On the wall shear stress gradient in fluid dynamics

The gradient of the fluid stresses exerted on curved boundaries, conventionallycomputed in terms of directional derivatives of a tensor, is here analyzed by usingthe notion of intrinsic derivative which represents the geometrically appropriate toolfor measuring tensor variations projected on curved surfaces. Relevant differences inthe two approaches are found by using the classical Stokes analytical solution for theslow motion of a fluid over a fixed sphere and a numerically generated three dimensionaldynamical scenario. Implications for theoretical fluid dynamics and for appliedsciences are finally discussed.