Skip to main content Accessibility help

Analytical theories of turbulence

  • Steven A. Orszag (a1)

This paper surveys the current state of analytical attempts at a theory of turbulence. The formulation of the problem in terms of moments is discussed. The difficulty posed by the closure problem is examined in detail using the quasinormal approximation as an example. The notion of dynamical relaxation by non-linear scrambling leads to the introduction of eddy relaxation times and the direct-interaction approximation. The properties of the direct-interaction approximation are indicated. Finally, a comparison is made between numerical solution of the equations of turbulence their and direct numerical simulation of the Navier–Stokes equations.

Hide All
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Edwards, S. F. 1964 J. Fluid Mech. 18, 239.
Grant, H. L., Stewart, R. W. & Moilliet, A. 1962 J. Fluid Mech. 12, 241.
Hebring, J. R. 1965 Phys. Fluids, 8, 2219.
Herring, J. R. 1966 Phys. Fluids, 9, 2106.
Kraichnan, R. H. 1959 J. Fluid Mech. 5, 497.
Kraichnan, R. H. 1961 J. Math. Phys. 2, 124.
Kraichnan, R. H. 1964a Phys. Fluids, 7, 1030.
Kraichnan, R. H. 1964b Phys. Fluids, 7, 1163.
Kraichnan, R. H. 1965 Phys. Fluids, 8, 575.
Kraichnan, R. H. 1966 Phys. Fluids, 9, 1728.
Millionschtchikov, M. D. 1941 Compt. Rend. Acad. Sci. URSS, 32, 615.
Ogura, Y. 1963 J. Fluid Mech. 16, 33.
Orszag, S. A. 1969 Phys. Fluids Suppl. II, 12, 250.
Orszag, S. A. & Bissonnette, L. R. 1967 Phys. Fluids, 10, 2603.
Orszag, S. A. & Kruskal, M. D. 1968 Phys. Fluids, 11, 43.
Proudman, I. & Reid, W. H. 1954 Phil. Trans. Roy. Soc. Lond. A 247, 163.
Stewart, R. W. & Townsend, A. A. 1951 Phil. Trans. Roy. Soc. Lond. A 243, 359.
Tatsumi, T. 1957 Proc. Roy. Soc. Lond. A 239, 16.
Taylor, G. I. 1921 Proc. Lond. Math. Soc. 20, 196.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed