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Investigating the power density spectrum of fluctuations in Rayleigh-Taylor(RT) interfacial mixing is a means of studying characteristic length- andtime-scales, anisotropies and anomalous processes. Guided by group theory,analysing the invariance-based properties of the fluctuations, our workexamines raw time series from hot-wire anemometry measurements in theexperiment by Akula et al., JFM 816, 619-660 (2017). The results suggest thatthe power density spectrum can be modelled as a compound function presented asthe product of a power law and an exponential. The data analysis is based onWhittle's approximation of the power density spectrum for independent zero-meannear-Gaussian signals to construct a Maximum likelihood Estimator (MLE) of theparameters. Those that maximise the log-likelihood are computed numericallythrough Newton-Raphson iteration. The Hessian of the log-likelihood is used toevaluate the Fisher information matrix and provide an estimate of thestatistical error on the obtained parameters. The Kolmogorov-Smirnov test isapplied to analyse the goodness-of-fit, by verifying the hypothesis that theratio between the observed periodogram and the estimated power density spectrumfollows a chi-squared probability distribution. The dependence of theparameters of the compound function is investigated on the range of modenumbers over which the fit is performed. In the domain where the relativeerrors of the power law exponent and the exponential decay rate are small andthe goodness-of-fit is excellent, the parameters of the compound function areclearly defined, in agreement with the theory. The study of the power-lawspectra in RT mixing data suggests that rigorous physics-based statisticalmethods can help researchers to see beyond visual inspection.

WWhittle Maximum Likelihood Estimate of spectral properties of Rayleigh-Taylor interfacial mixing using hot-wire anemometry experimental data