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We characterize blob-hole structures as equilibrium solutions for potential vorticity (PV) conserving systems. To demonstrate this, we consider equilibrium statistical mechanics of PV conserving fluids. We calculate partition function and free energy of the system, under the constraints that the energy and all the moments of PV are conserved. Equilibrium solutions are obtained by minimizing the free energy. As an example of analytical solutions from this approach, we consider solutions that conserve the energy and potential enstrophy. The connection of the obtained solutions to blob-hole structures is discussed.

Blob-Hole Structures as Non-Axisymmetric Equilibrium Solutions for Potential Vorticity Conserving Fluids