Unification of The Navier-Stokes Equation for Fluid Mechanics and Aeroacoustics

Abstract

The Navier-Stokes equation for a compressible Newtonian fluid is reassessed, in view of recent investigation results on the foundations of aeroacoustics. In the process, the role and necessity of the so-called Stokes' hypothesis is reconsidered, which in its current practice omits the bulk viscosity. In contrast, the relevance of a new generalized kinematic viscosity is proposed, along with a new methodology that will enable estimation of second coefficient of viscosity completely obviating the necessity of making the Stokes' hypothesis. This opens up the vista of a new formulation for the Navier-Stokes equation applicable for both the subjects of fluid mechanics and aeroacoustics in a unified approach.