Rayleigh-Taylor Turbulence Research Articles

Quantifying mixing of Rayleigh-Taylor turbulence

A systematic model is established to quantitatively predict the evolution of Rayleigh-Taylor turbulence at three different mixing levels and density ratios. Our predictions show great correspondence with the previous experiments and simulations and make an appropriate explanation for the distinct differences existing in experiments.

Kinetic energy and enstrophy transfer in compressible Rayleigh–Taylor turbulence

Abstract

Temporal-Spatial Evolution of Kinetic and Thermal Energy Dissipation Rates in a Three-Dimensional Turbulent Rayleigh-Taylor Mixing Zone.

In this work, the temporal–spatial evolution of kinetic and thermal energy dissipation rates in three-dimensional (3D) turbulent Rayleigh–Taylor (RT) mixing are investigated numerically by the lattice Boltzmann method. The temperature fields, kinetic and thermal energy dissipation rates with temporal–spatial evolution, the probability density functions, the fractal dimension of mixing interface, spatial scaling law of structure function for the kinetic and the thermal energy dissipation rates in 3D space are analysed in detail to provide an improved physical understanding of the temporal–spatial dissipation-rate characteristic in the 3D turbulent Rayleigh–Taylor mixing zone. Our numerical results indicate that the kinetic and thermal energy dissipation rates are concentrated in areas with large gradients of velocity and temperature with temporal evolution, respectively, which is consistent with the theoretical assumption. However, small scale thermal plumes initially at the section of half vertical height increasingly develop large scale plumes with time evolution. The probability density function tail of thermal energy dissipation gradually rises and approaches the stretched exponent function with temporal evolution. The slope of fractal dimension increases at an early time, however, the fractal dimension for the fluid interfaces is 2.4 at times t/τ ≥ 2, which demonstrates the self-similarity of the turbulent RT mixing zone in 3D space. It is further demonstrated that the second, fourth and sixth-order structure functions for velocity and temperature structure functions have a linear scaling within the inertial range.

Mixed mass of classical Rayleigh-Taylor mixing at arbitrary density ratios

The accurate prediction of mixed mass induced by turbulent Rayleigh-Taylor mixing is of fundamental importance for many natural phenomena and engineering applications; however, no quantitative theory based on it has been established yet. In this study, we establish a quantitative theory to predict its evolution at arbitrary density ratios by combining the theory of density-ratio-invariant mean species profiles, which was recently developed by us, and the closure model for the turbulent fluctuations presented in this letter. The transformation formula between mixed mass and mixing width is obtained; in addition, the quantitative variation of normalized mixed mass with respect to the density ratio is derived. The theoretical results agreed very well with the direct numerical simulations at varied density ratios. The study sheds light on the quantitative prediction of mixed mass in practical engineering applications such as inertial confinement fusion.

Suppression of Rayleigh-Taylor turbulence by time-periodic acceleration.

The dynamics of Rayleigh-Taylor turbulence convection in the presence of an alternating, time-periodic acceleration is studied by means of extensive direct numerical simulations of the Boussinesq equations. Within this framework, we discover a mechanism of relaminarization of turbulence: the alternating acceleration, which initially produces a growing turbulent mixing layer, at longer times suppresses turbulent fluctuation and drives the system toward an asymptotic stationary configuration. Dimensional arguments and linear stability theory are used to predict the width of the mixing layer in the asymptotic state as a function of the period of the acceleration.

Buoyancy-Driven Flow through a Bed of Solid Particles Produces a New Form of Rayleigh-Taylor Turbulence

Rayleigh-Taylor (RT) fluid turbulence through a bed of rigid, finite-size spheres is investigated by means of high-resolution direct numerical simulations, fully coupling the fluid and the solid phase via a state-of-the-art immersed boundary method. The porous character of the medium reveals a totally different physics for the mixing process when compared to the well-known phenomenology of classical RT mixing. For sufficiently small porosity, the growth rate of the mixing layer is linear in time (instead of quadratical) and the velocity fluctuations tend to saturate to a constant value (instead of linearly growing). We propose an effective continuum model to fully explain these results where porosity originated by the finite-size spheres is parametrized by a friction coefficient.

