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The Quarterly Journal of Mechanics and Applied Mathematics 1969 22(3):355-362; doi:10.1093/qjmam/22.3.355
© 1969 by Oxford University Press
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A NOTE ON COUPLING INTEGRALS FOR PROBLEMS OF INCOMPRESSIBLE FLUID FLOW

P. D. EHRENZWEIG

( Rutherford College of Technology Newcastle upon Tyne NE1 8ST )

In 1881, Lamb introduced toroidal and poloidal vectors for representing solenoidal fields. Fourier decompositions of these are known as toroidal and poloidal harmonics. The interactions between these, through the inertial terms of the Navier-Stokes equation, are studied in this paper, which complements an earlier investigation by Platzman in 1965. Particular attention is given to hexagonally-repeating flows, which are known to be common in thermal convection.


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