The Influence of Horizontal Boundaries on Ekman Circulation and Angular Momentum Transport in a Cylindrical Annulus

TL;DR

This study uses numerical simulations to explore how horizontal boundary conditions influence Ekman circulation and angular momentum transport in cylindrical annulus flows, relevant to MRI experiments.

Contribution

The paper introduces a detailed numerical analysis of boundary effects on flow structures and angular momentum transport in cylindrical annulus, with a new mechanism explaining Ekman flow dependence.

Findings

Horizontal boundary conditions significantly affect Ekman circulation.

Flow transitions from steady to unsteady with changing Reynolds number.

A proposed mechanism explains the boundary-dependent Ekman flow behavior.

Abstract

We present numerical simulations of circular Couette flow in axisymmetric and fully three-dimensional geometry of a cylindrical annulus inspired by Princeton MRI liquid gallium experiment. The incompressible Navier-Stokes equations are solved with the spectral element code Nek5000 incorporating realistic horizontal boundary conditions of differentially rotating rings. We investigate the effect of changing rotation rates (Reynolds number) and of the horizontal boundary conditions on flow structure, Ekman circulation and associated transport of angular momentum through the onset of unsteadiness and three-dimensionality. A mechanism for the explanation of the dependence of the Ekman flows and circulation on horizontal boundary conditions is proposed.