Structure of a Turbulent Puff in Pipe Flow

Abstract

The flow in a circular pipe of radius a driven by a constant and uniform axial force is investigated over a range of Reynolds numbers, including the critical value for laminar–turbulent transition. The Navier–Stokes equation for an incompressible viscous fluid is solved numerically by a spectral method as the initial value problem with the no-slip boundary condition on the pipe wall and periodic boundary conditions with period 16π a in the axial direction. The initial condition is given by the Hagen–Poiseuille flow (corresponding to the external force) superimposed with perturbations of finite amplitude. The long-term behaviour of the flow is qualitatively different depending on the Reynolds number Re = U a /ν, where U is the centerline velocity of the above Hagen–Poiseuille flow and ν is the kinematic viscosity of the fluid. For intermediate Reynolds numbers (3300≤ Re ≤4000) we find a locally turbulent region, called a “puff”, which is advected downstream with velocity close to the mean axial velocity. T...