Three-dimensional instability of elliptical flow

Details Three-dimensional instability of elliptical flow Three-dimensional instability of elliptical flow

Oct 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986phrvl..57.2160b&link_type=abstract

Physical Review Letters (ISSN 0031-9007), vol. 57, Oct. 27, 1986, p. 2160-2163. NSF-supported research.

Physics

205

Floquet Theorem, Flow Geometry, Flow Stability, Flow Velocity, Inviscid Flow, Three Dimensional Flow, Eigenvalues, Flow Distribution

Scientific paper

A clarification of the physical and mathematical nature of Pierrhumbert's (1986) three-dimensional short-wave inviscid instability of simple two-dimensional elliptical flow is presented. The instabilities found are independent of length scale, extending Pierrhumbert's conclusion that the structures of the instabilities are independent of length scale in the limit of large wave number. The fundamental modes are exact solutions of the nonlinear equations, and they are plane waves whose wave vector rotates elliptically around the z axis with a period of 2(pi)/Omega. The growth rates are shown to be the exponents of a matrix Floquet problem, and good agreement is found with previous results.

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