Turbulent mixing in a Richtmyer–Meshkov fluid layer after reshock: velocity and density statistics

Abstract

AbstractThe properties of turbulent mixing in a Richtmyer–Meshkov (RM) unstable fluid layer are studied under the impact of a single shock followed by a reshock wave using simultaneous velocity–density measurements to provide new insights into the physics of RM mixing. The experiments were conducted on a varicose ${\mathrm{SF} }_{6} $ fluid layer (heavy fluid) interposed in air (light fluid) inside a horizontal shock tube at an incident Mach number of 1.21 and a reflected reshock Mach number of 1.14. The light–heavy–light fluid layer is observed to develop a nonlinear growth pattern, with no transition to turbulence upon impact by a single shock (up to $tU/ \lambda = 23. 4$). However, upon reshock, enhanced mixing between the heavy and light fluids along with a transition to a turbulent state characterized by the generation of significant turbulent velocity fluctuations (${\sigma }_{u} / U\ensuremath{\sim} 0. 3$) is observed. The streamwise and spanwise root-mean-squared velocity fluctuation statistics show similar trends across the fluid layer after reshock, with no observable preference for the direction of the shock wave motion. The measured streamwise mass flux ($ \overline{{\rho }^{\ensuremath{\prime} } {u}^{\ensuremath{\prime} } } $) shows opposing signs on either side of the density peak within the fluid layer, consistent with the turbulent material transport being driven along the direction of the density gradient. Measurements of three of the six independent components of the general Reynolds stress tensor (${R}_{ij} = \overline{\rho { u}_{i}^{\ensuremath{\prime} \ensuremath{\prime} } { u}_{j}^{\ensuremath{\prime} \ensuremath{\prime} } } $) show that the self-correlation terms ${R}_{11} $ and ${R}_{22} $ are similar in magnitude across much of the fluid layer, and much larger than the cross-correlation term ${R}_{12} $. Most importantly, the Reynolds stresses (${R}_{ij} $) are dominated by the mean density, cross-velocity product term ($ \overline{\rho } \hspace{0.167em} \overline{{ u}_{i}^{\ensuremath{\prime} } { u}_{j}^{\ensuremath{\prime} } } $), with the mass flux product and triple correlation terms being negligibly smaller in comparison. A lack of homogeneous mixing (and, possibly, a long-term imprint of the initial conditions) is observed in the spanwise turbulent mass flux measurements, with important implications for the simulation and modelling of RM mixing flows.