Confirming Wave Turbulence Predictions in Rotating Turbulence

TL;DR

This study confirms that weak wave turbulence theory accurately predicts the energy spectrum of inertial waves in steady rotating turbulence, validating long-standing theoretical predictions.

Contribution

It demonstrates the existence of WTT-predicted inertial wave spectra in steady rotating turbulence and clarifies their coexistence with quasi 2D turbulence.

Findings

WTT predictions match the inertial wave component in steady rotating turbulence.

The inertial wave spectrum depends on four key parameters.

Limits are identified where WTT predictions no longer hold.

Abstract

Though highly impacting our lives, rotating turbulent flows are not well understood. These anisotropic three-dimensional disordered flows are governed by different nonlinear processes, each of which can be dominant in a different range of parameters. More than 20 years ago, Galtier used weak wave turbulence theory (WTT) to derive explicit predictions for the energy spectrum of rotating turbulence. The spectrum is an outcome of forward energy transfer by inertial waves, the linear modes of rotating fluid systems. This spectrum has not yet been observed in freely evolving flows. In this work, we show that the predicted WTT field does exist in steady rotating turbulence, alongside with the more energetic quasi two-dimensional turbulent field. By removing the 2D component from the steady state velocity field, we show that the remainder three-dimensional field consists of inertial waves and exactly obeys WTT predictions. Our analysis verifies the dependence of the energy spectrum on all four relevant parameters and provides limits, beyond which WTT predictions fail. These results provide a solid basis for new theoretical and experimental works focused on the coexistence of the quasi 2D field and the inertial waves field and on their interactions.