# Transition between advection and inertial wave propagation in rotating turbulence

## TL;DR

This study experimentally investigates the transition from advection to inertial wave propagation in rotating turbulence, revealing that the transition occurs when the Rossby number at a given scale reaches unity, with inertial waves dominating transport.

## Contribution

It provides the first detailed experimental analysis of the local and scale-dependent transition between advection and inertial wave propagation in rotating turbulence.

## Key findings

- Transition occurs at Rossby number of order unity.
- Inertial waves suppress local advection in rotating turbulence.
- Scale-by-scale analysis reveals local and spectral nature of transition.

## Abstract

In turbulent flows subject to strong background rotation, the advective mechanisms of turbulence are superseded by the propagation of inertial waves, as the effects of rotation become dominant. While this mechanism has been identified experimentally, the conditions of the transition between the two mechanisms are less clear. We tackle this question experimentally by tracking the turbulent front away from a solid wall where jets enter an otherwise quiescent fluid. Without background rotation, this apparatus generates a turbulent front whose displacement recovers the $z(t)\sim t^{1/2}$ law classically obtained with an oscillating grid and we further establish the scale-independence of the associated transport mechanism. When the apparatus is rotating at a constant velocity perpendicular to the wall where fluid is injected, not only does the turbulent front become mainly transported by inertial waves, but advection itself is suppressed because of the local deficit of momentum incurred by the propagation of these waves. Scale-by-scale analysis of the displacement of the turbulent front reveals that the transition between advection and propagation is local both in space and spectrally, and takes place when the Rossby number based on the considered scale is of unity, or equivalently, when the scale-dependent group velocity of inertial waves matched the local advection velocity.