Abstract
A numerical investigation is conducted of Rayleigh-B\'enard convection in a rectangular enclosure of aspect ratio 2:1 filled by a class of nonlinear viscoelastic fluids represented by the Phan Thien-Tanner (PTT) constitutive equation. The objective is to provide a detailed interpretation of the physical mechanisms involved in Rayleigh-B\'enard convection for a viscoelastic fluid. An energy analysis highlights the different physical mechanisms involved in oscillatory convection. The results show the contribution of the elastic terms in the evolution of the kinetic energy of the structures. At a second critical Rayleigh number the oscillatory convection with two rollers becomes stationary again.
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