Near-Inertial Oscillations of a Barotropic Vortex: Trapped Modes and Time Evolution

Abstract

Amplified motions in vortices have been observed in Gulf Stream rings and over seamounts. This paper uses the near-inertial oscillation approximation to model near-inertial motions in the presence of a barotropic vortical background flow. The resulting trapped modes are calculated: there is always at least one such mode, but higher modes may exist and these are obtained. The characteristics of the trapped mode depend on the quantity Γ/f0R2n where Γ is the circulation (integrated vorticity) of the ring, f0 is the local Coriolis frequency, and Rn is the nth Rossby radius of deformation, which may be interpreted as a combined measure of the vertical length scale and stratification. Asymptotic expressions are presented for the frequency of the gravest radial mode for strong and weak vortices. The calculated frequencies are compared to previous results, and good agreement is obtained. The initial value problem is also studied: the contribution of the trapped modes to the evolution of the near-inertial wave field is calculated, as is the contribution due to the continuous spectrum. The long time behavior of the continuous spectrum decays like (lnt)?1 and takes different forms in the vortex core and far from the vortex.