  The role of baroclinicity, which arises from the misalignment of pressure and
density gradients, is well-known in the vorticity equation, yet its role in the
kinetic energy budget has never been obvious. Here, we show that baroclinicity
appears naturally in the kinetic energy budget after carrying out the
appropriate scale decomposition. Strain generation by pressure and density
gradients, both barotropic and baroclinic, also results from our analysis.
These two processes underlie the recently identified mechanism of "baropycnal
work," which can transfer energy across scales in variable density flows. As
such, baropycnal work is markedly distinct from pressure-dilatation into which
the former is implicitly lumped in Large Eddy Simulations. We provide numerical
evidence from 1,024^3 direct numerical simulations of compressible turbulence.
The data shows excellent pointwise agreement between baropycnal work and the
nonlinear model we derive, supporting our interpretation of how it operates.
