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

TL;DR

This paper derives and analyzes the boundary fluxes of orbital rotation and spin in incompressible viscous flows interacting with stationary walls, offering new insights into vorticity dynamics and near-wall flow structures.

Contribution

It provides the first full expressions for boundary fluxes of orbital rotation and spin, elucidating their creation mechanisms and extending to enstrophy and vorticity dynamics.

Findings

Boundary coupling occurs only in the spin flux.

Boundary enstrophy fluxes relate to the velocity gradient tensor.

Spin-geometry interaction influences boundary vorticity dynamics.

Abstract

Vorticity is locally created on a boundary at the rate measured by the boundary vorticity flux, which can be further decomposed as the sum of the orbital rotation and the (generalized) spin. For 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, respectively. 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, and the two quadratic forms representing the spin-geometry interaction. The present exposition provides a new perspective to 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.