Strong spatial resonance in an air-filled, differentially heated rotating annulus

We examine the nonlinear interaction of rotating waves of azimuthal wave numbers m1=2 and m2=1 (i.e. strong spatial resonance) in an air-filled, differentially heated rotating annulus. Using a weakly nonlinear analysis that combines centre manifold reduction and numerical bifurcation analysis, we determine the dynamics close to a double Hopf bifurcation point where these modes interact. While previous studies have addressed higher-order weak spatial resonances, the strong 2–1 spatial resonance introduces quadratic terms in the reduced equations that can lead to unique dynamics. Our analysis predicts the emergence of stable, phase-locked mixed-mode rotating waves, which is consistent with experimental observations and indicates the distinct dynamics produced by strong spatial resonance.