Anisotropy and cyclone-anticyclone asymmetry in decaying rotating turbulence

TL;DR

This study experimentally investigates how background rotation influences the decay, anisotropy, and cyclone-anticyclone asymmetry in homogeneous turbulence, revealing a transition at a specific Rossby number and the role of shear instability in vorticity re-symmetrization.

Contribution

It provides new insights into the decay laws, anisotropy development, and vorticity asymmetry in rotating turbulence, highlighting the impact of initial conditions and shear instabilities.

Findings

Energy decay transitions from t^{-6/5} to t^{-3/5} at Ro ≈ 0.25.

Vertical layers of nearly constant vertical velocity form and thin over time.

Cyclone-anticyclone asymmetry develops then diminishes due to shear instability.

Abstract

The effect of a background rotation on the decay of homogeneous turbulence produced by a grid is experimentally investigated. Experiments have been performed in a channel mounted in the large-scale 'Coriolis' rotating platform, and measurements have been carried out in the planes normal and parallel to the rotation axis using particle image velocimetry. After a short period of about 0.4 tank rotation where the energy decays as $t^{-6/5}$, as in classical isotropic turbulence, the energy follows a shallower decay law compatible with $t^{-3/5}$, as dimensionally expected for energy transfers governed by the linear timescale $\Omega^{-1}$. The crossover occurs at a Rossby number $Ro \simeq 0.25$, without noticeable dependence with the grid Rossby number. After this transition, anisotropy develops in the form of vertical layers where the initial vertical velocity remains trapped. These layers of nearly constant vertical velocity become thinner as they are advected and stretched by the large-scale horizontal flow, producing significant horizontal gradient of vertical velocity which eventually become unstable. After the $Ro \simeq 0.25$ transition, the vertical vorticity field first develops a cyclone-anticyclone asymmetry, reproducing the growth law of the vorticity skewness, $S_\omega(t) \simeq (\Omega t)^{0.7}$, reported by Morize, Moisy & Rabaud [{\it Phys. Fluids} {\bf 17} (9), 095105 (2005)]. At larger time, however, the vorticity skewness decreases and eventually returns to zero. The present results indicate that the shear instability of the vertical layers contribute significantly to the re-symmetrisation of the vertical vorticity at large time, by re-injecting vorticity fluctuations of random sign at small scales. These results emphasize the importance of the initial conditions in the decay of rotating turbulence.