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.