  Magnetic fields, compressibility and turbulence are important factors in many
terrestrial and astrophysical processes. While energy dynamics, i.e. how energy
is transferred within and between kinetic and magnetic reservoirs, has been
previously studied in the context of incompressible magnetohydrodynamic (MHD)
turbulence, we extend shell-to-shell energy transfer analysis to the
compressible regime. We derive four new transfer functions specifically
capturing compressibility effects in the kinetic and magnetic cascade, and
capturing energy exchange via magnetic pressure. To illustrate their viability,
we perform and analyze four simulations of driven isothermal MHD turbulence in
the sub- and supersonic regime with two different codes. On the one hand, our
analysis reveals robust characteristics across regime and numerical method. For
example, energy transfer between individual scales is local and forward for
both cascades with the magnetic cascade being stronger than the kinetic one.
Magnetic tension and magnetic pressure related transfers are less local and
weaker than the cascades. We find no evidence for significant nonlocal
transfer. On the other hand, we show that certain functions, e.g., the
compressive component of the magnetic energy cascade, exhibit a more complex
behavior that varies both with regime and numerical method. Having established
a basis for the analysis in the compressible regime, the method can now be
applied to study a broader parameter space.