Entropy Generation Rates in Two-Dimensional Rayleigh-Taylor Turbulence Mixing.

Entropy generation rates in two-dimensional Rayleigh–Taylor (RT) turbulence mixing are investigated by numerical calculation. We mainly focus on the behavior of thermal entropy generation and viscous entropy generation of global quantities with time evolution in Rayleigh–Taylor turbulence mixing. Our results mainly indicate that, with time evolution, the intense viscous entropy generation rate and the intense thermal entropy generation rate occur in the large gradient of velocity and interfaces between hot and cold fluids in the RT mixing process. Furthermore, it is also noted that the mixed changing gradient of two quantities from the center of the region to both sides decrease as time evolves, and that the viscous entropy generation rate and thermal entropy generation rate constantly increase with time evolution; the thermal entropy generation rate with time evolution always dominates in the entropy generation of the RT mixing region. It is further found that a “smooth” function and a linear function are achieved in the spatial averaging entropy generation of RT mixing process, respectively.

Rayleigh-Taylor turbulence with singular nonuniform initial conditions

We perform direct numerical simulations of three dimensional Rayleigh-Taylor turbulence with a nonuniform singular initial temperature background. In such conditions, the mixing layer evolves under the driving of a varying effective Atwood number; the long-time growth is still self-similar, but not anymore proportional to $t^2$ and depends on the singularity exponent $c$ of the initial profile $\Delta T \propto z^c$. We show that the universality is recovered when looking at the efficiency, defined as the ratio of the variation rates of the kinetic energy over the heat flux. A closure model is proposed that is able to reproduce analytically the time evolution of the mean temperature profiles, in excellent agreement with the numerical results. Finally, we reinterpret our findings in the light of spontaneous stochasticity where the growth of the mixing layer is mapped into the propagation of a wave of turbulent fluctuations on a rough background.

Turbulent transport and mixing in transitional Rayleigh-Taylor unstable flow: A priori assessment of gradient-diffusion and similarity modeling.

Data from a 1152×760×1280 direct numerical simulation [N. J. Mueschke and O. Schilling, Phys.Fluids 21, 014106 (2009)PHFLE61070-663110.1063/1.3064120] of a Rayleigh-Taylor mixing layer modeled after a small-Atwood-number water-channel experiment is used to investigate the validity of gradient diffusion and similarity closures a priori. The budgets of the mean flow, turbulent kinetic energy, turbulent kinetic energy dissipation rate, heavy-fluid mass fraction variance, and heavy-fluid mass fraction variance dissipation rate transport equations across the mixing layer were previously analyzed [O. Schilling and N. J. Mueschke, Phys. Fluids 22, 105102 (2010)PHFLE61070-663110.1063/1.3484247] at different evolution times to identify the most important transport and mixing mechanisms. Here a methodology is introduced to systematically estimate model coefficients as a function of time in the closures of the dynamically significant terms in the transport equations by minimizing the L_{2} norm of the difference between the model and correlations constructed using the simulation data. It is shown that gradient-diffusion and similarity closures used for the turbulent kinetic energy K, turbulent kinetic energy dissipation rate ε, heavy-fluid mass fraction variance S, and heavy-fluid mass fraction variance dissipation rate χ equations capture the shape of the exact, unclosed profiles well over the nonlinear and turbulent evolution regimes. Using order-of-magnitude estimates [O. Schilling and N. J. Mueschke, Phys.Fluids 22, 105102 (2010)PHFLE61070-663110.1063/1.3484247] for the terms in the exact transport equations and their closure models, it is shown that several of the standard closures for the turbulent production and dissipation (destruction) must be modified to include Reynolds-number scalings appropriate for Rayleigh-Taylor flow at small to intermediate Reynolds numbers. The late-time, large Reynolds number coefficients are determined to be different from those used in shear flow applications and largely adopted in two-equation Reynolds-averaged Navier-Stokes (RANS) models of Rayleigh-Taylor turbulent mixing. In addition, it is shown that the predictions of the Boussinesq model for the Reynolds stress agree better with the data when additional buoyancy-related terms are included. It is shown that an unsteady RANS paradigm is needed to predict the transitional flow dynamics from early evolution times, analogous to the small Reynolds number modifications in RANS models of wall-bounded flows in which the production-to-dissipation ratio is far from equilibrium. Although the present study is specific to one particular flow and one set of initial conditions, the methodology could be applied to calibrations of other Rayleigh-Taylor flows with different initial conditions (which may give different results during the early-time, transitional flow stages, and perhaps asymptotic stage). The implications of these findings for developing high-fidelity eddy viscosity-based turbulent transport and mixing models of Rayleigh-Taylor turbulence are discussed.

