Bifurcation analysis of a viscoelastic fluid heated from below

► The thermal buoyancy convection of viscoelastic fluid in closed cavity heated from below is studied. ► The character of branching is examined by means of weakly-nonlinear analysis. ► To study the convective modes, the reduction to the set of nonlinear ODEs is introduced. ► Five different bifurcations are found in the system. Convection of a viscoelastic fluid in a square domain heated from below is investigated for the case of nondeformable free surfaces. To describe the rheological behavior of the fluid the generalized Oldroyd model is used. A weakly nonlinear analysis is performed in order to determine the character of branching for both the monotonic and oscillatory modes. We also perform a reduction of the boundary value-problem to the set of nonlinear amplitude equations. The analysis of this dynamic system demonstrates the onset and competition of five convection modes.