Babushkin I., Demin V.

High frequency vibrations of a cavity filled with a fluid in the presence of temperature inhomogeneity may induce regular mean flows, even when the static gravity is absent (the phenomenon of thermovibrational convection). Under certain conditions, when the “slow” component of velocity is equal to zero, the state of mechanical quasi-equilibrium takes place. In this paper the stability of quasi-equilibrium, different averaging stationary and oscillatory convective regimes and scenarios of transition to chaos in Hele - Shaw cell are investigated by experimental and theoretical methods when the cavity is heated from below and subjected to the influence of high frequency vibrations. The methods of video visualization and thermal measurements were used in experiment. The approximation of plane trajectories was applied to calculate numerically the fields of velocity and temperature and to analyze the scenarios of transitions to chaotic regimes. The boundaries of mechanical quasi-equilibrium stability, and boundaries of stationary and time - dependent convective regimes in Hele - Shaw cell are determined. So the stability map for different convective regimes is received on the plane of governing parameters: thermal and vibrational Rayleigh numbers. The certain scenario of transition to chaos is realized for moderate values of vibrational Rayleigh numbers. There is following sequence of regimes: mechanical quasi-equilibrium, stationary one vortex flow, stationary two vortex flow, pulsational two vortex regime, regular oscillatory four vortex regime with reunification of vortexes and chaotic oscillatory four vortex regime with reunification of vortexes. Also the structure of transitional convective flows was studied in dependence on time. Theoretical investigation was carried out on the base of Galerkin - Kantorovich method with the help of series expansions of temperature and stream function fields. Also the method of finite differences was used to verify the results received on the base of Galerkin – Kantorovich technique.