Symmetry properties and bifurcations of viscoelastic thermovibrational convection in a square cavity

To fill a gap in the literature about the specific dynamics of thermovibrational flow in a square cavity filled with a viscoelastic fluid when vibrations and the imposed temperature gradient are concurrent, a parametric investigation has been conducted to investigate the response of this system over a relatively wide subregion of the space of parameters (Pr_{g}=10; viscosity ratio ξ=0.5; nondimensional frequency Ω=25, 50, 75, and 100; and Ra_{ω}∈[Ra_{ω,cr},3.3×10^{4}], where Ra_{ω,cr} is the critical vibrational Rayleigh number). Through solution of the governing nonlinear equations formulated in the framework of the finitely extensible nonlinear elastic Chilcott-Rallison paradigm, it is shown that the flow is prone to develop a unique hierarchy of bifurcations where initially subharmonic spatiotemporal regimes can be taken over by more complex states driven by the competition of disturbances with different symmetries if certain conditions are considered. What drives a wedge between the cases with parallel and perpendicular vibrations is essentially the existence of a threshold to be exceeded to produce convection in the former case. Nevertheless, these two configurations share some interesting properties, which are reminiscent of the resonances and antiresonances typical of multicomponent mechanical structures. Additional insights into these behaviors are gained through consideration of quantities representative of the kinetic and elastic energy globally possessed by the system and its sensitivity to the initial conditions.