### Session KM: Instability: Richtmyer-Meshkov II and Rayleigh-Taylor

Chair: Andrew Cook, Lawrence Livermore National Laboratory
Room: Salt Palace Convention Center 251 A

 Tuesday, November 20, 2007 8:00AM - 8:13AM KM.00001: Miscible-Liquid experiments on the Rayleigh-Taylor and Richtmyer-Meshkov instabilities Guillaume Layes , Michael Roberts , Jeffrey Jacobs Experiments are presented in which an incompressible system of two miscible liquids is accelerated to produce the Richtmyer-Meshkov (RM) or Rayleigh-Taylor (RT) instabilities. The initially stably stratified liquid combination is contained within a rectangular tank that is accelerated on a vertical rail system. In the RM Experiments the tank is released from the top of the rail system, after which it impacts a spring that introduces the impulsive acceleration and the RM instability develops while the tank is in freefall. In the RT experiments, the same rail system is used; however, instead of impacting a spring the tank is accelerated downward using a weight and pulley system. The resulting fluid flows are observed using a high speed video camera traveling with the fluid system. The initial perturbations are either forced (by oscillating the tank in the horizontal or the vertical direction to produce gravity waves) or random (as a result of molecular motion or background noise). Tuesday, November 20, 2007 8:13AM - 8:26AM KM.00002: Effects on Initial Development of Rayleigh-Taylor Instabilities due to a change in Initial Conditions Freeman M. Peart , Robert A. Gore , Malcolm J. Andrews Initial condition effects on the initial development of Rayleigh-Taylor (RT) mixing will be presented. A small Atwood number water channel facility at Texas A{\&}M University has been used to provide a statistically steady experiment for the investigation of buoyancy driven turbulent mixing. Parallel streams of hot and cold water are initially separated by a splitter plate, the streams oriented in such a way to place the cold water above the hot water. At the end of the splitter plate, the two streams mix and form a buoyancy-driven RT mixing layer. Isotropic turbulence was introduced into the free streams using passive grids and the growth rate for the resultant RT mixing layer has been measured experimentally using image analysis techniques. Thus, we have been able to study the overall development of the mixing region using different initial conditions (isotropic turbulence). Our findings support the notion that the overall growth of RT mixing is strongly dependent on initial conditions, and our results provide a useful database for initialization of mix models. Tuesday, November 20, 2007 8:26AM - 8:39AM KM.00003: Linear Analysis of Rayleigh-Taylor Instability Between Immiscible Compressible Fluids in Cylindrical Geometry Huidan Yu , Daniel Livescu A linear stability analysis for the Rayleigh-Taylor instability (RTI) between two ideal inviscid compressible immiscible fluids in cylindrical geometry is performed. 3D cylindrical as well as 2D axisymmetric and circular unperturbed interfaces are considered and compared to the Cartesian case with planar interface. Focuses are on the effects of compressibility and geometrical convergence (or divergence) on the instability growth and the differences between implosion (gravity acting inward) and explosion (gravity acting outward). Compressibility can be characterized by two parameters - static Mach number based on isothermal sound speed and ratio of specific heats - which in general have opposite influence, stabilization and destabilization, on the instability growth, similar to the Cartesian case [D. Livescu, \textit{Phys. Fluids. }\textbf{16}, 118 (2004)]. Instability is found to grow faster in the 3D cylindrical case than in the Cartesian case in implosion but slower in explosion. In general, the difference between implosion and explosion is profound for the cylindrical cases but marginal for planar interface. For the 3D cylindrical case, instability grows faster in implosion than in explosion. For the 2D cases, the results above can be qualitatively different, depending on the Atwood numbers, interface radius, and compressibility parameters. Tuesday, November 20, 2007 8:39AM - 8:52AM KM.00004: Rayleigh-Taylor instability experiments with precise and arbitrary control of the initial interface shape Pierre Carles , Zhibin Huang , Antonio De Luca , Timothy Atherton , Matthew Bird , Charles Rosenblatt For a gravitationally-driven Rayleigh-Taylor instability, a dense fluid initially sits metastably atop a less dense fluid, a configuration that can be stabilized using a magnetic field gradient when one fluid is highly paramagnetic. On switching off the magnetic field, the instability occurs as the dense fluid falls under gravity. By affixing appropriately shaped magnetically-permeable materials to the outside of the cell, we impose arbitrarily-chosen, well-controlled, and jitter-free initial perturbations on the interface. This technique is used to examine both the linear and nonlinear regimes, including growth rates and nonlinear growth coefficients, as functions of the imposed perturbation wavelength and amplitude. Tuesday, November 20, 2007 8:52AM - 9:05AM KM.00005: Experimental study of Atwood number effects on the single-mode Rayleigh-Taylor instability Jeremy White , Jason Oakley , Mark Anderson , Riccardo Bonazza The growth of Rayleigh-Taylor (RT) spikes are studied experimentally for a single-mode, 2D initial condition. The experiments are performed using a magnetorheological (MR) fluid, composed of 4.5 micron spherical iron particles suspended in hexane with a small amount of oleic acid used as a surfactant. This mixture is suspended over aqueous salt solutions to achieve different Atwood number fluid pairs between 0.2 and 0.5. A discontinuous, membrane-less, and initially static interface is created by magnetically immobilizing the MR fluid while resting over ice of a prescribed shape. This technique results in a well defined initial perturbation. The temporal growth of the spikes is observed with a back-lit, high speed imaging system, and growth rates obtained from these experiments are compared with published analytical, experimental, and numerical results. The transition from linear to non-linear growth is also examined and compared with analytical