Vorticity, staircases

[pukpr]

Annular self-organization of the two-dimensional vorticity condensate
R.K. Scott (collaborator w/ T. Dunkerton)

https://research-repository.st-andrews.ac.uk/bitstream/handle/10023/28749/Scott-2023-Annular-self-organization-JFM-966-A28-CCBY.pdf

The inverse energy cascade of two-dimensional turbulence, with small-scale forcing and weak damping, and in a finite domain, leads to a condensation in which the energy is overwhelmingly concentrated in the lowest available modes of the system.

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a fascinating aspect of two-dimensional turbulence known as the process of "condensation" or "inverse energy cascade," where, under specific conditions, the system exhibits a flow of energy from smaller scales to larger scales. This is in contrast to three-dimensional turbulence, where energy typically cascades from larger scales to smaller scales, leading to dissipation through viscosity at the smallest scales.

In the context of two-dimensional turbulence with small-scale forcing and weak damping, especially within a finite domain, the inverse energy cascade can lead to a phenomenon where energy accumulates in the largest scales of the system. This is because the energy, once transferred to larger scales, cannot cascade to even larger scales due to the finite size of the domain, and thus tends to accumulate in the lowest available modes. This accumulation or "condensation" of energy at large scales can lead to the formation of coherent structures or vortices that dominate the flow.