Abstract
A flow that maximizes or minimizes the energy in a set of isovortical flows is stationary and stable. For example, in ideal, two-dimensional flow, a circular vortex with a monotonic vorticity profile is a maximum energy flow, and therefore stable. An overview is given of more complex flows to which this analysis can be extended. A large class of stable and localised vortex solutions exists when the background is a linear shear flow. The vortex is elongated in the direction of the background flow, and its vorticity anomaly must have the same sign as the background shear. The method is also applied to vortices attached to seamounts. It is found that a large class of stable anticyclones exists. If the seamount is circular there are also stable cyclones, but these are destabilized by noncircularities in the topographic shape, unlike the anticyclones. The results both for vortices in shear flows and vortices attached to seamounts can be extended from two-dimensional barotropic flow to three-dimensional quasigeostrophic flow.
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Nycander, J. (2003). Stable Vortices as Maximum or Minimum Energy Flows. In: Velasco Fuentes, O.U., Sheinbaum, J., Ochoa, J. (eds) Nonlinear Processes in Geophysical Fluid Dynamics. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0074-1_5
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DOI: https://doi.org/10.1007/978-94-010-0074-1_5
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