Angular momentum balance and vortex production in wall-bounded flows

Abstract

To produce a vortex, a torque must be applied to the fluid. In viscous fluids, the torques that produce turbulent vortices result from the loss of symmetry of the stress tensor, once the viscous friction exceeds the shear stress resistance of the fluid. In wall-bounded flows, in particular, the turbulent vortices form in a thin layer of fluid adjacent to the wall, practically coinciding with the so-called viscous sublayer, where the viscous friction reaches the largest values. The present paper determines a vortex structure for this sublayer, consistent with the well-known linearity of the diagram of the mean streamwise velocity of this region. The analysis enables us to calculate the diameter, angular velocity, and interaxis of the vortices in the viscous sublayer in steady-state conditions. The lifting force that makes the vortices migrate from the wall towards the mainstream flow is determined, and the crucial role played by gyroscopic precession in the reorientation of the vortex axis is discussed.