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Bayly, B. J.

Three-dimensional centrifugal-type instabilities in inviscid two- dimensional flows. (English) Zbl 0651.76018

Phys. Fluids 31, No. 1, 56-64 (1988).
The author extends the classical Rayleigh centrifugal instability theory to general inviscid two-dimensional flows, whose streamlines are convex closed curves with the magnitude of the circulation decreasing outward. Thus, a class of three-dimensional short-wave instabilities can be constructed, which are localized near the streamline cylinder.
Reviewer: J.E.Ffowcs Williams

Cited in 59 Documents

MSC:

76E05 Parallel shear flows in hydrodynamic stability
35Q99 Partial differential equations of mathematical physics and other areas of application

Keywords:

Rayleigh centrifugal instability theory; inviscid two-dimensional flows; three-dimensional short-wave instabilities
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\textit{B. J. Bayly}, Phys. Fluids 31, No. 1, 56--64 (1988; Zbl 0651.76018)
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References:

[1] J. W. S. Rayleigh, Proc. R. Soc. London Ser. A 93, 148 (1916).PRLAAZ0950-1207
[2] G. I. Taylor, Philos. Trans. R. Soc. London Ser. A 223, 289 (1923).PTRMAD0962-8428
[3] H. Görtler, Nachr. Ges. Wiss. Gottingen Math. Phys. Kl. Fachgruppe 2, 1 (1940).
[4] H. Görtler, NACA Tech. Memo. 1375, 1954.
[5] H. Bippes and H. Görtler, Acta Mech. 14, 251 (1972).AMHCAP0001-5970
[6] S. A. Ragab and A. H. Nayfeh, Phys. Fluids 24, 1405 (1981).PFLDAS0031-9171
[7] J. M. Floryan, Phys. Fluids 29, 2380 (1986).PFLDAS0031-9171
[8] V. I. Arnold, J. Mec. 5, 29 (1966).JOMCAR0021-7832
[9] D. Lynden-Bell and J. Katz, Proc. R. Soc. London Ser. A 378, 179 (1982).PRLAAZ1364-5021 · Zbl 0486.76034
[10] H. D. I. Abarbanel, D. D. Holm, J. E. Marsden, and T. S. Ratiu, Philos. Trans. R. Soc. London Ser. A 318, 349 (1986).PTRMAD0962-8428
[11] D. D. Holm, J. E. Marsden, T. S. Ratiu, and A. Weinstein, Phys. Rep. 123, 1 (1985).PRPLCM0370-1573
[12] H. D. I. Abarbanel and D. D. Holm, Phys. Fluids 30, 3369 (1987).PFLDAS0031-9171
[13] H. K. Moffatt, J. Fluid Mech. 173, 289 (1986).JFLSA70022-1120
[14] P. G. Drazin and W. H. Reid, Hydrodynamk Stability (Cambridge U.P., Cambridge, 1981).
[15] C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978). · Zbl 0417.34001
[16] W. Magnus and S. Winkler, Hill’s Equation (Wiley, New York, 1966). · Zbl 0158.09604
[17] V. I. Oseledec, Trans. Moscow Math. Soc. 19, 197 (1968).TMMSD40077-1554
[18] R. T. Pierrehumbert and S. E. Widnall, J. Fluid Mech. 114, 59 (1982).JFLSA70022-1120
[19] S. A. Orszag and A. T. Patera, J. Fluid Mech. 128, 347 (1983).JFLSA70022-1120
[20] T. Herbert, Phys. Fluids 26, 871 (1983).PFLDAS0031-9171
[21] R. T. Pierrehumbert, Phys. Rev. Lett. 57, 2157 (1986).PRLTAO0031-9007
[22] B. J. Bayly, Phys. Rev. Lett. 57, 2160 (1986).PRLTAO0031-9007
[23] M. J. Landman and P. G. Saffman, Phys. Fluids 30, 2339 (1987).PFLDAS0031-9171
[24] L. N. Howard and A. S. Gupta, J. Fluid Mech. 14, 463 (1962).JFLSA70022-1120
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