Authors: Akira Kageyama, Hantao Ji, Jeremy Goodman, Fei Chen and Ethan Shoshan

Title: Numerical and Experimental Investigation of Circulation in Short Cylinders

Keywords: magnetorotational instability, Taylor-Couette instability, jet flow, Ekman circulation, liquid metal experiment


Abstract: 
In preparation for an experimental study of magnetorotational
instability (MRI) in liquid metal, we explore Couette flows having
height comparable to the gap between cylinders, centrifugally stable
rotation, and high Reynolds number.  Experiments in water are compared
with numerical simulations.  Simulations show that
endcaps corotating with the outer cylinder drive a strong poloidal
circulation that redistributes angular momentum.  Predicted azimuthal
flow profiles agree well with experimental measurements.  Spin-down
times scale with Reynolds number as expected for laminar Ekman
circulation; extrapolation from two-dimensional simulations at $Re\le
3200$ agrees remarkably well with experiment at $Re\sim 10^6$.  This
suggests that turbulence does not dominate the effective viscosity.
Further detailed numerical studies reveal a strong radially inward
flow near both endcaps.  After turning vertically along the inner
cylinder, these flows converge at the midplane and depart the boundary
in a radial jet.  To minimize this circulation in
the MRI experiment, endcaps consisting of multiple, differentially
rotating rings are proposed.  Simulations predict that an adequate
approximation to the ideal Couette profile can be obtained with a few
rings.