A reduced dynamical model of convective flows in tall laterally heated cavities

Proper orthogonal decomposition (the Karhunen-Loeve expansion) is applied to convective flows in a tall differentially heated cavity. Empirical spatial eigenfunctions are computed from a multicellular solution at supercritical conditions beyond the first Hopf bifurcation. No assumption of periodicity is made, and the computed velocity and temperature eigenfunctions are found to be centro-symmetric. A low-dimensional model for the dynamical behaviour is then constructed using Galerkin projection. The reduced model successfully predicts the first Hopf bifurcation of the multicellular flow. Results determined from the low-order model are found to be in qualitative agreement with known properties of the full system even at conditions far from criticality.