Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-26T06:37:50.108Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Burgers, J. M. 1939 Mathematical examples illustrating relations occurring in the theory of turbulent fluid motion Proc. Acad. Sci. Amst. 17, 1–53.Google Scholar
Burgers, J. M. 1948 A mathematical model illustrating the theory of turbulence. Adv. Appl. Mech. 1.Google Scholar
Burgers, J. M. 1950a The formation of vortex sheets in a simplified type of turbulent motion Proc. Acad. Sci. Amst. 53, 122–133.Google Scholar
Burgers, J. M. 1950b Correlation problems in a one-dimensional model of turbulence Proc. Acad. Sci. Amst. 53, 247–260.Google Scholar
Burgers, J. M. 1964 Statistical problems connected with the solution of a nonlinear partial differential equation. In Nonlinear Problems of Engineering (ed. W. F. Ames), pp. 123–137. Academic.
Case, K. M. & Chiu, S. C. 1969 Burgers’ turbulence models Phys. Fluids, 12, 1799–1808.Google Scholar
Lee, J. 1971 Burgers’ turbulence model for a channel flow J. Fluid Mech. 47, 321–335.Google Scholar
Murray, J. D. 1968 Singular perturbations of a class of nonlinear hyperbolic and parabolic equations J. Math. & Phys. 47, 111–133.Google Scholar