Rayleigh-Taylor Instability

The Rayleigh-Taylor instability occurs when a light fluid is accelerated into a heavy fluid, and is a fundamental fluid-mixing mechanism. Any perturbation along the interface between the two fluids will grow. The width of the mixing layer at a given time is reduced by the development of turbulence. The growth rate of the instability and the rate of mixing between the two fluids depends on the effective viscosity of the two fluids.

This notion for a fluid in a gravitational field was first discovered by Lord Rayleigh [not Raleigh or Reyleigh] in the 1880s and later applied to all accelerated fluids by Sir Geoffrey Taylor in 1950.

Understanding the rate of mixing caused by Rayleigh-Taylor instabilities is important to a wide variety of applications, including inertial confinement fusion, nuclear weapons explosions and stockpile management, and supernova explosions. Avoiding Rayleigh-Taylor instability in inertial confinement fusion applications requires both very high precision in the target manufacture, and very high uniformity in the heating of the outside of the capsule--that is, very high symmetry.

Rayleigh-Taylor instabilities emerge in the implosion of both a fission primary device and a fusion secondary device. In the case of the fission primary, the instability arises when the shock wave from the lighter high explosive detonation reaches the much denser tamper. In the case of a fusion secondary, the instability arises when the lighter radiation implosion plasma in the hohlraum reaches the metalic core of the secondary.

Hydrodynamic instabilities play a major role in determining the efficiency and performance of inertial confinement fusion implosions. In laser-driven implosions, high-performance capsules require high aspect ratios (the ratio of the radius to the shell thickness). These capsules are susceptible to hydrodynamic instabilities of the Rayleigh-Taylor, Richtmyer-Meshkov, and Kelvin-Helmholtz varieties, which can in principle severely degrade capsule performance.

Rayleigh-Taylor instabilities develop behind the supernova blast wave on a time scale of a few hours. The importance of the Rayleigh-Taylor (RT) instability and turbulence in accelerating a thermonuclear flame in Type Ia supernovae (SNe Ia) is well recognized. Flame instabilities play a dominant role in accelerating the burning front to a large fraction of the speed of sound in a Type Ia supernova. The Kelvin-Helmholtz instabilities accompanying the RT in-stability in SNe Ia drives most of the turbulence in the star, and, as the flame wrinkles, it will interact with the turbulence generated on larger scales.

The early nonlinear phase of Rayleigh- Taylor (RT) growth is typically described in terms of the classic model of Layzer [1955] in which bubbles of light fluid rise into the heavy fluid at a constant rate determined by the bubble radius and the gravitational acceleration. However, this model is strictly valid only for planar interfaces and hence ignores any effects which might be introduced by the spherically converging interfaces of interest in inertial confinement fusion. The work of G.I. Bell [1951] and M.S. Plesset [1954] introduced the effects of spherical convergence on RT growth but only for the linear regime.

A generalization of the Layzer nonlinear bubble rise rate is given for a spherically converging flow of the type studied by Kidder [1974]. Kidder's self-similar (homogeneous) spherical implosion provided a simple formula for the bubble amplitude. This showed that, while the bubble initially rises with a constant velocity similar to the Layzer result, during the late phase of the implosion, an acceleration of the bubble rise rate occurs. The bubble rise rate is verified by comparison with full, 2-D hydrodynamics simulations.

Initially calculations were limited to two spatial dimensions in order to achieve maximum resolution. By the late 1990s sufficiently powerful massively parallel computers became available so that fully three-dimensional simulations can be carried out at comparable resolution. LLNL has employed the MIRANDA code to conduct several very large simulations (including 720 x 720 x 1620 and 1152 x 1152 x 1152 meshes) of Rayleigh-Taylor flows. These large-eddy simulations achieved unprecedented development in the flow, including observations of a mixing transition and early stages of what was likely the first simulation of the truly asymptotic behavior of the instability.

While fire-polishing keeps the small features suppressed in two dimensions, turbulence wrinkles the fusion flame on far smaller scales in the three-dimensional case, suggesting that the transition to the distributed thermonuclear burning regime occurs at higher densities in three dimensions.