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The fundamental solutions for irrotational and rotational Stokes flow in spheroidal geometry

Published online by Cambridge University Press:  01 July 2007

G. DASSIOS
G. DASSIOS*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge. e-mail: [email protected].
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Abstract

The Stokes operator E2 governs the irrotational axisymmetric Stokes flow and its square governs the corresponding rotational flow. In spheroidal coordinates the elements of the solution space ker E2 enjoy a spectral decomposition into separable eignefunction, while the elements of the ker E4 accept a spectral decomposition in terms of semiseparable eigensolutions involving 3D-by-3D eigenfunctions of the Gegenbauer operator. These spectral characteristics are utilized to construct the fundamental solutions for both the E2 and the E4 operators in spheroidal geometry. The fundamental solution for E2 is expressed in terms of the elements of the irrotational space ker E2, while the fundamental solution for E4 is expressed in terms of the corresponding generalized eigenfunctions alone.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 1 , July 2007 , pp. 243 - 253
Copyright
Copyright © Cambridge Philosophical Society 2007

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