Onset of convection cells in a horizontally rotating cylinder partially filled with liquid

Abstract

We investigate flow of liquid which is partially filled in a cylindrical container horizontally rotating about its axis of symmetry. Even if the rotation is slow enough to keep the liquid–gas interface almost undeformed, convection cells whose circulation axis is perpendicular to the container's rotational axis can be sustained. We conduct experiments by particle image velocimetry and direct numerical simulations with the S-CLSVOF and immersed boundary methods to reveal the condition of the Reynolds number, the aspect ratio of the container and the filling ratio of liquid for the onset of these convection cells. When the filling ratio is not too large, as the Reynolds number increases, convection cells appear through a pitchfork bifurcation in an infinitely long cylinder. This bifurcation becomes imperfect in the case of a finite-length cylinder. In contrast, when the filling ratio is large enough, convection cells appear through a subcritical bifurcation. Through these investigations, it becomes evident that the axial wavelength of sustained convection cells is an increasing function of the filling ratio in an infinitely long cylinder. In practice, to sustain intense convection cells, we should use a cylinder with the length equal to an integer multiple of the wavelength of the most unstable mode in the infinite-length cylinder. Although we focus on the liquid-pool regime with small Froude numbers, the critical Reynolds number for the pitchfork bifurcation weakly depends on the Froude number. This dependence is explained by considering the changes in the effective filling ratio and the convection velocity.