The Topology of Surface Skin Friction and Vorticity Fields in Wall-bounded Flows
نویسنده
چکیده
In previous studies, 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, Q and R respectively. However, these invariants 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 flow 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 it will be shown how the topology of the flow field on a no slip wall can be studied in terms of these invariants. INTRODUCTION A critical point is a point in a flow field where the velocity u1 = u2 = u3 = 0 and the streamline slope is indeterminate. Close to the critical point the velocity field can be described by the linear terms of a Taylor-series expansion. Two types of critical points can be described: one is the free slip critical point which is located away from a no slip wall and the other is the no slip critical point which occurs on a no slip wall. Free-slip critical points For free slip critical points, the velocity ui in xi space is given by u1 u2 u3 = . x1 . x2 . x3 = dx1/dt dx2/dt dx3/dt = A11 A12 A13 A21 A22 A23 A31 A32 A33 x1 x2 x3
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