Gravity modulation effect on the onset and nonlinear regimes of convection of viscoelastic fluid in a square cavity with adiabatic sidewalls

The influence of gravity modulation on the onset and nonlinear regimes of thermal buoyancy convection of a viscoelastic fluid in a square cavity with adiabatic lateral boundaries heated from below is investigated. The rheological behavior of the fluid is described using the Oldroyd model. Numerical data on the temporary evolution of small disturbances of the conductive state are used to determine the boundaries of linear stability to the disturbances of single- and two-vortex structure for different values of the modulation and rheological parameters. The calculations show that, depending on the parameter values, development of instability can be associated with synchronous, subharmonic, or quasiperiodic disturbances. The boundaries of instability to all these types of disturbances are defined. Stability maps in the parameter space showing the ranges where the modulation exerts a stabilizing or destabilizing effect are obtained. It is found that in some parameter ranges, the two-vortex disturbances, which were not the most dangerous in the absence of gravity, become responsible for the conductive state instability in a modulated gravity field. A merging of parametric instability zones of growing synchronous disturbances oscillating with zero mean with the main instability zone of growing synchronous disturbances oscillating with a nonzero mean is discovered. The influence of gravity modulation on the convection excitation type is studied for the cases with supercritical and subcritical bifurcations without modulation; unstable solutions are numerically computed in the subcritical bifurcation case. The structure and characteristics of nonlinear convection regimes are determined by numerically solving full nonlinear equations.