Annular self-organization of the two-dimensional vorticity condensate

Abstract

Self-organization of the vorticity condensate of forced two-dimensional turbulence is examined in analogy with the mixing of a background planetary vorticity gradient in geophysical flows. Starting from the theoretical vorticity profile of the condensate, different scenarios are illustrated by the construction of idealized angular momentum conserving rearrangements of vorticity into a staircase profile similar to the potential vorticity staircase of $\beta$ -plane turbulence. Two sets of numerical experiments are then presented that illustrate a similar self-organization of the background vorticity gradient in fully turbulent flows. In the first set of experiments, the flow is initialized with a laminar vortex dipole corresponding to the theoretical condensate vorticity profile. A fluctuation vorticity field is then induced by a stochastic forcing at smaller scales, which induces an azimuthally symmetric self-organization of the laminar flow into distinct annular bands. In the second set of experiments, the flow is initialized from rest with stochastic forcing generating a turbulent inverse energy cascade, out of which emerges the condensate in a self-consistent evolution as the turbulent energy accumulates at the domain scale. A self-organization of the condensate is again observed, giving a distinct annular structure on top of the theoretically predicted condensate profile. A major difference from the potential vorticity staircase of geophysical flows is the emergence in many cases of significantly non-monotonic radial vorticity profiles.