Initiation of turbulence and chaos in non-equilibrium inhomogeneous media: wave beams

Landa, P. S. and McClintock, P. V. E. (2011) Initiation of turbulence and chaos in non-equilibrium inhomogeneous media: wave beams. Journal of Physics A: Mathematical and Theoretical, 44 (47). -. ISSN 1751-8113

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Abstract

We show that wave excitation and propagation in an inhomogeneous medium lead to the simultaneous appearance of a huge number of waves with different phase velocities. This phenomenon arises in any medium with inhomogeneous parameters, e. g., in fluid jets where the inhomogeneity appears as a result of the boundary layer. Because of fluctuations (however small) the waves become randomized, i.e. turbulence develops. We demonstrate that the eigenvalues depend essentially on the frequency of the perturbation and on the distance from the initial section of a jet or wave beam. We show how to find the continuous set of eigenvalues-complex wavenumbers-and corresponding eigenfunctions for any given frequency. The implication of these results is that the transition to turbulence occurs, not through the excitation of a gradually increasing number of waves, as commonly supposed, but by the simultaneous excitation of a continuous wave spectrum.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Physics A: Mathematical and Theoretical
Uncontrolled Keywords:
/dk/atira/pure/researchoutput/libraryofcongress/qc
Subjects:
ID Code:
52349
Deposited By:
Deposited On:
24 Jan 2012 02:36
Refereed?:
Yes
Published?:
Published
Last Modified:
14 Jul 2020 03:05