Wavelet analysis of a Gaussian Kolmogorov signal

Synthetic turbulence, fractal interpolation, and large-eddy simulation

Fractal interpolation has been proposed in the literature as an efficient way to construct closure models for the numerical solution of coarse-grained Navier-Stokes equations. It is based on synthetically generating a scale-invariant subgrid-scale field and analytically evaluating its effects on large resolved scales. In this paper, we propose an extension of previous work by developing a multiaffine fractal interpolation scheme and demonstrate that it preserves not only the fractal dimension but also the higher-order structure functions and the non-Gaussian probability density function of the velocity increments. Extensive a priori analyses of atmospheric boundary layer measurements further reveal that this multiaffine closure model has the potential for satisfactory performance in large-eddy simulations. The pertinence of this newly proposed methodology in the case of passive scalars is also discussed.

Inertial range determination for aerothermal turbulence using fractionally differenced processes and wavelets

A fractionally differenced (FD) process is used to model aerothermal turbulence data, and the model parameters are estimated via wavelet techniques. Theory and results are presented for three estimators of the FD parameter: an "instantaneous" block-independent least squares estimator and block-dependent weighted least squares and maximum likelihood estimators. Confidence intervals are developed for the block-dependent estimators. We show that for a majority of the aerothermal turbulence data studied herein, there is a strong departure from the theoretical Kolmogorov turbulence over finite ranges of scale. A time-scale-dependent inertial range statistic is developed to quantify this departure.