Experimental study of libration-driven zonal flows in non-axisymmetric containers

TL;DR

This experimental study explores how non-axisymmetric boundaries influence libration-driven zonal flows in fluids, revealing intermittent turbulence at resonant frequencies and laminar flow outside these bands, with implications for celestial body dynamics.

Contribution

It provides new experimental insights into the effects of boundary ellipticity on libration-driven flows, highlighting the occurrence of turbulence and the independence of flow from geometry outside resonance.

Findings

Intermittent turbulence occurs at resonant frequencies with larger zonal flow amplitudes.

Outside resonance, the flow remains laminar and geometry-independent at first order.

The turbulence mechanism may involve elliptical instability growth and collapse.

Abstract

Orbital dynamics that lead to longitudinal libration of celestial bodies also result in an elliptically deformed equatorial core-mantle boundary. The non-axisymmetry of the boundary leads to a topographic coupling between the assumed rigidmantle and the underlying low viscosity fluid.The present experimental study investigates theeffect of non axisymmetric boundaries on the zonal flow driven by longitudinal libration. For large enough equatorial ellipticity, we report intermittent space-filling turbulence in particular bands of resonant frequency correlated with larger amplitude zonal flow. The mechanism underlying the intermittent turbulence has yet to be unambiguously determined. Nevertheless, recent numerical simulations in triaxial and biaxial ellipsoids suggest that it may be associated with the growth and collapse of an elliptical instability (Cebron et al., 2012). Outside of the band of resonance, we find that the background flow is laminar and the zonal flow becomes independent of the geometry at first order, in agreement with a non linear mechanism in the Ekman boundary layer (e.g. Calkins et al.; 2010, Sauret and Le Dizes, 2012b).