Onset of three-dimensionality in rapidly rotating turbulent flows

TL;DR

This study identifies the precise Reynolds number thresholds at which rapidly rotating turbulent flows transition from two-dimensional to three-dimensional behavior, revealing the underlying instabilities and mechanisms involved.

Contribution

The paper introduces a linear stability analysis combined with GPU-accelerated simulations to accurately determine the 2D-3D transition thresholds in turbulent flows.

Findings

Flow becomes unstable to 3D motion via centrifugal instability at Re ~ 10^3.

A second instability dominates at higher Re, possibly involving inertial wave excitation.

The analysis leverages modern GPU computing to explore high Reynolds number regimes.

Abstract

Turbulent flows driven by a vertically invariant body force were proven to become exactly two-dimensional above a critical rotation rate, using upper bound theory. This transition in dimensionality of a turbulent flow has key consequences for the energy dissipation rate. However, its location in parameter space is not provided by the bounding procedure. To determine this precise threshold between exactly 2D and partially 3D flows, we perform a linear stability analysis over a fully turbulent 2D base state. This requires integrating numerically a quasi-2D set of equations over thousands of turnover times, to accurately average the growth rate of the 3D perturbations over the statistics of the turbulent 2Dbase flow. We leverage the capabilities of modern GPUs to achieve this task, which allows us to investigate the parameter space up to Re = 10^5. At Reynolds numbers typical of 3D DNS and laboratory experiments, Re in [10^2, 5x10^3], the turbulent 2D flow becomes unstable to 3D motion through a centrifugal-type instability. However, at even higher Reynolds number another instability takes over. A candidate mechanism for the latter instability is the parametric excitation of inertial waves by the modulated 2D flow, a phenomenon that we illustrate with an oscillatory 2D Kolmogorov flow.