Rotating and thermocapillary-buoyancy-driven flow in a cylindrical enclosure with a partly free surface

In order to understand the characteristics of the complex flow driven by the combined thermocapillary-buoyancy effect and differential rotation of a cylindrical pool and a disk on the free surface, a series of unsteady three-dimensional numerical simulations were performed. Results indicate that the flow is axisymmetric and steady at a small temperature difference and low rotation rates. The basic meridional flow structures are composed of toroidal circulations. With an increase of the rotation rate and/or temperature difference, the basic flow transits to a three-dimensional oscillatory flow. Without rotation, the unstable thermocapillary-buoyancy flow is characterized by pulsating spoke patterns with the periodic growth and decay of temperature and velocity oscillations. When the disk and/or cylinder rotate, the oscillatory flow behaves as temperature and velocity fluctuation waves traveling in the azimuthal direction. The wave propagation velocity and direction, fluctuation amplitude, and wave number depend on the interaction of the thermocapillary, buoyancy, centrifugal and Coriolis forces. The critical conditions for the flow transition are determined. It is found that the critical thermocapillary Reynolds number initially increases before decreasing with the increase of the disk rotation rate, but the rotation of cylinder always retards the flow instability. In addition, the mechanisms of the flow instabilities are discussed and briefly summarized.