A study of turbulence and interacting inertial modes in a differentially-rotating spherical shell experiment

TL;DR

This study investigates inertial modes in a differentially rotating spherical shell, revealing a critical Rossby number where flow transitions occur, leading to wave-breaking, small-scale turbulence, and enhanced mean flows, with novel insights into mode interactions.

Contribution

It provides new experimental evidence of flow transitions and inertial mode behaviors in spherical Couette flow, including the scaling of critical Rossby number and mode interactions.

Findings

Inertial modes exist for negative Rossby numbers in the experiment.

A critical Rossby number scales with the Ekman number as E^{1/5}.

Flow transitions involve wave-breaking and increased small-scale turbulence.

Abstract

We present a study of inertial modes in a differentially rotating spherical shell (spherical Couette flow) experiment with a radius ratio of $\eta = 1/3$. Inertial modes are Coriolis-restored linear wave modes which often arise in rapidly rotating fluids. Recent experimental work has shown that inertial modes exist in a spherical Couette flow for $\Omega_{i}<\Omega_{o}$, where $\Omega_i$ and $\Omega_o$ is the inner and outer sphere rotation rate. A finite number of particular inertial modes has previously been found. By scanning the Rossby number from $-2.5 < Ro = (\Omega_{i}-\Omega_{o})/\Omega_{o} < 0$ at two fixed $\Omega_{o}$, we report the existence of similar inertial modes. However, the behavior of the flow described here differs much from previous spherical Couette experiments. We show that the kinetic energy of the dominant inertial mode dramatically increases with decreasing Rossby number that eventually leads to a wave-breaking and an increase of small-scale structures at a critical Rossby number. Such a transition in a spherical Couette flow has not been described before. The critical Rossby number scales with the Ekman number as0 $E^{1/5}$. Additionally, the increase of small-scale features beyond the transition transfers energy to a massively enhanced mean flow around the tangent cylinder. In this context, we discuss an interaction between the dominant inertial modes with a geostrophic Rossby mode exciting secondary modes whose frequencies match the triadic resonance condition.