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

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Abstract

The Rayleigh-Taylor instability (RTI) occurs in a broad range of processes in nature and technology. Analysing the power density spectrum of fluctuations in Rayleigh-Taylor (RT) flow is a means of highlighting characteristic length- and time-scales, anisotropies and anomalous processes. Raw time series from hot-wire anemometry measurements of Rayleigh-Taylor interfacial mixing experiment by Akula et al., JFM 816, 619-660 (2017) are considered as a sample case to adjust the parameters of a model power density spectrum. The results suggest that the power density spectrum of one of the flow components can be confidently modelled as the product of a power law and an exponential. The data analysis is based on Whittle's approximation of the power density spectrum for independent zero-mean near-Gaussian signals to construct a Maximum likelihood Estimator (MLE) of the parameters. Those that maximise the log-likelihood are computed numerically through Newton-Raphson iteration. The Hessian of the log-likelihood is used to evaluate the Fisher information matrix and provide an estimate of the statistical error on the obtained parameters. The Kolmogorov-Smirnov test is used to verify the hypothesis that the ratio between the observed periodogram and the estimated power density spectrum follows a chi-squared probability distribution. This step is performed to show goodness-of-fit. We also study the dependence of the model parameters on the range of mode numbers over which the fit is performed.
Original languageEnglish
Number of pages8
JournalChaos: an interdisciplinary journal of nonlinear science
Publication statusSubmitted - 2020

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