Karnig Mikaelian - Academia.edu (original) (raw)

Papers by Karnig Mikaelian

Physical Review E, 2016

We consider viscous fluids in spherical geometry, a lighter fluid supporting a heavier one. Chand... more We consider viscous fluids in spherical geometry, a lighter fluid supporting a heavier one. Chandrasekhar (Quart. J. Mech. Appl. Math. 8, 1 (1955)) analyzed this unstable configuration providing the equations needed to find, numerically, the exact growth rates for the ensuing Rayleigh-Taylor instability. He also derived an analytic, but approximate solution. We point out a weakness in his approximate dispersion relation (DR) and offer a somewhat improved one. A third DR, based on transforming a planar DR into a spherical one, suffers no unphysical predictions and compares reasonably well with the exact work of Chandrasekhar and a more recent numerical analysis of the problem (G.

Physical Review Fluids, 2016

In a typical Richtmyer-Meshkov experiment a fast moving flat shock strikes a stationary perturbed... more In a typical Richtmyer-Meshkov experiment a fast moving flat shock strikes a stationary perturbed interface between fluids A and B creating a transmitted and a reflected shock, both of which are perturbed. We propose shock tube experiments in which the reflected shock is stationary in the laboratory. Such a standing perturbed shock undergoes well known damped oscillations. We present the conditions required for producing such a standing shock wave which greatly facilitates the measurement of the oscillations and their rate of damping. We define a critical density ratio R critical in terms of the adiabatic indices of the two fluids, and a critical Mach number M s critical of the incident shock wave which produces a standing reflected wave. If the initial density ratio R of the two fluids is less than critical R then a standing shock wave is possible at M s =M s critical. Otherwise a standing shock is not possible and the reflected wave always moves in the direction opposite the incident shock. Examples are given for present-day operating shock tubes with sinusoidal or inclined interfaces. We consider the effect of viscosity which affects the damping rate of the oscillations. We point out that nonlinear bubble and spike amplitudes depend relatively weakly on the viscosity of the fluids, and that the interface area is a better diagnostic.

Physics of Fluids, 2014

We apply numerical and analytic techniques to study the Boussinesq approximation in Rayleigh-Tayl... more We apply numerical and analytic techniques to study the Boussinesq approximation in Rayleigh-Taylor and Richtmyer-Meshkov instabilities. In this approximation, one sets the Atwood number A equal to zero except where it multiplies the acceleration g or velocity-jump Δv. While this approximation is generally applied to low-A systems, we show that it can be applied to high-A systems also in certain regimes and to the “bubble” part of the instability, i.e., the penetration depth of the lighter fluid into the heavier fluid. It cannot be applied to the spike. We extend the Boussinesq approximation for incompressible fluids and show that it always overestimates the penetration depth but the error is never more than about 41%. The effect of compressibility is studied by analytic techniques in the linear regime which indicate that compressibility has the opposite effect and the Boussinesq approximation underestimates bubbles by about 14%. We also present direct numerical simulations of two c...

Physical Review E, 1996

We make a connection between the Schrodinger equation D qr+(F-V)%=0 and the Rayleigh equation D(p... more We make a connection between the Schrodinger equation D qr+(F-V)%=0 and the Rayleigh equation D(pDW)+(k /I)WDp kp-W=O which is used to study the Rayleigh-Taylor instability of fluids in a gravitational field. Here D is the differential operator d/dy, p(y) is the density profile of the fluid, W(y) is the perturbed fluid velocity, k is the wave number of the perturbation, and I' = y /g, where y is the growth rate of the instability and g is the strength of the gravitational field. The connection between the Rayleigh and the Schrodinger equations is made by defining a potential V(y} associated with p(y), a wave function 'P(y) associated with W(y), and an energy F associated with k. We consider several examples of the Rayleigh equation and show that they correspond to well-known problems in quantum mechanics such as a particle in a box, the harmonic oscillator, the Coulomb potential, etc. We illustrate the inversion symmetry of the Rayleigh equation under p(y)~1/p(y), and in an appendix we give and illustrate the more general potential V(y), which includes surface tension and shear flow, the latter associated with the Kelvin-Helmholtz instability.

Physics of Fluids A: Fluid Dynamics, 1991

Numerical and analytical results on the growth rate of the Richtmyer–Meshkov (RM) instability in ... more Numerical and analytical results on the growth rate of the Richtmyer–Meshkov (RM) instability in continuous density profiles are presented, and this paper relates them to the Rayleigh–Taylor (RT) instability by treating the shock as an instantaneous acceleration of incompressible fluids. Most of this work is in the linear regime, where it is found that density gradient stabilization is even more effective for the RM instability than for the RT instability. Recent experimental results are discussed and a numerical simulation of a shock-tube experiment with a continuous density profile between two gases is presented.

