The decay of turbulence in rotating flows

TL;DR

This study investigates how turbulence decays in rotating flows by combining simulations and theory, considering various initial conditions, parameters, and anisotropies, revealing how rotation and helicity influence decay laws and flow statistics.

Contribution

It provides a comprehensive parametric analysis of turbulence decay in rotating flows, integrating numerical simulations with phenomenological theory to explain the influence of initial conditions, helicity, and anisotropy.

Findings

Decay laws depend on initial conditions and flow parameters.

Rotation and helicity slow down energy decay.

Anisotropy develops during decay, affecting flow statistics.

Abstract

We present a parametric space study of the decay of turbulence in rotating flows combining direct numerical simulations, large eddy simulations, and phenomenological theory. Several cases are considered: (1) the effect of varying the characteristic scale of the initial conditions when compared with the size of the box, to mimic "bounded" and "unbounded" flows; (2) the effect of helicity (correlation between the velocity and vorticity); (3) the effect of Rossby and Reynolds numbers; and (4) the effect of anisotropy in the initial conditions. Initial conditions include the Taylor-Green vortex, the Arn'old-Beltrami-Childress flow, and random flows with large-scale energy spectrum proportional to $k^4$. The decay laws obtained in the simulations for the energy, helicity, and enstrophy in each case can be explained with phenomenological arguments that separate the decay of two-dimensional from three-dimensional modes, and that take into account the role of helicity and rotation in slowing down the energy decay. The time evolution of the energy spectrum and development of anisotropies in the simulations are also discussed. Finally, the effect of rotation and helicity in the skewness and kurtosis of the flow is considered.