Stabilizing and destabilizing effects of a solid-body rotation on quasi-two-dimensional shear layers

The effect of a solid-body rotation, characterized by an angular velocity Ω, on a two-dimensional mixing layer (in a plane perpendicular to Ω) of relative vorticity ω_2D, upon which is superposed a small three-dimensional turbulent perturbation, is considered. Using the Kelvin theorem in the frame rotating with il, and with the aid of arguments based on the straining of absolute vortex filaments by the basic velocity, it is shown that the rotation is always stabilizing (with respect to the nonrotating case) in the cyclonic case. In the anticyclonic case, a slight rotation is destabilizing. At a local Rossby number R₀ = |ω_2D|/ 2|Ω| of the order of 1, the anticyclonic rotation disrupts catastrophically the coherent structures of the mixing layer. Anticyclonic rotation becomes stabilizing again for R₀ <0.5. Also presented are three-dimensional numerical simulations which support the theory, and agree qualitatively with experimental results. The consequences for oceanic and atmospheric vortices are briefly discussed.