(untitled) (Advances in Applied Mathematics and Mechanics, 2018)
To improve the performance of complex viscous engineering flows, the focus should be on local dynamics (local processes and structures) measured by the space-time derivatives of the primary-variable fields, rather than these fields themselves. In the context of optimal flow management such as optimal configuration design and flow control, the local fluid dynamics on solid wall is of most direct relevance. For large Reynolds-number flows, we show that the on-wall local dynamics is highlighted by the balance between tangential pressure gradient and vorticity creation rate at the wall (boundary vorticity flux, BVF), namely the on-wall coupling of the compressing and shearing processes. This basic concept is demonstrated by previously unpublished and newly obtained numerical examples for external and internal flows, including the role of BVF as a faithful marker of the local appearance of boundary-layer separation and wall curvature discontinuity, and the use of BVF-based formulas to optimize the integrated performance of airfoil and compressor rotor blade.