Hostname: page-component-8448b6f56d-wq2xx Total loading time: 0 Render date: 2024-04-19T19:09:55.373Z Has data issue: false hasContentIssue false
  • English
  • Français

Path-integral methods for turbulent diffusion

Published online by Cambridge University Press:  20 April 2006

I. T. Drummond
I. T. Drummond
Affiliation:
Department of Applied Mathematics and Theoretical Physics. University of Cambridge, Silver Street, Cambridge CB3 9EW
Get access Rights & Permissions [Opens in a new window]

Abstract

We derive a path-integral representation for the effective diffusion function of a passive scalar field. We use it to calculate the long-time effective diffusivity in Gaussian turbulence in the near-Markovian limit. Our results confirm the negative effect of vorticity predicted by previous discussions. They also demonstrate that the helicity of the turbulence when present may be as important an influence as the vorticity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 123 , October 1982 , pp. 59 - 68
Copyright
© 1982 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

Feynman, R. P. & Hibbs, A. R. 1965 Quantum Mechanics and Path Integrals. McGraw-Hill.
Flatte, S. M. (ed.) 1979 Sound Transmission Through a Fluctuating Ocean. Cambridge University Press.
Graham, R. 1977 Lagrangian for diffusion in curved phase space. Phys. Rev. Lett. 38, 51.Google Scholar
Knobloch, R. 1977 The diffusion of scalar and vector fields by homogeneous turbulence. J. Fluid Mech. 83, 129.Google Scholar
Knobloch, E. 1980 On the relationship between Eulerian and Lagrangian turbulent diffusivities. Phys. Lett. 78A, 307.Google Scholar
Kraichnan, R. H. 1968 Small-scale structure of a scalar field convected by turbulence. Phys. Fluids 11, 945.Google Scholar
Kraichnan, R. H. 1970 Diffusion by a random velocity field. Phys. Fluids 13, 22.Google Scholar
Kraichnan, R. H. 1976 Diffusion of passive-scalar and magnetic fields by helical turbulence. J. Fluid Mech. 77, 753.Google Scholar
Kraichnan, R. H. 1977 Lagrangian velocity covariance in helical turbulence. J. Fluid Mech. 81, 385.Google Scholar
Onsager, L. & Machlup, S. 1953 Phys. Rev. 91, 1505.
Phythian, R. & Curtis, W. D. 1978 The effective long-time diffusivity for a passive scalar field in a Gaussian model flow. J. Fluid Mech. 89, 241.Google Scholar
Saffman, P. G. 1960 On the effect of molecular diffusivity in turbulent diffusion. J. Fluid Mech. 8, 273.Google Scholar
Taylor, G. I. 1921 Diffusion by continuous movements. Proc. Lond. Math. Soc. A 20, 196.Google Scholar