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On the general theory of contained rotating fluid motions

Published online by Cambridge University Press:  28 March 2006

H. P. Greenspan
H. P. Greenspan
Affiliation:
Mathematics Department, Massachusetts Institute of Technology, Cambridge, Mass.
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Abstract

A general linear theory is developed to describe the manner in which rigid fluid rotation is established from a prescribed initial state of motion in a container of arbitrary shape. The container rotates with uniform angular velocity and is filled with a viscous incompressible fluid.

A new mean circulation theorem is proved and used to separate the flow into geostrophic motion and inertial oscillations. The basic eigenvalue problem is studied and important properties concerning spectrum, orthogonality and completeness are deduced. The effect of viscosity on the inviscid modes is calculated in a manner that maintains the solution uniformly valid through the spin-up time. All modes decay in this time scale which characterizes the entire transition to rigid rotation in all configurations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 22 , Issue 3 , July 1965 , pp. 449 - 462
Copyright
© 1965 Cambridge University Press

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References

Greenspan, H. P., 1964 J. Fluid Mech. 20, 673.
Greenspan, H. P. & Howard, L. N. 1963 J. Fluid Mech. 17, 385.
Greenspan, H. P. & Weinbaum, S. 1965 J. Math. & Phys. (To be published.)