Vorticity and Stress Tensor

Abstract

The assumptions of the Navier-Stokes equations are reconsidered. Vorticity is one of the three basic isotropic motions of a fluid element about a point. Taking into consideration the isotropic and symmetric nature of the associated tensor, it was assumed that vorticity could not contribute to the viscous stresses and hence was omitted from subsequent derivations of the Navier-Stokes equations. Deviating from this classical approach, the effect of vorticity is included in the derivation of the stress tensor.The equation hence derived contains additional terms involving vortex viscosity. Analogous to Maxwell stress tensor in electromagnetic fields, another stress tensor is defined in a vorticity field. By treating vortices as physical structures, it is possible to define pressure and the shearing stress that deform the volume element.