Near-inertial oscillations of a barotropic vortex: Trapped modes and time evolution

Amplified motions in vortices have been observed in Gulf Stream rings and o ver seamounts. This paper uses the near-inertial oscillation approximation to model near-inertial motions in the presence of a barotropic vortical bac kground flow. The resulting trapped modes are calculated: there is always a t least one such mode, but higher modes may exist and these are obtained. T he characteristics of the trapped mode depend on the quantity Gamma/f(0)R(n )(2) where Gamma is the circulation (integrated vorticity) of the ring, f(0 ) is the local Coriolis frequency, and R-n is the nth Rossby radius of defo rmation, which may be interpreted as a combined measure of the vertical len gth scale and stratification. Asymptotic expressions are presented for the frequency of the gravest radial mode for strong and weak vortices. The calc ulated frequencies are compared to previous results, and good agreement is obtained. The initial value problem is also studied: the contribution of th e trapped modes to the evolution of the near-inertial wave field is calcula ted, as is the contribution due to the continuous spectrum. The long time b ehavior of the continuous spectrum decays like (lnt)(-1) and takes differen t forms in the vortex core and far from the vortex.