Physical Review A, 1983

We consider N superimposed fluids, having arbitrary initial perturbations at their N-1 interfaces... more We consider N superimposed fluids, having arbitrary initial perturbations at their N-1 interfaces, undergoing a Rayleigh-Taylor instability with constant acceleration. The time evolution of these perturbations is described by a sum over normal modes and in general is a combination of oscillation and exponential rise. We derive the equation governing their growth, discuss the case N =3 analytically, and give two numerical examples where we plot the time evolution of the perturbations at the four interfaces of five superimposed fluids. Our examples illustrate how the evolution depends on the density profile, on the wavelength of the perturbations, and on the initial conditions. 10. The case kt && 1 was treated by J. N. Hunt, Appl. Sci. Res. A 10, 45 (1961). This should not be confused with the linear approximation which requires only that the equation be linear in W(y). 4See, e.g.

Physical Review E, 1993

We consider the effect of viscosity on Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilit... more We consider the effect of viscosity on Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities by deriving a moment equation for fluids with arbitrary density and viscosity profiles, including surface tension. We apply our result to the classical case of two semi-infinite fluids with densities pl and p& and viscosities p, and p2. Treating a shock as an instantaneous acceleration we find that perturbations at the interface undergo damped oscillations when viscosity and surface tension are both present. For pure-2k 2vg viscosity the amplitude q(t) evolves according to g(t)/g(0) =1+(EUA /2kv)(1e ') where hv is the jump velocity imparted by the shock, A =(p2-p&)/(p2+pl), v=(p&+p2)/(pi+p2), k =2m/A, is the wave number of the perturbation, and t is time. We also consider the turbulent energy in accelerating fluids and calculate the reduction in E,", b"i,", as a function of v, and propose experiments to measure the effect of viscosity on RT and RM instabilities.

Material strength can affect the growth of the Rayleigh-Taylor instability in solid materials, wh... more Material strength can affect the growth of the Rayleigh-Taylor instability in solid materials, where growth occurs through plastic flow. In order to study this effect at megabar pressures, we have shocked metal foils using hohlraum x-ray drive on Nova, and observed the growth of pre-imposed modulations with x-ray radiography. Previous experiments employing Cu foils did not conclusively show strength effects

We present experimental results supporting physics based ejecta model development, where we assum... more We present experimental results supporting physics based ejecta model development, where we assume ejecta form as a special limiting case of a Richtmyer-Meshkov (RM) instability with Atwood number A =-I. We present and use data to test established RM spike and bubble growth rate theory through application of modern laser Doppler velocimetry techniques applied in a novel manner to coincidentally measure bubble and spike velocities from shocked metals. We also explore the link of ejecta formation from a solid material to its plastic flow stress at high-strain rates (l07/s) and high strains (700%).

Physical Review A, 1985

We present an analytic theory of Richtmyer-Meshkov instabilities in an arbitrary number N of stra... more We present an analytic theory of Richtmyer-Meshkov instabilities in an arbitrary number N of stratified fluids subjected to a shock. Following our earlier work on Rayleigh-Taylor instabilities, the theory assumes incompressible flow in which a shock is treated as an impulsive acceleration, g = Av 6 (T-T), Av being the jump velocity induced in the system by a shock at time x. We discuss the special cases N = 2 and N = 3, and illustrate both Rayleigh-Taylor and Richtmyer-Meshkov instabilities by examples patterned after Inertial Confinement Fusion implosions.

Physics of Plasmas, 2006

Radial profiles of nuclear burn in directly driven, inertial-confinement-fusion implosions have b... more Radial profiles of nuclear burn in directly driven, inertial-confinement-fusion implosions have been systematically studied for the first time using a proton emission imaging system sensitive to energetic 14.7MeV protons from the fusion of deuterium (D) and 3-helium (He3) at the OMEGA laser facility [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)]. Experimental parameters that were varied include capsule size, shell composition and thickness, gas fill pressure, and laser energy. Clear relationships have been identified between changes in a number of these parameters and changes in the size of the burn region, which we characterize here by the median “burn radius” Rburn containing half of the total DHe3 reactions. Different laser and capsule parameters resulted in burn radii varying from 20to80μm. For example, reducing the DHe3 fill pressure from 18to3.6atm in capsules with 20μm thick CH shells resulted in Rburn changing from 31to25μm; this reduction is attributed to increased fue...