Incompressible Rayleigh–Taylor Turbulence

Basic fluid equations are the main ingredient in the development of theories of Rayleigh–Taylor buoyancy-induced instability. Turbulence arises in the late stage of the instability evolution as a result of the proliferation of active scales of motion. Fluctuations are maintained by the unceasing conversion of potential energy into kinetic energy. Although the dynamics of turbulent fluctuations is ruled by the same equations controlling the Rayleigh–Taylor instability, here only phenomenological theories are currently available. The present review provides an overview of the most relevant (and often contrasting) theoretical approaches to Rayleigh–Taylor turbulence together with numerical and experimental evidence for their support. Although the focus is mainly on the classical Boussinesq Rayleigh–Taylor turbulence of miscible fluids, the review extends to other fluid systems with viscoelastic behavior, affected by rotation of the reference frame, and, finally, in the presence of reactions.

Influence of the mixing parameter on the second order moments of velocity and concentration in Rayleigh–Taylor turbulence

The purpose of this paper is to highlight the existence of simple algebraic expressions linking the second order moments of velocity and concentration in Rayleigh–Taylor turbulence, in the Boussinesq limit. Focusing on the concentration variance, these relations allow to underline the influence of mixing on the remaining second order correlations, as well as on the growth rate of the mixing zone.

Kinetic and thermal energy dissipation rates in two-dimensional Rayleigh-Taylor turbulence

The statistical properties of the kinetic εu and thermal εθ energy dissipation rates in two-dimensional Rayleigh-Taylor (RT) turbulence are studied by means of direct numerical simulations at small Atwood number and unit Prandtl number. Although εθ is important but εu can be neglected in the energy transport processes, the probability density functions of εu and εθ both show self-similarity properties during the RT evolution. The distributions are well fitted by a stretched exponential function and found to depart distinctly from the log-normal distribution for small amplitudes. Within the turbulent range, the intense dissipation events occur near the interfaces of hot and cold fluids, leading to a strong positive correlation between εu and εθ. Our results further reveal that although there is no constant fractal dimension for the fluid interfaces within the inertial range, the local fractal dimensions obtained at different times share similar scale-dependence.

Scale-to-scale energy and enstrophy transport in two-dimensional Rayleigh–Taylor turbulence

We apply a recently developed filtering approach, i.e. filter-space technique (FST), to study the scale-to-scale transport of kinetic energy, thermal energy, and enstrophy in two-dimensional (2D) Rayleigh–Taylor (RT) turbulence. Although the scaling laws of the energy cascades in 2D RT systems follow the Bolgiano–Obukhov (BO59) scenario due to buoyancy forces, the kinetic energy is still found to be, on average, dynamically transferred to large scales by an inverse cascade, while both the mean thermal energy and the mean enstrophy move towards small scales by forward cascades. In particular, there is a reasonably extended range over which the transfer rate of thermal energy is scale-independent and equals the corresponding thermal dissipation rate at different times. This range functions similarly to the inertial range for the kinetic energy in the homogeneous and isotropic turbulence. Our results further show that at small scales the fluctuations of the three instantaneous local fluxes are highly asymmetrically distributed and there is a strong correlation between any two fluxes. These small-scale features are signatures of the mixing and dissipation of fluids with steep temperature gradients at the fluid interfaces.

