Large scale effects on the decay of rotating helical and non-helical turbulence

TL;DR

This study uses direct numerical simulations to analyze how rotation and helicity influence the decay of 3D turbulence, revealing mode decoupling and different decay behaviors in rotating flows.

Contribution

It provides new insights into the decay dynamics of rotating helical and non-helical turbulence, highlighting mode decoupling and the role of anisotropic spectra.

Findings

Non-rotating turbulence follows classical decay rate t^{-10/7}.

Rotation causes decoupling of 2D and 3D modes with distinct decay behaviors.

Helicity influences decay, with 3D modes behaving isotropically and 2D modes constrained by rotation.

Abstract

Decaying three-dimensional (3D) turbulence is studied via direct numerical simulations (DNS) for an isotropic non-rotating flow and for rotating flows with and without helicity. We analyze the cases of moderate Rossby number and large Reynolds number focusing on the behavior of the energy spectrum at large scales and studying its effect on the time evolution of the energy and integral scales for $E(k) \sim k^4$ initial conditions. In the non-rotating case we observe the classical energy decay rate $t^{-10/7}$ and a growth of the integral length proportional to $t^{2/7}$ in agreement with the prediction obtained assuming conservation of the Loitsyanski integral. In the presence of rotation we observe a decoupling in the decay of the modes perpendicular to the rotation axis from the remaining 3D modes. These slow modes show a behavior similar to that found in two-dimensional (2D) turbulence whereas the 3D modes decay as in the isotropic case. We phenomenologically explain the decay considering integral conserved quantities that depend on the large scale anisotropic spectrum. The decoupling of modes is also observed for a flow with a net amount of helicity. In this case, the 3D modes decay as an isotropic fluid with a constant, constrained integral length, and the 2D modes decay as a constrained rotating fluid with maximum helicity.