Fluctuations spectra of specific kinetic energy, density, and mass flux in Rayleigh–Taylor mixing

Rayleigh–Taylor (RT) interfacial mixing is critically important in a broad range of processes in nature and technology. To understand self-similar RT dynamics, a bias free interpretation of data is in need. This work yields the physics properties and the anomalous scaling of Rayleigh–Taylor mixing based on the analysis of experimental data. Fluctuations spectra are analyzed of the specific kinetic energy of the velocity component in the acceleration direction, the density, and the mass flux. Theoretical foundations and statistical method are developed, under group theory guidance, to investigate unprocessed data, and identify with statistical confidence their spectral shapes. These include the mean values of the spectral shape's parameters, their relative errors, and the goodness of fit. The Anderson–Darling test is employed to inspect the residuals. The intervals of mode numbers are found, where the relative errors of the spectral shape parameters are small and the goodness of fit is excellent. We reveal that spectral shapes of fluctuations in RT mixing experiments can be well described by compound functions, represented by a product of a power law and an exponential. The data analysis based properties unambiguously identifies the dynamic specificity and heterogeneity of RT mixing.