  We present a study of a two-point spectral turbulence model (Local
Wave-Number model or LWN model) for the Rayleigh-Taylor (RT) instability. The
model outcomes are compared with statistical quantities extracted from
three-dimensional simulation of the RT problem. These simulations are
initialized with high wavenumber perturbations at the interface of a heavy
fluid placed on top of a light fluid so that the density gradient is in the
direction opposite to acceleration due to gravity. We consider flows of low to
medium density contrast and compare the LWN model against simulation data using
the mix-width evolution as the primary metric. The original model specified
physically reasonable but largely \emph{ad hoc} terms to account for the
inhomogeneous mechanisms involved in growing the mixing layer. We
systematically assess the role of each of the terms in the LWN model equations
by comparison with simulation. Two of these, the kinematic source term,
introduced to maintain a finite covariance between density and specific volume,
and a spectral distortion term, introduced as spectral modifications of the
density-specific-volume covariance, both result in severely over-predicting the
mix layer growth. A simplified model eliminating those two terms is shown to
improve the capture of both mix-width evolution as well as the turbulent mass
flux velocity profiles across the mix layer at different times. However, this
simplification reveals that fidelity to other metrics such as the
density-specific-volume covariance, and the turbulent kinetic energy are
somewhat compromised. The implications of this outcome are discussed with
respect to the physics of the RT problem, and we provide this study as a guide
for the practical use of such a model.
