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Abstract
Investigating the power density spectrum of fluctuations in RayleighTaylor (RT) interfacial mixing is a means of studying characteristic length, timescales, anisotropies, and anomalous processes. Guided by group theory, analyzing the invariancebased properties of the fluctuations, our paper examines raw time series from hotwire anemometry measurements in the experiment by Akula et al. [J. Fluid Mech. 816, 619 (2017)]. The results suggest that the power density spectrum can be modeled as a compound function presented 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 zeromean nearGaussian signals to construct a maximum likelihood estimator of the parameters. Those that maximize the loglikelihood are computed numerically through NewtonRaphson iteration. The Hessian of the loglikelihood is used to evaluate the Fisher information matrix and provide an estimate of the statistical error on the obtained parameters. The KolmogorovSmirnov test is applied to analyze the goodness of fit, by verifying the hypothesis that the ratio between the observed periodogram and the estimated power density spectrum follows a χ2 probability distribution. The dependence of the parameters of the compound function is investigated on the range of mode numbers over which the fit is performed. In the domain where the relative errors of the powerlaw exponent and the exponential decay rate are small and the goodness of fit is excellent, the parameters of the compound function are clearly defined, in agreement with the theory developed in the paper. The study of the powerlaw spectra in RT mixing data suggests that rigorous physicsbased statistical methods can help researchers to see beyond visual inspection.
Original language  English 

Article number  053107 
Number of pages  14 
Journal  Physical Review E  Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics 
Volume  102 
Issue number  5 
DOIs  
Publication status  Published  30 Nov 2020 
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Dive into the research topics of 'Whittle Maximum Likelihood Estimate of spectral properties of RayleighTaylor interfacial mixing using hotwire anemometry experimental data'. Together they form a unique fingerprint.Activities
 1 Contribution or participation in a conference

2018 AIP Congress
David Pfefferle (Keynote speaker/Invited speaker)
9 Dec 2018 → 13 Dec 2018Activity: Conferences and workshops › Contribution or participation in a conference