Power-law decay of homogeneous turbulence at low Reynolds numbers
The decay of nominally isotropic, homogeneous incompressible turbulence is studied by direct numerical simulations for Re-lambda in the range (5-50) with 256(3) spectral coefficients. A power-law decay of the turbulent energy is observed with exponents approximately equal to 1.5 and 1.25, apparently dependent on Re-lambda. A new complete similarity form for the double and triple velocity correlation functions, f(r,t) and k(r,t), is proposed for low to intermediate Re-lambda that is consistent with the Karmia-Howarth equation and the results of the numerical experiments. The results are also consistent with Saffman's proposed asymptotic behavior of f(r,t) for large separation r for runs with a decay exponent of 1.5. The so-called final period of decay is not observed.
Copyright © 1994 American Institute of Physics. Received 27 January 1994; accepted 11 July 1994. We thank Dr. Robert Rogallo for his generosity for providing the basic program for the simulations. He and Dr. Alan Wray provided valuable comments. We are also grateful to Professors P.E. Dimotakis, W.K. George, D.I. Pullin, and P.G. Saffman for stimulating discussions. This research was performed in part using the Intel Touchstone Delta System operated by Caltech on behalf of the Concurrent Supercomputing Consortium. This work was supported by the U.S. Air Force Office of Scientific Research under Grant No. AFOSR-91-0241.