A spectral model applied to homogeneous turbulence

Abstract

Because a spectral model describes distributions of turbulent energy and stress in wave-number space or, equivalently, in terms of a distribution of length scales, it can account for the variation of evolution rates with length scale. A spectral turbulence model adapted from a model introduced by Besnard, Rauenzahn, Harlow, and Zemach is applied here to homogeneous turbulent flows driven by constant mean-flow gradients and to free decay of such flows. To the extent permitted by the experimental data, initial turbulent spectra are inferred, and their evolutions in time are computed to obtain detailed quantitative predictions of the spectra, relaxation times to self-similarity, self-similar spectrum shapes, growth rates, and power-law time dependence of turbulent energies and dominant-eddy sizes, and integral data, such as the components of the Reynolds stress tensor and the Reynolds stress anisotropy tensor. The match to experimental data, within the limits of experimental uncertainties, is good. Some qualifications on the limits of validity of the model are noted. Among phenomena encountered for which the spectral description provides quantitative understanding are the convergence of the anisotropy tensor to a nonzero limit under conditions of free decay (i.e., incomplete return to isotropy, implying a Rotta constant of unity) and the apparent ‘‘return to anisotropy,’’ observed after an anisotropy tensor vanishes due to a temporary cancellation of positive and negative parts of a spectrum, which evolve at different rates.