Decomposition of the mechanical stress tensor: from the compressible Navier–Stokes equation to a turbulent potential flow model

We frame the mechanical stress tensor decomposition in a general procedure which involves the Helmholtz-Hodge decomposition. We highlight the impact of the mechanical stress tensor decomposition on the Navier-Stokes equation, with emphasis on the dissipation function. For fluids with low compressibility, we draw some insights on the Reynolds Averaged Navier-Stokes equations, and on the Reynolds stress tensor decomposition. We derive a turbulent potential flow model, and investigate the transition from viscous potential flow to turbulent potential flow. Under low Mach number approximation, we apply the turbulent potential flow model to one-dimensional propagation of large amplitude pressure waves in liquid-filled pipe.