We present an overview and recent understanding of
accelerated inhomogeneous flows, e.g.
shock-accelerated interfaces or Richtmyer-Meshkov
flows.1,2 We use the vortex paradigm1
and the visiometric approach2
and apply them to the shock-accelerated one-mode,
small-amplitude perturbed planar configuration and
cylinder in two dimensions and focus on scaling with
respect to Atwood number.
We quantify phenomena to validate simulations and
create models involving coherent space-time events.
our recent work,3-8 including:
finite, initial interfacial gradients (which carry
the initially deposited circulation) and their
subsequent steepening; vortex induced,
secondary baroclinic circulation generation which
creates unstable vortex bilayers that
dominate at intermediate times; vortex bilayer
roll-up and the appearance of “vortex projectiles”
(dipolar-like structures) and turbulent domains
which drive the mixing of species; possible
finite-time ill-posedness; and applicability of a
dipolar incompressible point-vortex model for
amplitude growth. All these events occur in an
essentially incompressible flow, if the initial
shock has M < 1.5. Finally, we discuss the
applicability of these ideas to recent high
resolution Rayleigh-Taylor simulations.
Hawley, J.F. and Zabusky, N.J., Vortex paradigm for
shock-accelerated density-stratified interfaces
1989. Phys. Rev Letters 63,
N.J., Vortex paradigm for accelerated
inhomogeneous flows: Visiometrics for the
Rayleigh-Taylor and Richtmyer-Meshkov
environments. Ann. Review of Fluid Mechanics,
1999. 31, 495-535.
Kotelnikov, A.D., Gulak, Y. & Peng, G. Amplitude
growth rate of a Richtmyer-Meshkov unstable
two-dimensional interface to intermediate times.
J. Fluid Mechanics, 475, 147-162. 2003.
Zabusky, N.J. and Zhang, S. Vortex-accelerated
secondary baroclinic vorticity deposition and
late intermediate time dynamics of a
two-dimensional RM interface. Phys. Fluids 15
(12), 3730-3744, 2003.
Zabusky, N.J., Peng, G., Gupta, S. Shock
Gaseous Cylinder Interactions: Dynamically
validated initial conditions provide excellent
agreement between experiments and Navier-Stokes
simulations to late-intermediate time. Phys.
Fluids 16(5), 1203-1216, 2004.
Zabusky, N.J. Peng, G.
Vortex dynamics and baroclinically forced inhomogeneous turbulence for
shock - planar heavy curtain interactions” J. of
Turbulence, 6, 1-27, 2005
and Peng, G. Vorticity deposition and evolution
in shock-accelerated flows: Analysis,
Computation and Experiment” in Proceedings of
the LANL symposium “Modeling and Simulation of
Variable Density and Compressible Turbulent
Mixing,” Mark A. Christon, Daniel Livescu, and
John A. Turner, eds, August 3-5 2005. pp7-9.
and Zabusky, N.
J. Circulation rate of change: A vortex approach
for validating and understanding accelerated
inhomogeneous flows through intermediate times.
Phys Fluids, to be published 2006.
Cabot, W. and Miller, P. The mixing transition
in Rayleigh–Taylor instability. J. Fluid
Mechanics, 511: 333-362, 2004
Cabot, W. and
Andrew Cook, A. Reynolds number effects on
Rayleigh-Taylor instability with possible
implications for type 1a supernovae. Nature
Physics 2, 562 – 568, 2006.