Abstract
The mass anomaly associated with piecewise constant symmetric potential vorticity (PV) vortices in rotating and stratified fluids is investigated. It is found that the absolute value of this mass anomaly depends linearly on the distance to the vortex centre and is therefore unbounded. This property of PV ball vortices is found under quasi‐geostrophic and semi‐geostrophic approximations, as well as the more general Euler dynamics. To overcome this difficulty, a new class of vortices is introduced. These vortices occupy, in all senses, a limited amount of volume and are therefore bounded. Unlike PV ball vortices, which have homogeneous PV, the new vortices have a central core of continuous PV of one sign and an outer shell of opposite signed PV, such that the amount of PV anomaly is zero.
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