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On Burgers' model equations for turbulence

Published online by Cambridge University Press:  29 March 2006

J. D. Murray
J. D. Murray
Affiliation:
Mathematical Institute, Oxford University
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Abstract

Burgers’ (1939) model equations for turbulence are considered analytically using a singular perturbation and nonlinear wave approach. The results indicate that there is an ultimate steady turbulent state. This is in agreement with the numerical results of Lee (1971) but not with Case & Chiu (1969): the last two papers start with a Fourier series approach.

A consequence of this model is that small disturbances ultimately grow into a single large domain of relatively smooth flow, accompanied by a vortex sheet in which strong vorticity is concentrated. This makes the results from the model different from those usually expected for turbulent flow fields. The model, as a result of its simplicity, has retained a degree of regularity which is not found in most forms of turbulence.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 59 , Issue 2 , 19 June 1973 , pp. 263 - 279
Copyright
© 1973 Cambridge University Press

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References

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