Fluctuations spectra in Rayleigh-Taylor interfacial mixing

Rayleigh-Taylor (RT) interfacial mixing plays a critical role in a broad range of processes in nature and technology, and understanding fluctuations spectra of self-similar RT mixing is in high demand. Guided by group theory, analyzing invariant properties of the fluctuations, we investigates the time series of raw data from hot-wire anemometry measurements in experiment by Akula et al. [J. Fluid Mech. 816, 619 (2017)]. We find that the power density spectrum can be modeled as a compound function represented by a product of a power law and an exponential. We apply rigorous physics-based statistical methods to estimate the model parameters, including their mean values and relative errors, to study the dependence of the parameters on the fitting interval, and to evaluate goodness-of-fit. We find that the values of the power law exponent and the exponential decay rate are distinct for fluctuations of each of the velocity components as well as of the density and the mass flux. Particularly, the power-law exponents are estimated as -2 and -1 for fluctuations of the velocity components in directions of the acceleration and the co-flowing streams, whereas they are close to -1 and-3/2 for fluctuations of the density and mass flux, achieving good agreement with group theory.