Approaches to turbulence in high-energy-density experiments

This paper provides a discussion of the properties of hydrodynamic systems at high energy density, discusses the methods of doing hydrodynamic experiments and discusses studies to date of the three primary instabilities-Richtmyer-Meshkov (RM), Rayleigh-Taylor (RT) and Kelvin-Helmholtz (KH). The first two of these have been systematically observed, but have not yet produced a system with a clear transition to turbulence. The KH instability remains to be systematically observed in its pure form, although some related effects such as spike tip broadening have been seen. However, the KH effects seen in some simulations of RT systems and supersonic jets have not been seen to date in experiments. We note that the time-dependent condition for turbulence of Zhou et al (2003 Phys. Plasmas 10 1883) is roughly equivalent to the Reynolds-number threshold of Dimotakis in that eddies will dissipate by turbulence in about one eddy-turnover time. We suggest that a plausible explanation of the absence of KH in several experimental systems may be that finite velocity gradients have quenched the instability. Finally, we argue that despite the smearing of the shear layer caused by viscous diffusion, KH instabilities have the potential to contribute to the generation of fluctuations at all scales, but only if the local shear layers are initially formed with a sufficiently steep velocity gradient.