In previous papers, Antunes and co-workers developed a theoretical model for nonlinear planar motions*motions X(t) taking place in one single direction*of rotors under #uid con"nement using simpli"ed #ow equations on the gap-averaged #uctuating quantities. The nonlinear solution obtained was shown to be consistent with a linearized solution for the same problem. Also, it displayed an encouraging qualitative agreement between the nonlinear theory and preliminary experimental results. Following a similar approach, the nonlinear theoretical model is here extended to cope with orbital rotor motions*motions X(t) and >(t) taking place in two di!erent orthogonal directions*by developing an exact formulation for the twodimensional dynamic #ow forces. Numerical simulations of the nonlinear rotor}#ow coupled system are presented and compared with the linearized model. These yield similar results when the eccentricity and the spinning velocity are low. However, if such conditions are not met, the qualitative dynamics stemming from the linearized and nonlinear models may be quite distinct. Preliminary experimental results also indicate that the nonlinear #ow model leads to better predictions of the rotor dynamics when the eccentricity is signi"cant, when approaching instability, and for linearly unstable regimes.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.