Pressure–strain interaction. I. On compression, deformation, and implications for Pi-D

The pressure–strain interaction describes the rate per unit volume that energy is converted between bulk flow and thermal energy in neutral fluids or plasmas. The term has been written as a sum of the pressure dilatation and the collisionless analog of viscous heating referred to as $Pi−D$⁠, which isolates the power density due to compressible and incompressible effects, respectively. It has been shown that $Pi−D$ can be negative, which makes its identification as collisionless viscous heating troubling. We argue that an alternate decomposition of pressure–strain interaction can be useful for interpreting the underlying physics. Since $Pi−D$ contains both normal deformation and shear deformation, we propose grouping the normal deformation with the pressure dilatation to describe the power density due to converging/diverging flows, with the balance describing the power density purely due to shear deformation. We then develop a kinetic theory interpretation of compression, normal deformation, and shear deformation. We use the results to determine the physical mechanisms that can make $Pi−D$ negative. We argue that both decompositions can be useful for the study of energy conversion in weakly collisional or collisionless fluids and plasmas, and implications are discussed.