Self-similar Rayleigh-Taylor mixing with accelerations varying in time and space.

As a ubiquitous paradigm of instabilities and mixing that occur in instances as diverse as supernovae, plasma fusion, oil recovery, and nanofabrication, the Rayleigh-Taylor (RT) problem is rightly regarded as important. The acceleration of the fluid medium in these instances often depends on time and space, whereas most past studies assume it to be constant or impulsive. Here, we analyze the symmetries of RT mixing for variable accelerations and obtain the scaling of correlations and spectra for classes of self-similar dynamics. RT mixing is shown to retain the memory of deterministic conditions for all accelerations, with the dynamics ranging from superballistic to subdiffusive. These results contribute to our understanding and control of the RT phenomena and reveal specific conditions under which Kolmogorov turbulence might be realized in RT mixing.

Erratum: Whittle maximum likelihood estimate of spectral properties of Rayleigh-Taylor interfacial mixing using hot-wire anemometry experimental data [Phys. Rev. E 102, 053107 (2020)].

This corrects the article DOI: 10.1103/PhysRevE.102.053107.

Supernovae and the Arrow of Time.

Supernovae are explosions of stars and are a central problem in astrophysics. Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities develop during the star's explosion and lead to intense interfacial RT/RM mixing of the star materials. We handle the mathematical challenges of the RT/RM problem based on the group theory approach. We directly link the conservation laws governing RT/RM dynamics to the symmetry-based momentum model, derive the model parameters, and find the analytical solutions and characteristics of RT/RM dynamics with variable accelerations in the linear, nonlinear and mixing regimes. The theory outcomes explain the astrophysical observations and yield the design of laboratory experiments. They suggest that supernova evolution is a non-equilibrium process directed by the arrow of time.

Whittle maximum likelihood estimate of spectral properties of Rayleigh-Taylor interfacial mixing using hot-wire anemometry experimental data.

Investigating the power density spectrum of fluctuations in Rayleigh-Taylor (RT) interfacial mixing is a means of studying characteristic length, timescales, anisotropies, and anomalous processes. Guided by group theory, analyzing the invariance-based properties of the fluctuations, our paper examines raw time series from hot-wire anemometry measurements in the experiment by Akula et al. [J. Fluid Mech. 816, 619 (2017)JFLSA70022-112010.1017/jfm.2017.95]. 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 zero-mean near-Gaussian signals to construct a maximum likelihood estimator of the parameters. Those that maximize 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 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 χ^{2} 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 power-law 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 power-law spectra in RT mixing data suggests that rigorous physics-based statistical methods can help researchers to see beyond visual inspection.

Supernova, nuclear synthesis, fluid instabilities, and interfacial mixing.

Supernovae and their remnants are a central problem in astrophysics due to their role in the stellar evolution and nuclear synthesis. A supernova's explosion is driven by a blast wave causing the development of Rayleigh-Taylor and Richtmyer-Meshkov instabilities and leading to intensive interfacial mixing of materials of a progenitor star. Rayleigh-Taylor and Richtmyer-Meshkov mixing breaks spherical symmetry of a star and provides conditions for synthesis of heavy mass elements in addition to light mass elements synthesized in the star before its explosion. By focusing on hydrodynamic aspects of the problem, we apply group theory analysis to identify the properties of Rayleigh-Taylor and Richtmyer-Meshkov dynamics with variable acceleration, discover subdiffusive character of the blast wave-induced interfacial mixing, and reveal the mechanism of energy accumulation and transport at small scales in supernovae.

Interface dynamics: Mechanisms of stabilization and destabilization and structure of flow fields.

Interfacial mixing and transport are nonequilibrium processes coupling kinetic to macroscopic scales. They occur in fluids, plasmas, and materials over celestial events to atoms. Grasping their fundamentals can advance a broad range of disciplines in science, mathematics, and engineering. This paper focuses on the long-standing classic problem of stability of a phase boundary-a fluid interface that has a mass flow across it. We briefly review the recent advances in theoretical and experimental studies, develop the general theoretical framework directly linking the microscopic interfacial transport to the macroscopic flow fields, discover mechanisms of interface stabilization and destabilization that have not been discussed before for both inertial and accelerated dynamics, and chart perspectives for future research.

What is certain and what is not so certain in our knowledge of Rayleigh-Taylor mixing?

Past decades significantly advanced our understanding of Rayleigh-Taylor (RT) mixing. We briefly review recent theoretical results and numerical modelling approaches and compare them with state-of-the-art experiments focusing the reader's attention on qualitative properties of RT mixing.

Acceleration and turbulence in Rayleigh-Taylor mixing.

Past decades have significantly advanced our ability to probe turbulent mixing in Rayleigh-Taylor flows, in both experiments and simulations. Yet, our basic understanding remains elusive and requires better basis. For instance, observations do not substantiate the rudimentary dimensional arguments to the same degree of certainty as in classical three-dimensional turbulence. We provide a plausible scenario based on a momentum-driven model. The results presented are specific enough that they can be used to interpret experimental and numerical simulation data.

High-performance holographic technologies for fluid-dynamics experiments.

Modern technologies offer new opportunities for experimentalists in a variety of research areas of fluid dynamics. Improvements are now possible in the state-of-the-art in precision, dynamic range, reproducibility, motion-control accuracy, data-acquisition rate and information capacity. These improvements are required for understanding complex turbulent flows under realistic conditions, and for allowing unambiguous comparisons to be made with new theoretical approaches and large-scale numerical simulations. One of the new technologies is high-performance digital holography. State-of-the-art motion control, electronics and optical imaging allow for the realization of turbulent flows with very high Reynolds number (more than 10(7)) on a relatively small laboratory scale, and quantification of their properties with high space-time resolutions and bandwidth. In-line digital holographic technology can provide complete three-dimensional mapping of the flow velocity and density fields at high data rates (over 1000 frames per second) over a relatively large spatial area with high spatial (1-10 microm) and temporal (better than a few nanoseconds) resolution, and can give accurate quantitative description of the fluid flows, including those of multi-phase and unsteady conditions. This technology can be applied in a variety of problems to study fundamental properties of flow-particle interactions, rotating flows, non-canonical boundary layers and Rayleigh-Taylor mixing. Some of these examples are discussed briefly.

Review of theoretical modelling approaches of Rayleigh-Taylor instabilities and turbulent mixing.

We review the theoretical developments in the field of Rayleigh-Taylor instabilities and turbulent mixing, discuss what is known and what is not known about the phenomenon, and outline the features of similarity of the turbulent mixing process. Based on the physical intuition and on the results of rigorous theoretical studies, we put forward some new ideas on how to grasp the essentials of the mixing process and consider the influence of momentum transport on the invariants and on scaling and statistical properties of the unsteady turbulent mixing.