Energy spectrum of two-dimensional isotropic rapidly rotating turbulence

TL;DR

This paper investigates the energy spectrum in rapidly rotating two-dimensional turbulence, confirming a theoretical $K^{-2}$ spectrum through asymptotic analysis and numerical simulations, bridging the gap between theory and observable phenomena.

Contribution

It derives and verifies the $K^{-2}$ energy spectrum in 2D rotating turbulence using a nonlinear amplitude equation and numerical simulations, addressing isotropy assumptions.

Findings

The $K^{-2}$ energy spectrum is confirmed in rapidly rotating turbulence.

Numerical simulations support the theoretical derivation.

Inertial wave turbulence explains the observed spectrum.

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 ($Ro\ll 1$), which was initially obtained by Zeman (1994) and Zhou (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.