Experimental and numerical study of mean zonal flows generated by librations of a rotating spherical cavity

TL;DR

This paper combines experimental and numerical methods to investigate steady zonal flows induced by librations in a rotating spherical cavity, confirming theoretical predictions and revealing new flow features.

Contribution

It provides the first combined experimental and numerical validation of Busse's weakly nonlinear analytical solution for libration-driven zonal flows in spherical cavities.

Findings

Zonal flow is a retrograde solid body rotation independent of libration frequency and Ekman number.

Flow amplitude scales with the square of libration amplitude.

An unexpected prograde flow appears near the outer wall at the equator.

Abstract

We study both experimentally and numerically the steady zonal flow generated by longitudinal librations of a spherical rotating container. This study follows the recent weakly nonlinear analysis of Busse (2010), developed in the limit of small libration frequency - rotation rate ratio, and large libration frequency - spin-up time product. Using PIV measurements as well as results from axisymmetric numerical simulations, we confirm quantitatively the main features of Busse's analytical solution: the zonal flow takes the form of a retrograde solid body rotation in the fluid interior, which does not depend on the libration frequency nor on the Ekman number, and which varies as the square of the amplitude of excitation. We also report the presence of an unpredicted prograde flow at the equator near the outer wall.