that constrains turbulent energy cascade in stratified fluid and contributes to structure oceanic and atmospheric flows.