A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing

A two-length scale, second moment turbulence model (Reynolds averaged Navier-Stokes, RANS) is proposed to capture a wide variety of single-phase flows, spanning from incompressible flows with single fluids and mixtures of different density fluids (variable density flows) to flows over shock waves. The two-length scale model was developed to address an inconsistency present in the single-length scale models, e.g. the inability to match both variable density homogeneous Rayleigh-Taylor turbulence and Rayleigh-Taylor induced turbulence, as well as the inability to match both homogeneous shear and free shear flows. The two-length scale model focuses on separating the decay and transport length scales, as the two physical processes are generally different in inhomogeneous turbulence. This allows reasonable comparisons with statistics and spreading rates over such a wide range of turbulent flows using a common set of model coefficients. The specific canonical flows considered for calibrating the model include homogeneous shear, single-phase incompressible shear driven turbulence, variable density homogeneous Rayleigh-Taylor turbulence, Rayleigh-Taylor induced turbulence, and shocked isotropic turbulence. The second moment model shows to compare reasonably well with direct numerical simulations (DNS), experiments, and theory in most cases. The model was then applied to variable density shear layer and shock tube data and shows to be in reasonable agreement with DNS and experiments. The importance of using DNS to calibrate and assess RANS type turbulence models is also highlighted.

Large-scale analysis of unconfined self-similar Rayleigh–Taylor turbulence

The large-scale properties of unconfined Rayleigh–Taylor turbulence are investigated using an eddy-damped quasi-normal markovianized approximation. Within this framework, turbulent spectra are shown to undergo at late times and at large scales, an evolution dominated by non-linear backscattering processes. As a result, the analysis predicts that large scale initial conditions are eventually forgotten: there is no large scale invariant and no equivalent of a principle of permanence of large eddies. Additional properties of Rayleigh–Taylor large scales are also discussed. In particular, their scaling and anisotropy are examined, with an emphasis put on the combined influence of buoyancy production and non-linearities. The different assumptions and predictions of this work are verified by performing an implicit large eddy simulation of a Rayleigh–Taylor configuration.

Local dissipation scales in two-dimensional Rayleigh-Taylor turbulence.

We examine the distribution of the local dissipation scale η, Q(η), and its temporal evolution in two-dimensional (2D) Rayleigh-Taylor (RT) turbulence using direct numerical simulations at small Atwood number and unit Prandtl number. Within the self-similarity regime of the mixing zone evolution, distributions of η at small scales are found to be insensitive to the large-scale anisotropy of the system and independent of position and of the temporal evolution of the mixing zone. Our results further reveal that the present measured Q(η) agrees with those previously observed in homogeneous isotropic turbulence and in turbulent pipe flows, at least for the smallest scales around the classical Kolmogorov dissipation scale. However, the RT case seems to show a different trend from the other two cases for large scales, which may attributed to the absence of the inertial-range intermittency for the velocity field in 2D RT turbulence.

Multiscale modeling and nested simulations of three-dimensional ionospheric plasmas: Rayleigh–Taylor turbulence and nonequilibrium layer dynamics at fine scales

Multiscale modeling and high resolution three-dimensional simulations of nonequilibrium ionospheric dynamics are major frontiers in the field of space sciences. The latest developments in fast computational algorithms and novel numerical methods have advanced reliable forecasting of ionospheric environments at fine scales. These new capabilities include improved physics-based predictive modeling, nesting and implicit relaxation techniques that are designed to integrate models of disparate scales. A range of scales, from mesoscale to ionospheric microscale, are included in a 3D modeling framework. Analyses and simulations of primary and secondary Rayleigh–Taylor instabilities in the equatorial spread F (ESF), the response of the plasma density to the neutral turbulent dynamics, and wave breaking in the lower region of the ionosphere and nonequilibrium layer dynamics at fine scales are presented for coupled systems (ions, electrons and neutral winds), thus enabling studies of mesoscale/microscale dynamics for a range of altitudes that encompass the ionospheric E and F layers. We examine the organizing mixing patterns for plasma flows, which occur due to polarized gravity wave excitations in the neutral field, using Lagrangian coherent structures (LCS). LCS objectively depict the flow topology and the extracted scintillation-producing irregularities that indicate a generation of ionospheric density gradients, due to the accumulation of plasma. The scintillation effects in propagation, through strongly inhomogeneous ionospheric media, are induced by trapping electromagnetic (EM) waves in parabolic cavities, which are created by the refractive index gradients along the propagation paths.

