The decay of Batchelor and Saffman rotating turbulence

TL;DR

This study investigates how initial large-scale spectral differences influence the decay of rotating turbulence, revealing that long-range correlations affect decay rates and that different modes follow distinct power laws.

Contribution

It demonstrates that the decay of rotating turbulence is influenced by initial spectral conditions and anisotropic correlations, challenging the idea that decay rate is independent of initial spectra.

Findings

Decay rates differ for 2D and 3D modes.

Long-range correlations impact the decay process.

Power laws align with anisotropic von Kármán-Howarth predictions.

Abstract

The decay rate of isotropic and homogeneous turbulence is known to be affected by the large-scale spectrum of the initial perturbations, associated with at least two cannonical self-preserving solutions of the von K\'arm\'an-Howarth equation: the so-called Batchelor and Saffman spectra. The effect of long-range correlations in the decay of anisotropic flows is less clear, and recently it has been proposed that the decay rate of rotating turbulence may be independent of the large-scale spectrum of the initial perturbations. We analyze numerical simulations of freely decaying rotating turbulence with initial energy spectra $\sim k^4$ (Batchelor turbulence) and $\sim k^2$ (Saffman turbulence) and show that, while a self-similar decay cannot be identified for the total energy, the decay is indeed affected by long-range correlations. The decay of two-dimensional and three-dimensional modes follows distinct power laws in each case, which are consistent with predictions derived from the anisotropic von K\'arm\'an-Howarth equation, and with conservation of anisotropic integral quantities by the flow evolution.