Similarity of decaying isotropic turbulence with a passive scalar

Direct numerical simulations have been carried out for decaying homogeneous isotropic turbulence in a periodic box. Data for both the velocity and passive scalar fields are considered, the latter for several values of the Schmidt number Sc . The focus is on how the three-dimensional spectra $E(k,t)$ and Eθ (k,t) and the spectral transfer functions $T(k,t)$ and Tθ (k,t) satisfy similarity during decay. The evolution of these four quantities provides qualified support for the equilibrium similarity proposal of George (1992 a, b ). In particular, this proposal provides a reliable means of calculating the transfer functions, starting with known distributions of $E(k,t)$ and Eθ (k,t) . However, at sufficiently large values of the wavenumber k , normalizations by Kolmogorov and Batchelor variables yield a better collapse of these quantities than the use of equilibrium similarity The distributions of Eθ (k,t) and Tθ (k,t) do not depend on Sc , when the latter is in the range 0.7 \,\, Sc \,\, 7 , irrespective of the normalization adopted. The velocity derivative skewness and mixed velocity–scalar derivative skewness approach constant values as t increases. This is in disagreement with equilibrium similarity but in accord with the observed high-wavenumber collapse of Kolmogorov and Batchelor normalized distributions of $E(k,t)$ and Eθ (k,t) .