  Turbulent Richtmyer--Meshkov instability (RMI) is investigated through a
series of high resolution three dimensional smulations of two initial
conditions with eight independent codes. The simulations are initialised with a
narrowband perturbation such that instability growth is due to non-linear
coupling/backscatter from the energetic modes, thus generating the lowest
expected growth rate from a pure RMI. By independently assessing the results
from each algorithm, and computing ensemble averages of multiple algorithms,
the results allow a quantification of key flow properties as well as the
uncertainty due to differing numerical approaches. A new analytical model
predicting the initial layer growth for a multimode narrowband perturbation is
presented, along with two models for the linear and non-linear regime combined.
Overall, the growth rate exponent is determined as $\theta=0.292 \pm 0.009$, in
good agreement with prior studies; however, the exponent is decaying slowly in
time. $\theta$ is shown to be relatively insensitive to the choice of mixing
layer width measurement. The asymptotic integral molecular mixing measures
$\Theta=0.792\pm 0.014$, $\Xi=0.800 \pm 0.014$ and $\Psi=0.782\pm 0.013$ which
are lower than some experimental measurements but within the range of prior
numerical studies. The flow field is shown to be persistently anisotropic for
all algorithms, at the latest time having between 49\% and 66\% higher kinetic
energy in the shock parallel direction compared to perpendicular and does not
show any return to isotropy. The plane averaged volume fraction profiles at
different time instants collapse reasonably well when scaled by the integral
width, implying that the layer can be described by a single length scale and
thus a single $\theta$. Quantitative data given for both ensemble averages and
individual algorithms provide useful benchmark results for future research.
