A note on kinetic energy, dissipation and enstrophy

Abstract

We show that the dissipation rate of a Newtonian fluid with constant shear viscosity has three constituents from dilatation, vorticity, and surface strain. The last one, being associated with the most complicated manners of fluid deformation, only contributes to the change of internal energy but not that of kinetic energy. The distinction of these dissipation constituents is used to identify typical compact flow structures at high Reynolds numbers, such as shock waves, thin vortex layers, and filaments. This identification is of particular interest in studying turbulence structures. We then cast the incompressible version of the simplified kinetic-energy transport equation to a novel form, which is free from the work rate done by surface stresses but in which the full dissipation reenters. This result is of relevance to the physical routes via which turbulent energy is transferred to small scales.