Weakly nonlinear analysis of a localized disturbance in Poiseuille flow

In this article, we investigate, via a perturbation analysis, some importan t nonlinear features related to the process of transition to turbulence in a wall-bounded flow subject to a spatially localized disturbance that is ha rmonic in time. We show that the perturbation expansion, truncated at secon d order, is able to capture the generation of streamwise vorticity as a wea kly nonlinear effect, The results of the perturbation approach are discusse d in comparison with direct numerical simulation data for a sample case by extracting the contribution of the different orders. The main aim is to pro vide a tool to select the most effective nonlinear interactions to enlighte n the essential features of the transitional process.