# Weakly nonlinear analysis of thermoacoustic bifurcations in the Rijke tube

@article{Orchini2016WeaklyNA, title={Weakly nonlinear analysis of thermoacoustic bifurcations in the Rijke tube}, author={Alessandro Orchini and Georgios Rigas and Matthew P. Juniper}, journal={Journal of Fluid Mechanics}, year={2016}, volume={805}, pages={523 - 550} }

In this study we present a theoretical weakly nonlinear framework for the prediction of thermoacoustic oscillations close to Hopf bifurcations. We demonstrate the method for a thermoacoustic network that describes the dynamics of an electrically heated Rijke tube. We solve the weakly nonlinear equations order by order, discuss their contribution on the overall dynamics and show how solvability conditions at odd orders give rise to Stuart–Landau equations. These equations, combined together…

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