Self-similarity and internal structure of turbulence induced by Rayleigh–Taylor instability

1999 ◽  
Vol 399 ◽  
pp. 1-48 ◽  
Author(s):  
S. B. DALZIEL ◽  
P. F. LINDEN ◽  
D. L. YOUNGS
Keyword(s):  
Spatial Structure ◽  
Internal Structure ◽  
Initial Conditions ◽  
Salt Water ◽  
Concentration Field ◽  
Taylor Instability ◽  
Mixing Zone ◽  
Measured Velocity ◽  
Rigid Barrier ◽  
Rayleigh Taylor Instability

This paper describes an experimental investigation of mixing due to Rayleigh–Taylor instability between two miscible fluids. Attention is focused on the gravitationally driven instability between a layer of salt water and a layer of fresh water with particular emphasis on the internal structure within the mixing zone. Three-dimensional numerical simulations of the same flow are used to give extra insight into the behaviour found in the experiments.The two layers are initially separated by a rigid barrier which is removed at the start of the experiment. The removal process injects vorticity into the flow and creates a small but significant initial disturbance. A novel aspect of the numerical investigation is that the measured velocity field for the start of the experiments has been used to initialize the simulations, achieving substantially improved agreement with experiment when compared with simulations using idealized initial conditions. It is shown that the spatial structure of these initial conditions is more important than their amplitude for the subsequent growth of the mixing region between the two layers. Simple measures of the growth of the instability are shown to be inappropriate due to the spatial structure of the initial conditions which continues to influence the flow throughout its evolution. As a result the mixing zone does not follow the classical quadratic time dependence predicted from similarity considerations. Direct comparison of external measures of the growth show the necessity to capture the gross features of the initial conditions while detailed measures of the internal structure show a rapid loss of memory of the finer details of the initial conditions.Image processing techniques are employed to provide a detailed study of the internal structure and statistics of the concentration field. These measurements demonstrate that, at scales small compared with the confining geometry, the flow rapidly adopts self-similar turbulent behaviour with the influence of the barrier-induced perturbation confined to the larger length scales. Concentration power spectra and the fractal dimension of iso-concentration contours are found to be representative of fully developed turbulence and there is close agreement between the experiments and simulations. Other statistics of the mixing zone show a reasonable level of agreement, the discrepancies mainly being due to experimental noise and the finite resolution of the simulations.

scholarly journals Transition stages of Rayleigh–Taylor instability between miscible fluids

2001 ◽  
Vol 443 ◽  
pp. 69-99 ◽  
Author(s):  
ANDREW W. COOK ◽  
PAUL E. DIMOTAKIS
Keyword(s):  
Growth Rates ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Density Ratio ◽  
Reynolds Numbers ◽  
Taylor Instability ◽  
Initial Growth ◽  
Mixing Zone ◽  
Miscible Fluids ◽  
Rayleigh Taylor Instability

Direct numerical simulations (DNS) are presented of three-dimensional, Rayleigh–Taylor instability (RTI) between two incompressible, miscible fluids, with a 3:1 density ratio. Periodic boundary conditions are imposed in the horizontal directions of a rectangular domain, with no-slip top and bottom walls. Solutions are obtained for the Navier–Stokes equations, augmented by a species transport-diffusion equation, with various initial perturbations. The DNS achieved outer-scale Reynolds numbers, based on mixing-zone height and its rate of growth, in excess of 3000. Initial growth is diffusive and independent of the initial perturbations. The onset of nonlinear growth is not predicted by available linear-stability theory. Following the diffusive-growth stage, growth rates are found to depend on the initial perturbations, up to the end of the simulations. Mixing is found to be even more sensitive to initial conditions than growth rates. Taylor microscales and Reynolds numbers are anisotropic throughout the simulations. Improved collapse of many statistics is achieved if the height of the mixing zone, rather than time, is used as the scaling or progress variable. Mixing has dynamical consequences for this flow, since it is driven by the action of the imposed acceleration field on local density differences.

