Two-dimensionalization of the flow driven by a slowly rotating impeller in a rapidly rotating fluid

TL;DR

This study investigates how turbulent flow driven by a rotating impeller becomes two-dimensional as the Rossby number decreases, revealing the roles of large-scale rotation and inertial wave wakes in this process.

Contribution

It provides new insights into the transition to two-dimensional flow in rotating turbulence driven by non-axisymmetric forcing, highlighting the role of inertial wave wakes.

Findings

Flow becomes more two-dimensional at low Rossby numbers.

Inertial wave wakes are stable at low Rossby numbers.

Shear layers become disordered at Rossby numbers near 1.

Abstract

We characterize the two-dimensionalization process in the turbulent flow produced by an impeller rotating at a rate $\omega$ in a fluid rotating at a rate $\Omega$ around the same axis for Rossby number $Ro=\omega/\Omega$ down to $10^{-2}$. The flow can be described as the superposition of a large-scale vertically invariant global rotation and small-scale shear layers detached from the impeller blades. As $Ro$ decreases, the large-scale flow is subjected to azimuthal modulations. In this regime, the shear layers can be described in terms of wakes of inertial waves traveling with the blades, originating from the velocity difference between the non-axisymmetric large-scale flow and the blade rotation. The wakes are well defined and stable at low Rossby number, but they become disordered at $Ro$ of order of 1. This experiment provides insight into the route towards pure two-dimensionalization induced by a background rotation for flows driven by a non-axisymmetric rotating forcing.