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.

scholarly journals Coriolis force-assisted inertial confinement fusion

2019 ◽  
Vol 37 (01) ◽  
pp. 55-60
Author(s):  
F. Winterberg
Keyword(s):  
Gravitational Field ◽  
Coriolis Force ◽  
New York Times ◽  
Taylor Instability ◽  
Magnetized Plasma ◽  
Target Chamber ◽  
Laser Fusion ◽  
Nernst Effect ◽  
Spherical Target ◽  
Rayleigh Taylor Instability

AbstractA fundamental problem for the realization of laser fusion through the implosion of a spherical target is Kidder's E−1/6 law, where E is the energy needed for ignition, proportional to the 6th power of the ratio R/R0, where R0 and R are the initial and final implosion radii, respectively. This law implies that the ignition energy is very sensitive to the ratio R0/R, or vice versa, the ratio R0/R is very insensitive to the energy input, with R0/R limited by the Rayleigh–Taylor instability. According to still classified data of the Centurion–Halite experiment at the Nevada Test Site, ignition would require an energy of ${\rm E}\simeq 50\,{\rm MJ}$, 25 times larger than the 2 MJ laser at the National Ignition Facility (NIF) reported in the New York Times. This means that even a tenfold increase from 2 to 20 MJ would only decrease the R/R0 ratio by an insignificant factor of 10−1/6 ≃ 0.7. To overcome this problem, it is proposed that the spherical target is replaced with a hollowed-out, rapidly rotating, cm-size ferromagnetic target, accelerated by a rotating traveling magnetic wave to a rotational velocity of ~1 km/s, at the limit of its tensile strength. In a rotating reference system, the general theory of relativity predicts the occurrence of negative gravitational field masses in the center of rotation, with their source located in the Coriolis force field. The density of this negative gravitational field mass can be larger than the magnitude of the positive mass density of a neutron star. The repulsive gravitational force causes the centrifugal force. For a magnetized plasma placed in the rapidly spinning, hollowed-out target chamber, this repulsive force can be balanced by the magnetic force generated by thermomagnetic currents of the Nernst effect. Such a configuration does not suffer from the Rayleigh–Taylor instability, but becomes a small magnetohydrodynamic generator, amplifying the magnetic field to values about equal to those of the Nernst effect, axially confining the plasma. By placing the spinning target in the center of a lithium vortex, the fusion neutrons absorbed in the vortex can breed tritium, and at the same time remove heat from the target chamber to sustain the Nernst effect. A hot spot is thereby produced in the target chamber, which launches a thermonuclear burn wave into a cylindrical deuterium–tritium configuration. With the stability of a rapidly rotating target greatly increased, and the range of 10 MeV electrons in the wall of the cm-size ferromagnetic target, an intense 10 MeV relativistic electron beam drawn from a 10 MJ Marx generator should be sufficient to implode the target for thermonuclear ignition.

Rayleigh-Taylor Instability of a Stratified Plasma

1974 ◽  
Vol 29 (3) ◽  
pp. 518-523 ◽  
Author(s):  
K. M. Srivastava
Keyword(s):  
Magnetic Field ◽  
Boussinesq Approximation ◽  
Short Wave ◽  
Taylor Instability ◽  
Larmor Radius ◽  
Finite Larmor Radius ◽  
Wave Disturbances ◽  
Magnetic Field Gradients ◽  
Rayleigh Taylor Instability ◽  
The Magnetic Field

We have investigated the effect of finite Larmor radius on the Rayleigh-Taylor instability of a semi-infinite, compressible, stratified and infinitely conducting plasma. The plasma is assumed to have a one dimensional density and magnetic field gradients. The eigenvalue problem has been solved under Boussinesq approximation for disturbances parallel to the magnetic field. It has been established that for perturbation parallel to the magnetic field, the system is stable for both stable and unstable stratification. For perturbation perpendicular to the magnetic field, the problem has been solved without Boussinesq approximation. The dispersion relation has been discussed in the two limiting cases, the short and long wave disturbances. It has been observed that the gyroviscosity has a destabilizing influence from k = 0 to k = 4.5 for ß* = 0.1 and for ß* = 0.1 up to k* = 2.85 and then onwards it acts as a stabilizing agent. It has a damping effect on the short wave disturbances. For some parameters, the largets imaginary part has been shown in Figs. 1 and 2

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.

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 Rarefaction-driven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime

2018 ◽  
Vol 838 ◽  
pp. 320-355 ◽  
Author(s):  
R. V. Morgan ◽  
W. H. Cabot ◽  
J. A. Greenough ◽  
J. W. Jacobs
Keyword(s):  
Rarefaction Wave ◽  
Three Dimensional ◽  
Single Mode ◽  
Taylor Instability ◽  
Nonlinear Regime ◽  
Diffuse Interface ◽  
Late Time ◽  
Two Dimensional ◽  
Rayleigh Taylor Instability ◽  
Atwood Number

Experiments and large eddy simulation (LES) were performed to study the development of the Rayleigh–Taylor instability into the saturated, nonlinear regime, produced between two gases accelerated by a rarefaction wave. Single-mode two-dimensional, and single-mode three-dimensional initial perturbations were introduced on the diffuse interface between the two gases prior to acceleration. The rarefaction wave imparts a non-constant acceleration, and a time decreasing Atwood number, $A=(\unicode[STIX]{x1D70C}_{2}-\unicode[STIX]{x1D70C}_{1})/(\unicode[STIX]{x1D70C}_{2}+\unicode[STIX]{x1D70C}_{1})$, where $\unicode[STIX]{x1D70C}_{2}$ and $\unicode[STIX]{x1D70C}_{1}$ are the densities of the heavy and light gas, respectively. Experiments and simulations are presented for initial Atwood numbers of $A=0.49$, $A=0.63$, $A=0.82$ and $A=0.94$. Nominally two-dimensional (2-D) experiments (initiated with nearly 2-D perturbations) and 2-D simulations are observed to approach an intermediate-time velocity plateau that is in disagreement with the late-time velocity obtained from the incompressible model of Goncharov (Phys. Rev. Lett., vol. 88, 2002, 134502). Reacceleration from an intermediate velocity is observed for 2-D bubbles in large wavenumber, $k=2\unicode[STIX]{x03C0}/\unicode[STIX]{x1D706}=0.247~\text{mm}^{-1}$, experiments and simulations, where $\unicode[STIX]{x1D706}$ is the wavelength of the initial perturbation. At moderate Atwood numbers, the bubble and spike velocities approach larger values than those predicted by Goncharov’s model. These late-time velocity trends are predicted well by numerical simulations using the LLNL Miranda code, and by the 2009 model of Mikaelian (Phys. Fluids., vol. 21, 2009, 024103) that extends Layzer type models to variable acceleration and density. Large Atwood number experiments show a delayed roll up, and exhibit a free-fall like behaviour. Finally, experiments initiated with three-dimensional perturbations tend to agree better with models and a simulation using the LLNL Ares code initiated with an axisymmetric rather than Cartesian symmetry.

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.

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