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Two-dimensional turbulence near the viscous limit

Published online by Cambridge University Press:  29 March 2006

J. S. A. Green
J. S. A. Green
Affiliation:
Department of Meteorology, Imperial College, London
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Abstract

Two-dimensional incompressible motion is generated by a steady external body force varying sinusoidally with a transverse co-ordinate. Such flow is found to be unstable for Reynolds numbers greater than 2½, and under these conditions evolves towards a new steady state. This ‘steady-eddy’ state is itself unstable in a sense, and its breakdown suggests the catastrophic onset of a cascade of turbulence. The mechanics of this cascade can be represented by a kind of recursion system in which the turbulence dynamics of one scale is repeated in the next, and a law of turbulent stress results. The spectrum of kinetic energy generated by a steady input of momentum at a discrete wavelength shows a rapid decrease (as k−5) towards shorter wavelengths but a much slower decrease (as k) towards longer wavelengths.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 62 , Issue 2 , 23 January 1974 , pp. 273 - 287
Copyright
© 1974 Cambridge University Press

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References

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