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Numerical solutions and laser-Doppler measurements of spin-up

Published online by Cambridge University Press:  12 April 2006

Alex Warn-Varnas ,
William W. Fowlis ,
Steve Piacsek  and
Sang Myung Lee
Alex Warn-Varnas
Affiliation:
Naval Research Laboratory, Washington D.C. 20375 Present address: Naval Ocean Research and Development Activity, Bay St Louis, Mississippi. 39520.
William W. Fowlis
Affiliation:
Florida State University, Tallahassee Present address: NASA, Marshall Space Flight Center, Alabama 35812.
Steve Piacsek
Affiliation:
Naval Research Laboratory, Washington D.C. 20375
Sang Myung Lee
Affiliation:
Florida State University, Tallahassee
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Abstract

The spin-up flow in a cylinder of homogeneous fluid has been examined both experimentally and numerically. The primary motivation for this work was to check numerical solution schemes by comparing the numerical results with laboratory measurements obtained with a rotating laser-Doppler velocimeter. The laser-Doppler technique is capable of high accuracy with small space and time resolution, and disturbances of the flow are virtually negligible. A series of measurements was made of the zonal flow over a range of Ekman numbers (1·06 × 10−3 ≤ E ≤ 3·30 × 10−3) and Rossby numbers (0·10 [les ]|ε| [les ] 0·33) at various locations in the interior of the flow. These measurements exceed previous ones in accuracy. The weak inertial modes excited by the impulsive start are detectable. The numerical simulations used the primitive equations in axisymmetric form and employed finite-difference techniques on both constant and variable grids. The number of grid points necessary to resolve the Ekman layers was determined. A thorough comparison of the simulations and the experimental measurements is made which includes the details of the amplitude and frequency of the inertial modes. Agreement to within the experimental tolerance is achieved. Analytical results for conditions identical to those in the experiments are not available but some similar linear and nonlinear theories are also compared with the experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 85 , Issue 4 , 27 April 1978 , pp. 609 - 639
Copyright
© 1978 Cambridge University Press

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