Instability of three-dimensional flow due to rotation and surface-tension driven effects in a shallow pool with partly free surface

Abstract

Abstract The fundamental characteristics of the three-dimensional flow induced by rotation and surface-tension driven effects subjected to a horizontal temperature gradient in a shallow cylindrical pool with a disk on the free surface are investigated through a series of numerical simulations. The aspect ratio (height/radius) of the system considered in this work is 0.06 and the radius ratio is 0.3. The results indicate that the basic flow is axisymmetric and steady. It behaves as rich flow structures in the meridian plane. However, with the increase of the rotation and thermocapillary Reynolds numbers, the flow will undergo a transition to a three-dimensional oscillatory flow, which is characterized by the temperature and velocity fluctuation waves traveling in azimuthal direction. The direction and velocity of wave propagation, fluctuation amplitude and wave number are dependent on the interactions of the thermocapillary, centrifugal and Coriolis forces. The critical conditions for the onset of flow instabilities are obtained. The stability diagram is presented, which shows the critical thermocapillary Reynolds number varies with the rotation rates of the pool and disk. In particular, when the disk counter-rotates with the pool, three different flow states are observed and mapped with different thermocapillary Reynolds numbers. Besides, the origins of these flow instabilities in different unstable state regimes are discussed and briefly summarized in this paper.