The topology of skin friction and surface vorticity fields in wall-bounded flows

Abstract

In previous studies, the three invariants (P, Q and R) of the velocity gradient tensor have been widely used to investigate turbulent flow structures. For incompressible flows, the first invariant P is zero and the topology of turbulent flow structures can be investigated in terms of the second and third invariants, Q and R, respectively. However, all these three invariants are zero at a no-slip wall and can no longer be used to identify and study structures at the surface in any wall-bounded flow. An alternative scheme is presented here for the classification of critical points at a no-slip wall; the skin friction vector field at the wall is given by the wall normal gradients of the streamw..