The invariants of the no-slip tensor in wall-bounded flows

Abstract

The three invariants of the velocity gradient tensor have been used to study turbulent flow structures. For incompressible flow the first invariant P is zero and the topology of the flow structures can be investigated in terms of the second and third invariants. However, the invariants Q and R are zero at a no-slip wall and can no longer be used to identify and study structures at the surface in a wall-bounded flow. At the wall, the velocity field can be described by a no-slip Taylor-series expansion. Like the velocity gradient tensor, it is possible to define the invariants P, Q and R of the no-slip tensor. In this paper flow structures on a no-slip boundary will be studied in terms of thes..