Isotropic forms of vorticity and velocity structure function equations in several turbulent shear flows

Isotropic forms of the vorticity and velocity structure function equations are valid in the logarithmic regions of a fully developed turbulent duct flow and a boundary layer over a wide range of Reynolds numbers. These equations are also valid in a low Reynolds number turbulent wake and a high Reynolds number atmospheric surface layer. However, these equations are not satisfied in the near-wall region of duct and boundary layer flows where the production of vorticity is significantly larger than the dissipation. The appropriateness of the equations as indicators of local isotropy is discussed in the context of the present and other published measurements.