  We study energy scale-transfer in Rayleigh-Taylor (RT) flows by
coarse-graining in physical space without Fourier transforms, allowing scale
analysis along vertical direction. Two processes are responsible for kinetic
energy flux across scales: baropycnal work $\Lambda$, due to large-scale
pressure gradients acting on small-scales of density and velocity, and
deformation work $\Pi$, due to multi-scale velocity. Our coarse-graining
analysis shows how these fluxes exhibit self-similar evolution that is
quadratic-in-time, similar to RT mixing layer. We find that $\Lambda$ is a
conduit for potential energy, transferring energy non-locally from the largest
scales to smaller scales in the inertial range where $\Pi$ takes over. In 3D,
$\Pi$ continues a persistent cascade to smaller scales, whereas in 2D $\Pi$
re-channels the energy back to larger scales despite the lack of vorticity
conservation in 2D variable density flows. This gives rise to a positive
feedback loop in 2D-RT (absent in 3D) in which mixing layer growth and the
associated potential energy release are enhanced relative to 3D, explaining the
oft-observed larger $\alpha$ values in 2D simulations. Despite higher bulk
kinetic energy levels in 2D, small inertial scales are weaker than in 3D.
Moreover, the net upscale cascade in 2D tends to isotropize the large-scale
flow, in stark contrast to 3D. Our findings indicate the absence of net upscale
energy transfer in 3D-RT as is often claimed; growth of large-scale bubbles and
spikes is not due to "mergers" but solely due to baropycnal work $\Lambda$.
