Two-dimensional perturbations in a suddenly blocked channel flow

The stability of the laminar flow established after the sudden closure of a channel is investigated by numerical simulations of the Navier-Stokes and continuity equations. The basic flow computed by the present approach agrees satisfactorily with the one obtained by other authors using a Pohlhausen technique. A stability analysis performed computing the time development of 2-D perturbations of small amplitude shows that the flow is more unstable than predicted by a quasi-steady approach. The large amplitude perturbations detected in previous experimental visualizations of decelerating channel and pipe flows are qualitatively reproduced. The results of the simulations show that the amplification of the perturbation is accompanied by the formation of vortices which survive for long time. Finally, the spatial longitudinal energy spectrum is examined and the existence of a wavenumber range in which the slope of the spectrum ranges from -3 to -4 is observed. The numerical simulations in the nonlinear regime allow to have a deeper insight into the physical mechanism leading to the appearance of turbulence.