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The Quarterly Journal of Mechanics and Applied Mathematics 1977 30(2):131-142; doi:10.1093/qjmam/30.2.131
© 1977 by Oxford University Press
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NONLINEAR THEORY OF TAYLOR INSTABILITY OF SUPERPOSED FLUIDS OF DIFFERENT DENSITIES IN THREE DIMENSIONS

N. R. RAJAPPA and T. AMARANATH

( Department of Aeronautical Engineering, Indian Institute of Technology Madras 600036
Department of Mathematics, Indian Institute of Technology Madras 600036 )

The problem of three-dimensional instability of superposed fluids of different densities is considered here. The two-dimensional Taylor instability of superposed fluids is extended to the three-dimensional case when the horizontal planform consists of rectangular cells. A third-order nonlinear perturbation theory is given by using the method of strained coordinast for this singular perturbation problem. Marginal stability curves are given for different values of the density ratio. The results for the case of an air-liquid interface are also derived in the Appendix.


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