Journal of Fluid Mechanics

Isotropy of the small scales of turbulence at low Reynolds number

J.  Kim a1 and R. A.  Antonia a2
a1 Center for Turbulence Research, NASA-Ames Research Center, Moffett Field, CA 94035, USA
a2 Department of Mechanical Engineering, University of Newcastle, New South Wales, 2308, Australia

Article author query
kim j   [Google Scholar] 
antonia ra   [Google Scholar] 


Spectral local isotropy tests are applied to direct numerical simulation data, mainly at the centreline of a fully developed turbulent channel flow. Despite the small Reynolds number of the simulation, the high-wavenumber behaviour of velocity and vorticity spectra is consistent with local isotropy. This consistency is verified by the relationship between streamwise wavenumber spectra and spanwise wavenumber spectra. The high-wavenumber behaviour of the pressure spectrum is also consistent with local isotropy and compares favourably with the calculation of Batchelor (1951), which assumes isotropy and joint normality of the velocity field at two points in space. The latter assumption is validated by the shape but not the magnitude of the quadruple correlation of the streamwise velocity fluctuation at small separations. There is only partial support for local spectral isotropy away from the centreline as the magnitude of the mean strain rate increases.

(Published Online April 26 2006)
(Received November 4 1991)
(Revised December 2 1992)