scholarly journals The Inhibition of the Rayleigh-Taylor Instability by Rotation

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Kyle A. Baldwin ◽  
Matthew M. Scase ◽  
Richard J. A. Hill
Keyword(s):  
Coriolis Force ◽  
Rotation Rate ◽  
Initial Conditions ◽  
Taylor Instability ◽  
Numerical Work ◽  
Long Wavelength ◽  
Rate Dependent ◽  
Dense Fluid ◽  
Rayleigh Taylor Instability ◽  
Standard Techniques

Abstract It is well-established that the Coriolis force that acts on fluid in a rotating system can act to stabilise otherwise unstable flows. Chandrasekhar considered theoretically the effect of the Coriolis force on the Rayleigh-Taylor instability, which occurs at the interface between a dense fluid lying on top of a lighter fluid under gravity, concluding that rotation alone could not stabilise this system indefinitely. Recent numerical work suggests that rotation may, nevertheless, slow the growth of the instability. Experimental verification of these results using standard techniques is problematic, owing to the practical difficulty in establishing the initial conditions. Here, we present a new experimental technique for studying the Rayleigh-Taylor instability under rotation that side-steps the problems encountered with standard techniques by using a strong magnetic field to destabilize an otherwise stable system. We find that rotation about an axis normal to the interface acts to retard the growth rate of the instability and stabilise long wavelength modes; the scale of the observed structures decreases with increasing rotation rate, asymptoting to a minimum wavelength controlled by viscosity. We present a critical rotation rate, dependent on Atwood number and the aspect ratio of the system, for stabilising the most unstable mode.

scholarly journals On the “Early-Time” Evolution of Variables Relevant to Turbulence Models for the Rayleigh-Taylor Instability

2010 ◽  
Author(s):  
Bertrand Rollin ◽  
Malcolm J. Andrews
Keyword(s):  
Turbulence Model ◽  
Initial Conditions ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Early Time ◽  
Variable Density ◽  
Taylor Instability ◽  
Turbulent Regime ◽  
Rayleigh Taylor Instability

We present our progress toward setting initial conditions in variable density turbulence models. In particular, we concentrate our efforts on the BHR turbulence model [1] for turbulent Rayleigh-Taylor instability. Our approach is to predict profiles of relevant variables before fully turbulent regime and use them as initial conditions for the turbulence model. We use an idealized model of mixing between two interpenetrating fluids to define the initial profiles for the turbulence model variables. Velocities and volume fractions used in the idealized mixing model are obtained respectively from a set of ordinary differential equations modeling the growth of the Rayleigh-Taylor instability and from an idealization of the density profile in the mixing layer. A comparison between predicted profiles for the turbulence model variables and profiles of the variables obtained from low Atwood number three dimensional simulations show reasonable agreement.

Effect of Initial Conditions on the Development of Rayleigh–Taylor Instability

2015 ◽  
Vol 36 (2) ◽  
pp. 139-150 ◽  
Author(s):  
V. B. Rozanov ◽  
P. A. Kuchugov ◽  
N. V. Zmitrenko ◽  
Yu. V. Yanilkin
Keyword(s):  
Initial Conditions ◽  
Taylor Instability ◽  
Rayleigh Taylor Instability

Density Ratio and Entrainment Effects on Asymptotic Rayleigh–Taylor Instability

2017 ◽  
Vol 140 (5) ◽  
Author(s):  
Assaf Shimony ◽  
Guy Malamud ◽  
Dov Shvarts
Keyword(s):  
Numerical Study ◽  
Density Ratio ◽  
Three Dimensional ◽  
Growth Parameter ◽  
Taylor Instability ◽  
Mixing Zone ◽  
Mixing Process ◽  
Mixing Parameters ◽  
Rayleigh Taylor Instability ◽  
Self Similar

A comprehensive numerical study was performed in order to examine the effect of density ratio on the mixing process inside the mixing zone formed by Rayleigh–Taylor instability (RTI). This effect exhibits itself in the mixing parameters and increase of the density of the bubbles. The motivation of this work is to relate the density of the bubbles to the growth parameter for the self-similar evolution, α, we suggest an effective Atwood formulation, found to be approximately half of the original Atwood number. We also examine the sensitivity of the parameters above to the dimensionality (two-dimensional (2D)/three-dimensional (3D)) and to numerical miscibility.