Physics of Fluids, 1994

This Letter considers the evolution of perturbations at an interface between two fluids subjected... more This Letter considers the evolution of perturbations at an interface between two fluids subjected to an oblique shock. The normal component of the shock generates the Richtmyer–Meshkov (RM) instability, and the parallel component generates the Kelvin–Helmholtz (KH) instability. If a constant normal acceleration is also present it induces the Rayleigh–Taylor (RT) instability or, depending on the sign of gA (g=acceleration, A=Atwood number), it acts to stabilize the KH and RM instabilities. Treating the shock as an instantaneous acceleration, analytic formulas are derived for the evolution of the perturbations. This Letter illustrates with an application to inertial-confinement-fusion capsules.

Physics of Fluids, 1996

A diffusion model is applied to calculate the turbulent mixing width at an ablating surface. It i... more A diffusion model is applied to calculate the turbulent mixing width at an ablating surface. It is proposed that the general model be tested first on well-determined and easily accessible stabilizing mechanisms such as surface tension, viscosity, density gradient, or finite thickness. In this model the turbulent mixing width h is directly correlated with the growth rate γ of the perturbations in the presence of stabilizing mechanisms: h/hclass=(γ/γclass)1/2, where hclass=0.07 Agτ2 and γclass=√Agk (where A is the Atwood number, g is the acceleration, τ is the time, and k =2π/λ =2π/(ωhclass), ω being a dimensionless constant in the model). The method is illustrated with several examples for hablation, each based on a different γablation. Direct numerical simulations are presented comparing h with and without density gradients. In addition to mixing due to the Rayleigh–Taylor instability, the diffusion model is applied to the Kelvin–Helmholtz and the Richtmyer–Meshkov mixing layers.

Physics of Fluids, 2009

We report numerical simulations and analytic modeling of shock tube experiments on Rayleigh–Taylo... more We report numerical simulations and analytic modeling of shock tube experiments on Rayleigh–Taylor and Richtmyer–Meshkov instabilities. We examine single interfaces of the type A/B where the incident shock is initiated in A and the transmitted shock proceeds into B. Examples are He/air and air/He. In addition, we study finite-thickness or double-interface A/B/A configurations such as air/SF6/air gas-curtain experiments. We first consider conventional shock tubes that have a “fixed” boundary: A solid endwall which reflects the transmitted shock and reshocks the interface(s). Then we focus on new experiments with a “free” boundary—a membrane disrupted mechanically or by the transmitted shock, sending back a rarefaction toward the interface(s). Complex acceleration histories are achieved, relevant for inertial confinement fusion implosions. We compare our simulation results with a generalized Layzer model for two fluids with time-dependent densities and derive a new freeze-out conditio...

Physics Letters A, 1983

Abstract We describe the interaction among the normal modes of the Rayleigh-Taylor instability in... more Abstract We describe the interaction among the normal modes of the Rayleigh-Taylor instability in stratified fluids subjectec to a constant acceleration. We find that all the modes as well as the initial conditions at all the interfaces influence the evolution of perturbations at any one interface.

Physical Review Letters, 1996

The evolution of the Rayleigh-Taylor instability in a compressible medium has been investigated b... more The evolution of the Rayleigh-Taylor instability in a compressible medium has been investigated both at an accelerating embedded interface and at the ablation front in experiments on the Nova laser. Planar targets of brominated plastic for the ablation front and brominated plastic backed by a titanium payload for the embedded interface were ablatively accelerated by the x-ray drive generated in a gold Hohlraum. When the perturbation is at the ablation front, short wavelength modes are stabilized, whereas at the embedded interface the shortest wavelengths grow the most. [S0031-9007(96)00348-1]

Physical Review Letters, 1994

ABSTRACT

Physical Review E, 2014

When a fluid pushes on and accelerates a heavier fluid, small perturbations at their interface gr... more When a fluid pushes on and accelerates a heavier fluid, small perturbations at their interface grow with time and lead to turbulent mixing. The same instability, known as the Rayleigh-Taylor instability, operates when a heavy fluid is supported by a lighter fluid in a gravitational field. It has a particularly deleterious effect on inertial-confinement-fusion implosions and is known to operate over 18 orders of magnitude in dimension. We propose analytic expressions for the bubble and spike amplitudes and mixing widths in the linear, nonlinear, and turbulent regimes. They cover arbitrary density ratios and accelerations that are constant or changing relatively slowly with time. We discuss their scalings and compare them with simulations and experiments.