Is high Reynolds number turbulence locally isotropic?

Preliminary results show that in high Reynolds number (R-lambda 1,000) shear flow the skewness of the derivative of the longitudinal velocity fluctuations in the direction of the mean shear become small, however, the super-skewness <(partial derivative(u)/partial derivative(y))(5)>/<(partial derivativeu/partial derivativey)(2)>(5/2) is of order 10 with no diminution with Reynolds number. We conclude that the velocity field is anisotropic even at very high Reynolds number. This fundamental aspect of the velocity field is compared with the well known anisotropy observed in passive scalars.