Spectral simulations of laminar-turbulent transition in plane Poiseuille flow and comparison with experiments

Abstract

Laminar-turbulent transition in plane Poiseuille flow is simulated using the FourierChebyshev spectral method to integrate the three-dimensional time-dependent NavierStokes equations. For pressure computation, a new algorithm has been developed which enforces incompressibility and boundary conditions exactly even in the discretised equations. Detailed comparisons of the numerical results have been made with the vibrating-ribbon experiments of Nishioka et al. It is established that the numerical simulations reproduce the experimentally observed transition process up to the “spike” stage.