Physical structures of boundary fluxes of orbital rotation and spin for incompressible viscous flow

• Published in: Applied mathematics and mechanics Vol. 46; no. 4; pp. 745 - 762
• Main Authors: Chen, Tao, Liu, Tianshu
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2025; Springer Nature B.V
• Edition: English ed.
• Subjects: Applications of Mathematics; Classical Mechanics; Differential geometry; Dynamics; Fluid flow; Fluid- and Aerodynamics; Fluxes; Incompressible flow; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Partial Differential Equations; Quadratic forms; Rotation; Sums; Tensors; Velocity gradient; Viscous flow; Vorticity; boundary vorticity flux (BVF); O351.2; boundary enstrophy dynamics; O331; spin; Lyman vorticity dynamics; 76D05; orbital rotation; 76D17; O357.1
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-025-3238-9

Vorticity is locally generated on a boundary at a rate measured by the boundary vorticity flux (BVF), which can be further decomposed into the sum of the orbital rotation and the generalized spin (specifically, the sum of shear and streaming vorticity) under the field description. For an incompressible viscous flow interacting with a stationary wall, the full expressions of the boundary fluxes of the orbital rotation and the spin are derived, for the first time, to elucidate their boundary creation mechanisms. Then, these new findings are successfully extended to the study of the boundary enstrophy dynamics, as well as the Lyman vorticity dynamics as an alternative interpretation to the boundary vorticity dynamics. Interestingly, it is found that the boundary coupling of the longitudinal and transverse processes is only embodied in the boundary spin flux, which is definitely not responsible for the generation of the boundary orbital-rotation flux. In addition, the boundary fluxes of enstrophy are directly associated with the boundary source of the second principal invariant of the velocity gradient tensor (VGT) and the two quadratic forms representing the spin-geometry interaction. The present exposition provides a new perspective and an additional dimension for understanding the vorticity dynamics on boundaries, which could be valuable in clarifying the formation mechanisms of near-wall coherent structures and flow noise at the fundamental level.