The Role of Normal and Non-Normal Contributions to Enstrophy Production in the Near-Wall Region of a Turbulent Channel Flow

TL;DR

This study decomposes enstrophy production in turbulent channel flow into normal and non-normal contributions, revealing that fluctuating normal straining dominates near-wall vorticity amplification despite expectations of non-normal effects being more significant.

Contribution

It introduces a novel decomposition of strain rate and vorticity into normal and non-normal parts, providing detailed insight into enstrophy production mechanisms near walls.

Findings

Normal straining in the transverse direction is the most important individual term.

Non-normal contributions are generally smaller and can be negative.

Local orthogonal straining amplifies vorticity before it develops into rotation.

Abstract

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 of the enstrophy production, the purely fluctuating contribution is the dominant term and that 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, the most important individual term involves the fluctuating, normal straining in the transverse direction. Furthermore, the reason that the term that involves only non-normal contributions is smaller on average than that involving normal straining coupled to non-normal vorticity is that in the former case there are individual constituents that are negative in the mean. Hence, we not only explain the nature of near-wall enstrophy production in greater detail, but highlight how local straining 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 sufficiently to gain a solid body rotational component.