Rayleigh-Benard convection in viscoelastic liquid bridges

Rayleigh-Benard convection in a floating zone held by the surface tension between two supporting disks at different temperatures is considered. Through direct numerical solution of the mixed parabolic-elliptic-hyperbolic set of governing equations in complete time-dependent and nonlinear form, we investigate the still unknown patterns and spatio-temporal states that are produced when the fluid has viscoelastic properties. The following conditions are examined: Prandtl number Pr = 8, aspect ratio (A = length/diameter) in the range 0.17 <= A <= 1 and different values of the elasticity number (0 <= theta <= 0.2). It is shown that, in addition to elastic overstability, an important ingredient of the considered dynamics is the existence of multiple solutions i.e. 'attractors' coexisting in the space of phases and differing with respect to the basin of attraction. We categorize the emerging states as modes with dominant vertical or horizontal vorticity and analyse the related waveforms, generally consisting of standing waves with central symmetry or oscillatory modes featuring almost parallel rolls, which periodically break and reform in time with a new orientation in space. In order to characterize the peculiar features of these flows, the notions of disturbance node and the topological concept of 'knot' are used. Azimuthally travelling waves are also possible in certain regions of the space of parameters, though they are generally taken over by convective modes with dominant pulsating nature as the elasticity parameter is increased. The case of an infinite horizontal layer is finally considered as an idealized model to study the asymptotic fluid-dynamic behaviour of the liquid bridge in the limit as its aspect ratio tends to zero.