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The Quarterly Journal of Mechanics and Applied Mathematics 1966 19(2):197-215; doi:10.1093/qjmam/19.2.197
© 1966 by Oxford University Press
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THE RAYLEIGH PROBLEM FOR A TWO-LAYER FLUID

D. A. MACDONALD

( Department of Mathematics, Manchester University )

The motion which results when an infinite plane wall moves impulsively in its own plane in a semi-infinite two-layer fluid system (see Fig. 1, below) is examined.

Solutions are given for the special case where the kinematic viscosities, v1 and v2, of the two fluids have only a small relative difference and for the general case of arbitrary viscosities. In the latter solution a useful technique for obtaining inverse Laplace Transforms is used. Numerical comparison of the two solutions furnishes agreement to the expected degree of accuracy.

The exact solution is used for the case of air lying over water and profiles showing the variation of velocity with various values of the dimensionless parameters z/{checkmark}(v1t) and y/{checkmark}(v1t) are given.

The analogous heat conduction problem is stated.


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