Power-law decay of homogeneous turbulence at low Reynolds numbers

Abstract

The decay of nominally isotropic, homogeneous incompressible turbulence is studied by direct numerical simulations for Reλ in the range (5–50) with 2563 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 Reλ. 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 Reλ that is consistent with the Kármán–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.