EVOLUTION AND DIAGNOSTICS OF THE NONLINEAR RICHTMYER-MESHKOV INSTABILITY

1. EVOLUTION AND DIAGNOSTICS OF THE NONLINEAR RICHTMYER-MESHKOV INSTABILITY • Marcus Herrmann • Snezhana I. Abarzhi • Center for Turbulence Research, Stanford • FLASH Center, University of Chicago DIAGNOSTICS MOTIVATION • RMI develops relatively to a background motion • with velocity at which • the interface would move if it would be planar • RMI evolution is accompanied by oscillations • caused by sound waves • In simulations • the time-scale is set by the velocity • the high frequency components are captured • the curvature and velocity are both monitored • only the asymptotic values of the velocity and • curvature are evaluated accurately • Richtmyer-Meshkov instability develops when a shock refracts through the fluids interface. • The shock-induced turbulent mixing plays a key role in high energy density physics and astrophysics: • inertial fusion, plasmas, laser-matter interaction • supernovae • impact dynamics and planetary interiors … • “How to quantify these flows reliably?” • is a primary issue for observations. MULTI-SCALE DYNAMICS MODELING of RMI • The characteristics of RM flow is • the coherent structure of bubbles and spikes, described by two (independent) length-scales: wavelength l and amplitude h. • Our theory found that • RM bubbles flatten and decelerate • nonlinear coherent dynamics has a multi-scale • character with independent contributions of h and l. • Our simulations • solved fully compressible Navier-Stokes equations • treated the interface as a discontinuity using • hybrid tracking-capturing scheme Log-log velocity vs time velocity v = dh/dt and curvature z(t)depend on one another dh/dt ~ f(z( t ) l) white square is our solution; black square is the single-scale model of Shvarts1995,2001 which violates the conservation laws A=0.66 A=0.55 RMI evolution • oscillations caused by sound waves • unknown contribution of higher order terms • prevent an accurate estimate of v(t) CONCLUSION The dynamics of RM coherent structure is governed by two independent length scales, the structure period and the amplitude, and is essentially multi-scale process. A=0.78 A=0.9 Linear theory, Wouchuk2001 Experiments, Jacobs1997 A=0.66 Mach=1.1 A=0.9 Bubbles are in the center, spikes are on the sides, Mach = 1.2.Atwood = 0.55, 0.66, 0.78, 0.9 (top to bottom), same time intervals. Comparison with… • References: • S. I. Abarzhi et. al., Phys. Lett. A 317, 470 ((2003) • M. Herrmann. S. I. Abarzhi, P. Moin, Evolution and diagnostics of the nonlinear Richtmyer-Meshkov instability, under consideration, JFM Acknowledgements: The work was supported by DOE/ASC and NRL