Re-examination of vorticity transfer theory

The averaging procedure required to generate the Reynolds equations for turbulent shear flows results in a loss of information. The system of equations is no longer closed, and additional assumptions are required. The classical closure assumptions are based on Taylor's vorticity transfer theory and Prandtl's momentum transfer theory. In this paper we show that the former is in a very fundamental sense incorrect in that only for very special forms of the eddy exchange coefficient (including a constant coefficient) does turbulent 'diffusion' of vorticity also conserve momentum. For expository purposes much of the discussion is centered on an idealized simple two-dimensional wake in which momentum and vorticity are conserved transferable properties.