Stable and unstable vortices attached to seamounts

Abstract

We examine the properties of stationary, barotropic flows over isolated topographic features such as seamounts. According to a general variational principle, flows that maximize or minimize the energy in a set of isovortical flows are stationary and stable. Using this, it is shown that a large class of stable and stationary attached anticyclones exists at a seamount. Those with positive potential vorticity (PV) are maximum energy states, while those with negative PV are minimum energy states. If the seamount is circular, there are also stable attached cyclones, but these are destabilized by irregularities in the topographic shape, unlike the anticyclones. Numerical simulations broadly support these theoretical predictions, but also highlight the importance of time-dependent processes, particularly in cases in which the vortex collides with the seamount.