Multiple solutions, oscillons and strange attractors in thermoviscoelastic marangoni convection

Through numerical solution of the governing time-dependent and non-linear Navier-Stokes equations cast in the framework of the Oldroyd-B model, the supercritical states of thermal Marangoni-Bénard convection in a viscoelastic fluid are investigated for increasing values of the relaxation time while keeping fixed other parameters (the total viscosity of the fluid, the Prandtl number and the intensity of the driving force, Ma=300). A kaleidoscope of patterns is obtained revealing the coexistence of different branches of steady and oscillatory states in the space of parameters in the form of multiple solutions. In particular, two main families of well-defined attractors are identified, i.e. multicellular steady states and oscillatory solutions. While the former are similar for appearance and dynamics to those typically produced by thermogravitational hydrodynamic disturbances in layers of liquid metals, the latter display waveforms ranging from pervasive standing waves to different types of spatially localised oscillatory structures (oscillons). On the one hand, these localised phenomena contribute to increase the multiplicity of solutions and, on the other hand, give rise to interesting events, including transition to chaos and phenomena of intermittency. In some intervals of the elasticity number, the interference among states corresponding to different branches produces strange attractors for which we estimate the correlation dimension by means of the algorithm originally proposed by Grassberger and Procaccia