Secondary instability induced by thermocapillary effect in half-zone liquid bridge of high Prandtl number fluid

Abstract

We investigate the secondary instability of thermocapillary-driven convection in a high-Pr liquid bridge (Pr = 4) of half-zone geometry via direct numerical simulation. The convection is known to exhibit a three-dimensional time-dependent ‘oscillatory’ state with a distinct azimuthal modal structure, that is, spatio-temporally periodic state after the onset of the primary instability. We indicate that the convection exhibits another transition to spatio-temporally quasi-periodic states by increasing the intensity of the thermocapillary effect. The proper orthogonal decomposition (POD) is employed in order to extract the variation of the flow structures before/after the secondary instability. After the primary instability, one finds the oscillatory flow with a fundamental azimuthal modal number. It is indicated that the flow field consists of the primary component with the fundamental modal structure and the components with fundamental modal structures of higher harmonics of the primary components. Those components dominate the whole flow field. After the onset of secondary instability, additional components emerge in the flow; those components consist of the the fundamental azimuthal modal structures, which are different from higher harmonics of the primary flow field. We determine the onset condition or critical Reynolds number for the secondary instability Re_c⁽²⁾ by monitoring the development of the energy of the newley arisen components. It is found that the secondary instability evaluated through decomposed flow structures via nonlinear simulation corresponds to that predicted through Floquet modes via linear stability analysis.