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

Abstract

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.

Velocity Fluctuations Spectra in Experimental Data on Rayleigh–Taylor Mixing

“…Careful data analysis found excellent agreement with the group theory predictions [28]. It was also consistent with the group theory discovery that RT mixing can keep order and, in fact, retain memory of deterministic conditions, even at late times [9,24,28,29].…”

“…The signs of spectral shape parameters are α, β < 0, because, in RT mixing with constant acceleration, larger velocities correspond to larger length scales. The use of the compound function in RT spectra is discussed in detail in our earlier works [25,25,28]. The compound function E(k) ∼ k α exp(βk) is applied in turbulence to describe realistic spectra in experiments and observations [9,13,14,16,17,25,[30][31][32].…”

“…In this work, we analyze data in the experiments [12] to further understand the properties of RT mixing. Our earlier works studied the fluctuations of the cross-stream velocity component, the density and the mass flux [25,28]. Here we analyze the fluctuations of each of three velocity components.…”

“…To combat these difficulties, and advance understanding of RT mixing, rigorous data analysis is required [25,25]. Substantial success has recently been achieved, with the data analysis method employed in this paper characterizing the fluctuations spectra of specific kinetic energy, density and mass flux in the direction of the acceleration for an RTI experiment, which has evaded theory analysis for some time due to the inhomogeneity in the fluid densities [26][27][28]. Careful data analysis found excellent agreement with the group theory predictions [28].…”

“…Substantial success has recently been achieved, with the data analysis method employed in this paper characterizing the fluctuations spectra of specific kinetic energy, density and mass flux in the direction of the acceleration for an RTI experiment, which has evaded theory analysis for some time due to the inhomogeneity in the fluid densities [26][27][28]. Careful data analysis found excellent agreement with the group theory predictions [28]. It was also consistent with the group theory discovery that RT mixing can keep order and, in fact, retain memory of deterministic conditions, even at late times [9,24,28,29].…”