Unstably Stratified Homogeneous Turbulence as a Tool for Turbulent Mixing Modeling

In this paper, we propose a kind of buoyancy-driven flow leading to unstably stratified homogeneous (USH) turbulence. This approach is developed in the context of incompressible Navier–Stokes equations under Boussinesq approximation. We show that USH turbulence is a valuable tool for understanding and modeling turbulent mixing induced by Rayleigh-Taylor (RT) instability. It is a much simpler configuration than “RT turbulence” which is in fact inhomogeneous. Thus, it gives insights in the basic mechanisms of buoyancy-driven turbulence, namely the interplay between buoyancy production, nonlinearities and dissipation. Besides, despite their differences both types of turbulence share very similar features for the large scale characteristics as well as for the inertial range spectrum structure.

Reactive Rayleigh–Taylor turbulent mixing: a one-dimensional-turbulence study

We study the problem of reactive Rayleigh–Taylor turbulence in the Boussinesq framework using one-dimensional-turbulence (ODT) simulations. In this problem a reaction zone between overlying heavy/cold reactants and underlying light/hot products moves against gravity. First, we show that ODT results for global quantities in non-reactive Rayleigh–Taylor turbulence are within those from direct numerical simulations (DNS). This comparison give us confidence in using ODT to study unexplored flow regimes in the reactive case. Then, we show how ODT predicts an early stage of reactive Rayleigh–Taylor turbulence that behaves similarly to the non-reactive case, as observed in previous DNS. More importantly, ODT indicates a later stage where the growth of the reaction zone reduces considerably. The present work can be seen as a step towards the study of supernova flames with ODT.

Temporal evolution and scaling of mixing in two-dimensional Rayleigh-Taylor turbulence

We report a high-resolution numerical study of two-dimensional (2D) miscible Rayleigh-Taylor (RT) incompressible turbulence with the Boussinesq approximation. An ensemble of 100 independent realizations were performed at small Atwood number and unit Prandtl number with a spatial resolution of 2048 × 8193 grid points. Our main focus is on the temporal evolution and the scaling behavior of global quantities and of small-scale turbulence properties. Our results show that the buoyancy force balances the inertial force at all scales below the integral length scale and thus validate the basic force-balance assumption of the Bolgiano-Obukhov scenario in 2D RT turbulence. It is further found that the Kolmogorov dissipation scale η(t) ∼ t1/8, the kinetic-energy dissipation rate ɛu(t) ∼ t−1/2, and the thermal dissipation rate ɛθ(t) ∼ t−1. All of these scaling properties are in excellent agreement with the theoretical predictions of the Chertkov model [“Phenomenology of Rayleigh-Taylor turbulence,” Phys. Rev. Lett. 91, 115001 (2003)]10.1103/PhysRevLett.91.115001. We further discuss the emergence of intermittency and anomalous scaling for high order moments of velocity and temperature differences. The scaling exponents \documentclass[12pt]{minimal}\begin{document}$\xi ^r_p$\end{document}ξpr of the pth-order temperature structure functions are shown to saturate to \documentclass[12pt]{minimal}\begin{document}$\xi ^r_{\infty }\simeq 0.78 \pm 0.15$\end{document}ξ∞r≃0.78±0.15 for the highest orders, p ∼ 10. The value of \documentclass[12pt]{minimal}\begin{document}$\xi ^r_{\infty }$\end{document}ξ∞r and the order at which saturation occurs are compatible with those of turbulent Rayleigh-Bénard (RB) convection [A. Celani, T. Matsumoto, A. Mazzino, and M. Vergassola, “Scaling and universality in turbulent convection,” Phys. Rev. Lett. 88, 054503 (2002)]10.1103/PhysRevLett.88.054503, supporting the scenario of universality of buoyancy-driven turbulence with respect to the different boundary conditions characterizing the RT and RB systems.