Some Basic Aspects of the Triple Decomposition of the Relative Motion near a Point

The triple decomposition of the relative motion near a point (TDM) ― based on the extraction of a so-called “effective” pure shearing motion ― has been recently proposed by the present author. The relative motion near a point has been decomposed through the analysis of a “frozen” flow field at a given instant in time. This approach has been motivated by the fact that vorticity cannot distinguish between pure shearing motions and the actual swirling motion of a vortex. The TDM results in two additive vorticity parts and two additive strainrate parts of distinct nature: the shear component associated with a pure shearing motion and the residual one. Some basic aspects of this novel decomposition technique are treated in the present paper. These aspects include: pure shearing motion and shearing elements in 3D, orbital compactness vs. arbitrary axial strain of a vortex, the interpretation of residual vorticity and the concept of residual circulation (i.e. a surface quadrature of the residual vorticity) for the description of vortex strength, and qualitative comparison of the TDM vorticity outcome with other known vorticity-decomposition techniques