Negative potential vorticity lenses

Abstract

The dynamical properties of inviscid fluid lenses, which rotate faster than the local Coriolis, were studied through numerical experiments. Such lenses have negative potential vorticity and generally require nonlinear dynamical balances. A solution scheme was used that preserved exactly the relevant nonlinearity of the Euler equations. The experiments described here were designed to determine how the lens evolution depends upon initial conditions. When the lens is isolated from background flows it was found that large initial anticyclonic particle spin tends to produce quasi-periodic behavior in the hydrodynamic fields. On the other hand, large initial deformation produced erratic solutions with both subinertial and superinertial frequency components. An investigation of the response of an initially circular lens to a steady background deforming flow was made. Two equilibrium solutions were found for this setting. The boundary between the equilibrium solutions and oscillating solutions was found to be extremely sensitive to initial conditions and other model parameters. However, as initial spin magnitude was increased, a decrease in the magnitude of environmental deformation required to achieve either equilibrium configuration was observed.