Journal of the Physical Society of Japan
Vol.73 No.9, September, 2004 pp.2424-2437
DOI : 10.1143/JPSJ.73.2424

Numerical and Experimental Investigation of Circulation in Short Cylinders

Akira Kageyama*, Hantao Ji1**, Jeremy Goodman2***, Fei Chen1**** and Ethan Shoshan3

Earth Simulator Center, Japan Agency for Marine-Earth Science and Technology, Yokohama 236-0001
1Princeton Plasma Physics Laboratory, Princeton, NJ 08543, U.S.A.
2Princeton University Observatory, Princeton, NJ 08544, U.S.A.
3Rutgers University, Piscataway, NJ 08854, U.S.A.

(Received March 11, 2004)

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 3200 agrees remarkably well with experiment at Re 106. 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.


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