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 Eè (k, t ) and the spectral transfer functions T (k, t) and Tè (k, t ) satisfy similarity during decay. The evolution of these four quantities provides qualified support for the equilibrium similarity proposal of George (1992a, b). In particular, this proposal provides a reliable means of calculating the transfer functions, starting with known distributions of E(k, t) and Eè (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 Eè (k, t) and Tè (k, t) do not depend on Sc, when the latter is in the range 0.7Sc7, 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 Eè (k, t ).