An upper bound on the size of sub-mesoscale coherent Vortices

Abstract

Laboratory experiments show that ageostrophic instability can "break up" a parallel flow into a sequence of axisymmetric eddies. This is a plausible scenario for the generation of sub-mesoscale coherent Vortices (SCVs). Here we show that conservation of mass, energy and potential vorticity enables one to very simply calculate the radius of the axisymmetric eddy and the wavelength of the nonlinear instability. The latter agrees more closely with laboratory experiments than does the wavelength predicted by linearized stability theory. It energy is not conserved, say because of wave radiation into the lower layer, then the preceding calculation establishes an upper bound on the radius of the eddy. We offer this as an explanation of the observed small size of SCVs.