Multicellular states of viscoelastic thermovibrational convection in a square cavity

The problem of pure thermovibrational flow in a two-dimensional square cavity containing a viscoelastic liquid is investigated in the framework of a numerical approach based on the governing balance equations for mass, momentum, and energy in their complete and non-linear time-dependent form. For problem closure, these equations are complemented with the transport equation for the elastic stress formulated using the finitely extensible nonlinear elastic Chilcott-Rallison (FENE-CR) constitutive model. A complete parametric study is carried out to highlight the different path of evolution taken by the considered viscoelastic fluid with respect to the corresponding Newtonian counterpart when the Gershuni number is increased. Attention is paid to the patterning scenario in terms of time-averaged flow and related multicellular structures. It is shown that the triadic relationship among the typical characteristic time scales involved in these phenomena, namely, the thermally diffusive time, the fluid relaxation time, and the period of vibrations, can lead to a kaleidoscope of states, which differ in regard to the prevailing symmetry and the related spatiotemporal behaviors. Moreover, the complex interaction between the external vibrations and the elastic property of the polymer molecules, mediated by viscous effects, can produce an interesting "intermittent response."