- Access by Xinjiang University
Transport Processes as Foundations of the Heisenberg and Obukhoff Theories of Turbulence
Phys. Rev. 93, 4 – Published 1 January, 1954
DOI: https://doi.org/10.1103/PhysRev.93.4
Abstract
The transfer of energy across the spectrum is investigated by the method of the harmonic analysis of the Navier-Stokes equation. The phase correlation which enters into the transfer is determined by the statistical considerations of transport processes. The results obtained allow a theoretical explanation to be given to the Heisenberg and Obukhoff postulates, delimiting the conditions of their applicability. By extending the above considerations of transport processes to shear flow, the production of turbulent energy from the mean flow is determined in spectral terms. As an application, the spectral laws for energy and shear are derived, and compared with measurements.
References (13)
- W. Heisenberg, Z. Physik 124, 628 (1948) S. Chandrasekhar, Astrophys. J. 110, 329 (1949)
- T. von Karman, Proc. Natl. Acad. Sci. U. S. 34, 530 (1948)
- A. Obukhoff, Compt. rend. acad. sci. U. R. S. S. 32, 19 (1941) Bull. acad. sci. U. R. S. S. Sér. géograph. et géophys. 32, 453 (1941)
- A. N. Kolmogoroff, Compt. rend. acad. sci. U. R. S. S. 30, 301 (1941) ibid.32, 16 (1941)
- Prof. J. M. Burgers Proc. Acad. Sci. Amsterdam 43, 8 (1940) Advances in Applied Mechanics 1, 182 (1948) Proc. Acad. Sci. Amsterdam 53, 122, 247, 393, 718, 732 (1950)
- L. Onsager, Nuovo cimento, Suppl. 6, Ser. 9, No. 2, 279 (1949) Phys. Rev. 68, 286 (1945)
- C. M. Tchen, J. Chem. Phys. 20, 214 (1952)
- C. M. Tchen, "Mean Value and Correlation Problems Connected with the Motion of Small Particles Suspended in a Turbulent Fluid," Mededeelingen No. 51, (1947), Laboratorium voor Aero- en Hydrodynamica der Technische Hogeschool, Delft, Netherlands
- C. M. Tchen, J. Research Natl. Bur. Standards 46, 480 (1951)
- Eugene N. Parker, Phys. Rev. 90, 221 (1953) "The Concept of Physical Subsets and Application to Hydrodynamic Theory," Technical Memorandum No. 988, March 153, Mechelson Laboratory, Inyokern, China Lake, California (unpublished)
- C. M. Tchen, J. Research Natl. Bur. Standards 50, 51 (1953)
- P. S. Klebanoff, Natl. Advisory Comm. Aeronaut. Tech. Notes (to be published)
- John Laufer, Natl. Advisory Comm. Aeronaut. Tech. Notes, No. 2954 (1953)