  This paper investigates the influence of different broadband perturbations on
the evolution of a Richtmyer--Meshkov turbulent mixing layer initiated by a
Mach 1.84 shock traversing a perturbed interface separating gases with a
density ratio of 3:1. Both the bandwidth of modes in the interface
perturbation, as well as their relative amplitudes, are varied in a series of
carefully designed numerical simulations at grid resolutions up to
$3.2\times10^9$ cells. Three different perturbations are considered,
characterised by a power spectrum of the form $P(k)\propto k^m$ where $m=-1$,
$-2$ and $-3$. The growth of the mixing layer is shown to strongly depend on
the initial conditions, with the growth rate exponent $\theta$ found to be
$0.5$, $0.63$ and $0.75$ for each value of $m$ at the highest grid resolution.
The asymptotic values of the molecular mixing fraction $\Theta$ are also shown
to vary significantly with $m$; at the latest time considered $\Theta$ is
$0.56$, $0.39$ and $0.20$ respectively. Turbulent kinetic energy (TKE) is also
analysed in both the temporal and spectral domains. The temporal decay rate of
TKE is found not to match the predicted value of $n=2-3\theta$, which is shown
to be due to a time-varying {normalised dissipation rate $C_\epsilon$}. In
spectral space, the data follow the theoretical scaling of $k^{(m+2)/2}$ at low
wavenumbers and tend towards $k^{-3/2}$ and $k^{-5/3}$ scalings at high
wavenumbers for the spectra of transverse and normal velocity components
respectively. The results represent a significant extension of previous work on
the Richtmyer--Meshkov instability evolving from broadband initial
perturbations and provide useful benchmarks for future research.
