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Weakly Nonlinear Analysis of a Localized Disturbance in Poiseuille Flow
Author(s) -
Ponziani D.,
Casciola C. M.,
Zirilli F.,
Piva R.
Publication year - 2000
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.00145
Subject(s) - nonlinear system , perturbation (astronomy) , hagen–poiseuille equation , turbulence , vorticity , bounded function , mechanics , disturbance (geology) , direct numerical simulation , physics , flow (mathematics) , vortex , mathematics , control theory (sociology) , statistical physics , mathematical analysis , computer science , geology , reynolds number , paleontology , control (management) , quantum mechanics , artificial intelligence
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.