Weakly Nonlinear Analysis of a Localized Disturbance in Poiseuille Flow - Ponziani, D.; Casciola, C. M.; Zirilli, F.; Piva, R. (Studies in applied mathematics (Cambridge), 2000)
In this article, we investigate, via a perturbation analysis, some important nonlinear features related to the process of transition to turbulence in a wall‐bounded flow subject to a spatially localized disturbance that is harmonic in time. We show that the perturbation expansion, truncated at second order, is able to capture the generation of streamwise vorticity as a weakly nonlinear effect. The results of the perturbation approach are discussed in comparison with direct numerical simulation data for a sample case by extracting the contribution of the different orders. The main aim is to provide a tool to select the most effective nonlinear interactions to enlighten the essential features of the transitional process.