Boundary Vorticity Flux and Engineering Flow Management (Advances in Applied Mathematics and Mechanics, 2018)
To improve the performance of complex viscous engineering flows, thefocus should be on local dynamics (local processes and structures)measured by the space-time derivatives of the primary-variablefields, rather than these fields themselves. In the context ofoptimal flow management such as optimal configuration design andflow control, the local fluid dynamics on solid wall is of mostdirect relevance. For large Reynolds-number flows, we show that theon-wall local dynamics is highlighted by the balance betweentangential pressure gradient and vorticity creation rate at the wall(boundary vorticity flux, BVF), namely the on-wall coupling of thecompressing and shearing processes. This basic concept isdemonstrated by previously unpublished and newly obtained numericalexamples for external and internal flows, including the role of BVFas a faithful marker of the local appearance of boundary-layerseparation and wall curvature discontinuity, and the use ofBVF-based formulas to optimize the integrated performance of airfoiland compressor rotor blade.