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Turbulent Richtmyer--Meshkov instability (RMI) is investigated through aseries of high resolution three dimensional smulations of two initialconditions with eight independent codes. The simulations are initialised with anarrowband perturbation such that instability growth is due to non-linearcoupling/backscatter from the energetic modes, thus generating the lowestexpected growth rate from a pure RMI. By independently assessing the resultsfrom each algorithm, and computing ensemble averages of multiple algorithms,the results allow a quantification of key flow properties as well as theuncertainty due to differing numerical approaches. A new analytical modelpredicting the initial layer growth for a multimode narrowband perturbation ispresented, along with two models for the linear and non-linear regime combined.Overall, the growth rate exponent is determined as $\theta=0.292 \pm 0.009$, ingood agreement with prior studies; however, the exponent is decaying slowly intime. $\theta$ is shown to be relatively insensitive to the choice of mixinglayer width measurement. The asymptotic integral molecular mixing measures$\Theta=0.792\pm 0.014$, $\Xi=0.800 \pm 0.014$ and $\Psi=0.782\pm 0.013$ whichare lower than some experimental measurements but within the range of priornumerical studies. The flow field is shown to be persistently anisotropic forall algorithms, at the latest time having between 49\% and 66\% higher kineticenergy in the shock parallel direction compared to perpendicular and does notshow any return to isotropy. The plane averaged volume fraction profiles atdifferent time instants collapse reasonably well when scaled by the integralwidth, implying that the layer can be described by a single length scale andthus a single $\theta$. Quantitative data given for both ensemble averages andindividual algorithms provide useful benchmark results for future research.

Late-time growth rate, mixing and anisotropy in the multimode narrowband Richtmyer--Meshkov Instability: the $\theta$-Group Collaboration