Effects of bottom topography on the spin-up in a cylinder

Fabian Burmann,Jerome Noir

doi:10.1063/1.5051111

Abstract

Motivated by better understanding the long-standing issue of the role of topography on the transport of angular momentum in rapidly rotating fluids, we conducted spin-up experiments in a straight cylinder with a regular pavement of rectangular blocks at the bottom. We perform particle image velocimetry measurements to monitor the decay of the initial differential motion generated by the sudden increase of the container rotation rate. We observe that the re-synchronization time, the so-called spin-up time, is shorter in the presence of topography with a minimum at a particular length scale of the topography pattern. We show evidence of energy transport by inertial waves as well as non-linear mechanisms leading to a scaling of the spin-up time significantly different from the classical E−1/2 in the absence of topography.

Highlights

Rotating flows are omnipresent in planetary dynamics, whether considering liquid cores, subsurface oceans, or gaseous atmospheres
Regarding the Rossby number, we find a decrease of the spin-up time with increasing Rossby number, indicating that the finite Rossby number might still have an effect on the dynamics in the system
In the limit of small Rossby and small Ekman numbers, the spin-up time in a cylinder with flat end walls is dictated by the so-called Ekman pumping, a flow normal to the boundary layer

Summary

Introduction

Rotating flows are omnipresent in planetary dynamics, whether considering liquid cores, subsurface oceans, or gaseous atmospheres. The effects of topography on the flows in these liquid layers have been addressed mostly for stratified fluids such as the Earth’s atmosphere and oceans, where internal waves play a fundamental role.. The case of a cylindrical annulus with a variable height on the top and bottom end walls has been investigated theoretically, numerically, and experimentally.. The case of a cylindrical annulus with a variable height on the top and bottom end walls has been investigated theoretically, numerically, and experimentally.10 Even though they differ in the exact configurations, all models find the existence of thermal Rossby waves. In a more core-like geometry, Calkins et al. numerically investigated the effect of a single Gaussian ridge penetrating the outer core, leading to a resonance of the zonal flow with a Rossby wave. The mechanism underlying the transport of energy and angular momentum from the scale of the topography to the large scale of the zonal flow or the small scales of local vortices have yet to be identified

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Conclusion