Profile of a two-dimensional vortex condensate beyond the universal limit

Vladimir Parfenyev
Phys. Rev. E 106, 025102 – Published 10 August 2022
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Abstract

It is well known that an inverse turbulent cascade in a finite (2π×2π) two-dimensional periodic domain leads to the emergence of a system-sized coherent vortex dipole. We report a numerical hyperviscous study of the spatial vorticity profile inside one of the vortices. The exciting force was shortly correlated in time, random in space, and had a correlation length lf=2π/kf with kf ranging from 100 to 12.5. Previously, it was found that in the asymptotic limit of small-scale forcing, the vorticity exhibits the power-law behavior Ω(r)=(3ε/α)1/2r1, where r is the distance to the vortex center, α is the bottom friction coefficient, and ε is the inverse energy flux. Now we show that for a spatially homogeneous forcing with finite kf the vorticity profile becomes steeper, with the difference increasing with the pumping scale but decreasing with the Reynolds number at the forcing scale. Qualitatively, this behavior is related to a decrease in the effective pumping of the coherent vortex with distance from its center. To support this statement, we perform an additional simulation with spatially localized forcing, in which the effective pumping of the coherent vortex, on the contrary, increases with r, and show that in this case the vorticity profile can be flatter than the asymptotic limit.

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  • Received 15 April 2022
  • Accepted 25 July 2022

DOI:https://doi.org/10.1103/PhysRevE.106.025102

©2022 American Physical Society

Physics Subject Headings (PhySH)

Fluid DynamicsNonlinear DynamicsStatistical Physics & Thermodynamics

Authors & Affiliations

Vladimir Parfenyev*

  • Landau Institute for Theoretical Physics, Russian Academy of Sciences, 1-A Akademika Semenova av., 142432 Chernogolovka, Russia and National Research University Higher School of Economics, Faculty of Physics, Myasnitskaya 20, 101000 Moscow, Russia

  • *parfenius@gmail.com

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Issue

Vol. 106, Iss. 2 — August 2022

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