With a clearer apprehension of the role of Netonian Motive I want t define vorticity in tems of spiral behaviour.
Thus it is not sufficient to define vorticity in terms of circulation or rotational motive, it must be defined in tems of convergent and or divergent rotational motive, which means interns of a trochoidal vorticular shell system.
The vector notion of divergence will be explored, but modified by the use of Normans concept of spread, and also by the introduction of twistors and Twistorque. The notion of a twistor will be extended to include twistors and twistorques that have a variable radius, and their combination with rotating vectors bases on exponential forms to define a trochoidal motion field .
The divergence formula will be derived for such a system, and used in the definition of fluid vorticity.
Once fluid vorticity is defined, thn spaciometric density will be defined as a count of fractal regions of vortices. With this Spaciometry secure I can use spaciometric density as a model for kinaesthetic or mechanical density, which will then feed into Newtons reference frame, and inform the description of fluid mechanics.
Fluid mechanics cannot ignore viscosity, but I would seek a direct definition of viscosity in terms of inter fluid element vorticity modulated by intra fluid element vorticity, which would allow viscosity and vorticity to be interchangeable ar different levels or fractal scales..
Finally turbulence as a fractal distribution of vorticity in a viscous medium will be explored.
The gradient is the divergences of the function as a lineal combination. As a vector projection the gradient is a vertical or orthogonal projection of the "higher space" "vector' (or combinations) into a subspace. it is the shadow of the projected space onto a subspace. This is a Grassmannian idea of reversion, involving the Inner product.