  We prove that inter-scale transfer of kinetic energy in compressible
turbulence is dominated by local interactions. In particular, our results
preclude direct transfer of kinetic energy from large-scales directly to
dissipation scales, such as into shocks, in high Reynolds number turbulence as
is commonly believed. Our assumptions on the scaling of structure functions are
weak and enjoy compelling empirical support. Under a stronger assumption on
pressure dilatation co-spectrum, we show that mean kinetic and internal energy
budgets statistically decouple beyond a transitional "conversion" range. Our
analysis establishes the existence of an ensuing inertial range over which mean
SGS kinetic energy flux becomes constant, independent of scale. Over this
inertial range, mean kinetic energy cascades locally and in a conservative
fashion, despite not being an invariant.