Compressibility effects in Rayleigh–Taylor instability-induced flows

2010 ◽  
Vol 368 (1916) ◽  
pp. 1681-1704 ◽  
Author(s):  
S. Gauthier ◽  
B. Le Creurer
Keyword(s):  
Compressible Flows ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Density Fluctuations ◽  
Taylor Instability ◽  
Turbulent Regime ◽  
Developed Turbulence ◽  
Perfect Fluids ◽  
Rayleigh Taylor Instability ◽  
Compressibility Effects

We present a tentative review of compressibility effects in Rayleigh–Taylor instability-induced flows. The linear, nonlinear and turbulent regimes are considered. We first make the classical distinction between the static compressibility or stratification, and the dynamic compressibility owing to the finite speed of sound. We then discuss the quasi-incompressible limits of the Navier–Stokes equations (i.e. the low-Mach number, anelastic and Boussinesq approximations). We also review some results about stratified compressible flows for which instability criteria have been derived rigorously. Two types of modes, convective and acoustic, are possible in these flows. Linear stability results for perfect fluids obtained from an analytical approach, as well as viscous fluid results obtained from numerical approaches, are also reviewed. In the turbulent regime, we introduce Chandrasekhar’s observation that the largest structures in the density fluctuations are determined by the initial conditions. The effects of compressibility obtained by numerical simulations in both the nonlinear and turbulent regimes are discussed. The modifications made to statistical models of fully developed turbulence in order to account for compressibility effects are also treated briefly. We also point out the analogy with turbulent compressible Kelvin–Helmholtz mixing layers and we suggest some lines for further investigations.

Rotational suppression of Rayleigh–Taylor instability

2002 ◽  
Vol 457 ◽  
pp. 181-190 ◽  
Author(s):  
G. F. CARNEVALE ◽  
P. ORLANDI ◽  
YE ZHOU ◽  
R. C. KLOOSTERZIEL
Keyword(s):  
Coriolis Force ◽  
Boussinesq Approximation ◽  
Taylor Instability ◽  
Vortex Rings ◽  
Mixing Zone ◽  
Rayleigh Taylor Instability ◽  
Atwood Number

It is demonstrated that the growth of the mixing zone generated by Rayleigh–Taylor instability can be greatly retarded by the application of rotation, at least for low Atwood number flows for which the Boussinesq approximation is valid. This result is analysed in terms of the effect of the Coriolis force on the vortex rings that propel the bubbles of fluid in the mixing zone.

An Appropriate Metric to Switch on a Turbulence Model for Rayleigh-Taylor Instability Driven Mixing

2011 ◽  
Author(s):  
Bertrand Rollin ◽  
Malcolm J. Andrews
Keyword(s):  
Turbulence Model ◽  
Inertial Confinement Fusion ◽  
Initial Conditions ◽  
Turbulence Models ◽  
Variable Density ◽  
Taylor Instability ◽  
Engineering Applications ◽  
Modal Model ◽  
Rayleigh Taylor Instability ◽  
Rt Instability

Rayleigh-Taylor (RT) instability occurs at a perturbed interface between fluids of different densities, when the lighter fluid is accelerated into the heavier fluid (∇p · ∇ρ < 0, where p is pressure, and ρ is density). In time, as the two fluids seek to reduce their combined potential energy, the mixing becomes turbulent. This fundamental instability is observed, and plays a key role, in numerous natural phenomena, e.g. supernovae explosions, and in engineering applications, e.g. Inertial Confinement Fusion (ICF). The importance of initial condition (ICs) effects on the growth and mixing of Rayleigh-Taylor instability open an opportunity for “design” of RT turbulence for engineering, and question our current predictive capability. Indeed, commonly used turbulence models used for engineering applications are tuned for fully developed turbulence, whereas RT instability is a dynamic process that evolves toward turbulence under the influence of ICs. Therefore, our efforts aim at defining a procedure for properly accounting for initial conditions in variable density (RT) turbulence models. Our strategy is to have a model for the “early” evolution of the RT instability that will produce the initial conditions for the turbulence model. We already dispose of a modal model to evolve the RT mixing layer starting from almost any initial conditions. The present work is a first look at determining an appropriate metric for switching from the modal model to a variable density turbulence model.

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