predictions using the approach attributed to Fermi by Layzer. Tuesday, November 20, 2007 9:05AM - 9:18AM KM.00006: Experimental study of Rayleigh-Taylor Instability utilizing a paramagnetic liquid combination Omid Gohardani , Rebecca Oemke , Jeffrey Jacobs An experimental study of Rayleigh-Taylor instability is presented that utilizes the properties of a magnetic liquid. A gravitationally unstable miscible combination of a paramagnetic salt solution and one of two nonmagnetic solutions is stabilized by exposing it to a magnetic field gradient. Both liquids are contained within a Plexiglas tank positioned between the poles of a large electromagnet. The suspension of the heavy paramagnetic fluid over the lighter non-magnetic one is attained by a magnetic field gradient produced by the contoured pole caps of the electromagnet. Rayleigh-Taylor Instability commences with the rapid removal of power to the electromagnet resulting in the heavy fluid falling under gravitational influence. The resulting instability is visualized utilizing planar laser-induced fluorescence and back- lit photography. Experiments initiated with an apparent flat interface evolve into a random surface pattern with the dominant length scale approximated by the fastest growing wavelength as given by viscous linear stability theory. The mean mixing zone width measurements exhibit an $\alpha A g t^{2}$ dependence with the value of $\alpha$ in agreement with previous experiments. Tuesday, November 20, 2007 9:18AM - 9:31AM KM.00007: Mitigation of Hydrodynamic Instabilities in Direct-Drive ICF Targets Through the Use of High-Z Overcoats and Prepulses Lee Phillips The most successful means of reducing the impact of hydrodynamic instabilities in ICF targets are to decrease the Rayleigh-Taylor growth rate by shaping the adiabat and to reduce the seeds of R-T growth. The latter can be accomplished to a great extent by target manufacture and optical laser smoothing, but the residual R-T seeds are still unacceptably large, and a subject to Richtmeyer-Meshkov amplification during the target compression stage, before R-T growth begins. We report here on simulations of targets incorporating a thin, high-Z (metallic) overcoat. The overcoat converts incident UV laser energy to soft X-rays, which produce a higher ablation velocity and consequently smaller Richtmeyer-Meshkov growth and a smaller seed for the R-T instability. Penetration of X-rays from the overcoat into the ablator also shapes the adiabat and reduces the R-T growth rate, but more effective adiabat shaping can be accomplished through the use of laser prepulses or spikes, as has been widely reported. Here we explore new target designs that combine the use of overcoats with laser spikes in an attempt to both reduce the seed for the R-T instability as well as its growth rate. We examine in detail as well the situations in which both overcoats and prepulses can worsen target stability in order to arrive at a set of constraints for optimal target design. Supported by the US DOE. Tuesday, November 20, 2007 9:31AM - 9:44AM KM.00008: Rayleigh-Taylor Instability with Ideal Gases Andrew Cook , Britton Olson Turbulence developed from Rayleigh-Taylor instability between two compressible fluids is widely regarded as a low Mach number phenomenon. Numerical simulations of the flow are typically performed either with incompressible flow solvers or else in computational domains that are small compared to the pressure scale height. Simulations in larger domains have reported an upper bound on the turbulent Mach number of 0.25 to 0.6. However, some recent large-eddy simulations in very large domains have produced a surprising new phenomenon. Visualizations from the simulations will be presented along with quantitative discussion of the results. Tuesday, November 20, 2007 9:44AM - 9:57AM KM.00009: Dissipative Dynamics of Turbulent Kinetic Energy and Density Variance in Rayleigh-Taylor Instability-Induced Mixing and Application to Turbulence Modeling Oleg Schilling , Nicholas Mueschke The dynamics of the density variance, turbulent kinetic energy dissipation rate, and density variance dissipation rate are examined in the context of turbulent Rayleigh-Taylor mixing. Mean and fluctuating fields from a $1152\times 720\times 1280$ direct numerical simulation of a small Atwood number Rayleigh-Taylor mixing layer are used to construct the unclosed terms in the corresponding transport equations. The gradient- diffusion and scale-similarity approximations used to close these equations are tested by comparing the profiles of the terms in the unclosed transport equations a priori with the corresponding profiles of the modeled terms. Optimized model parameters yielding good agreement between the unclosed terms and their models are determined. Implications for turbulent transport modeling of Rayleigh-Taylor instability-induced mixing are discussed. Tuesday, November 20, 2007 9:57AM - 10:10AM KM.00010: Numerical simulations of Rayleigh-Taylor (RT) turbulence with complex acceleration history Praveen Ramaprabhu , Guy Dimonte , Malcolm Andrews Complex acceleration histories of an RT unstable interface are important in validating turbulent mix models. Of particular interest are alternating stages of acceleration and deceleration, since the the associated demixing is a discriminating test of such models. We have performed numerical simulations of a turbulent RT mixing layer subjected to two stages of acceleration separated by a stage of deceleration. The profile was chosen from earlier Linear Electric Motor experiments with which we compare our results. The acceleration phases produce classical RT unstable growth ($t^{2})$ with growth rates comparable to earlier results of turbulent RT simulations. The calculations are challenging as dominant bubbles become shredded as they reverse direction in response to the reversal in g, placing increased demands on numerical resolution. The shredding to small scales is accompanied by a peaking of the molecular mixing during the RT stable stage. In general, we find that simulations agree with experiments when initialized with broadband initial perturbations, but not for an annular shell. Other effects such as the presence of surface tension in the LEM experiments (but not in our simulations) further complicate this picture.