Journal of Fluid Mechanics


Approach to the 4/5 law in homogeneous isotropic turbulence

a1 Discipline of Mechanical Engineering, University of Newcastle, NSW 2308, Australia

Article author query
antonia ra   [Google Scholar] 
burattini p   [Google Scholar] 


Kolmogorov's similarity hypotheses and his 4/5 law are valid at very large Reynolds numbers. For flows encountered in the laboratory, the effect of a finite Reynolds number and of the non-stationarity or inhomogeneity associated with the large scales can affect the behaviour of the scales in the inertial range significantly. This paper focuses on the source of inhomogeneity in two types of flows, those dominated mainly by a decay of energy in the streamwise direction and those which are forced, through a continuous injection of energy at large scales. Results based on a parameterization of the second-order velocity structure function indicate that the normalized third-order structure function approaches 4/5 much more rapidly for forced than for decaying turbulence. This trend is supported by grid turbulence measurements and numerical data in a periodic box.

(Published Online February 27 2006)
(Received August 29 2005)
(Revised December 6 2005)