The role of normal and non-normal contributions to enstrophy production in the near-wall region of a turbulent channel flow

The turbulent boundary layer is a region where both preferential dissipation of energy and the production of significant vorticity arises as a consequence of the strong velocity gradients. Previous work has shown that, following a Reynolds decomposition, the purely fluctuating component of the enstrophy production is the dominant term. Near the wall this varies in a complex manner with height. In this study, we additionally decompose the strain rate and vorticity terms into normal and non-normal components using a Schur decomposition and are able to explain all these features in terms of contributions at different heights from constituents involving different combinations of normal and non-normal quantities. What is surprising about our results is that, while the mean shear and the action of larger-scale structures should mean that non-normal effects are of over-riding importance at the wall, the most important individual term involves the fluctuating normal strain rate in the transverse direction. In part, this is because of a strong correlation between this term and the non-normal vorticity with a transverse axis, but it is also the case that individual components of the purely non-normal enstrophy production are negative in the mean. Hence, a local strain rate that is orthogonal to the direction of the dominant mean and fluctuating shear plays a crucial role in amplifying vorticity that is yet to have developed a local component. These conclusions support the emphasis in the control literature on the transverse velocity components at the wall.