Symmetry breaking perturbative flows to retrieve resonant modes in plane shear layers Takeshi Akinaga a,c , Tomoaki Itano b , Sotos Generalis c,* a Marie Sklodowska Curie International Incoming Fellow b Department of Pure and Applied Physics, Faculty of Engineering Science, Kansai University, Osaka 564-8680, Japan c System Analytics Research Institute, Aston University, Birmingham, B4 7ET, United Kingdom Abstract We propose a simple computational procedure in order to resolve the degen- eracy, which invariably exists on the background of fluid motion associated with a channel of infinite extent. The procedure is applied to elucidate the bifurcation structure for the particular case of laterally heated flow with the addition of a perturbative Poiseuille flow component. The introduction of a symmetry breaking perturbation as the simplest imperfection alters the bi- furcation tree of the original shear flow. As a result, the previously unknown higher order nonlinear solutions for the unperturbed flow are discovered, without implementing classical stability theory. Keywords: Bifurcation, nonlinear stability, 2:1 resonance, homotopy, symmetry breaking perturbation PACS: 47.10. -g 1. Introduction and Methodology It is well known in quantum mechanics that a spectral line composed by different components can be split under the presence of a static perturbative magnetic field. This fact, the so-called Zeeman effect, implies that multiple * Corresponding author Email addresses: s.c.generalis@aston.ac.uk (Sotos Generalis ), s.c.generalis@aston.ac.uk (Sotos Generalis ) Preprint submitted to Physica D March 10, 2015 arXiv:1503.02625v1 [physics.flu-dyn] 9 Mar 2015