Indirect physical mechanism of viscous forces: Vortex stretching and twisting

Abstract

In this paper, the indirect physical mechanism of viscous forces, i.e., vortex stretching and twisting, is theoretically explored. The local flow in the immediate neighborhood of a flat plate is analyzed. Only the viscous forces are considered. By introducing oppositely signed streamwise vorticity in such a region, the induced velocity and vorticity fields are obtained. Because the induced streamwise velocity varies along with both the wall-normal and spanwise directions, induced vertical and spanwise vorticities are generated. The induction sequence is first clarified. Then, two indirect effects of viscous forces are identified. The induced spanwise vorticity leads to the original two-dimensional spanwise vorticity increasing and decreasing alternately across the span, as the vortex stretching effect of viscous forces. The local spanwise vortex is distorted at positions where the streamwise vorticity is introduced, and the appearance of induced vertical vorticity at the same positions enhances this effect, as the vortex twisting effect of viscous forces.