Symmetry breaking of rotating convection due to Non-Oberbeck-Boussinesq effects

Abstract

The non-Oberbeck--Boussinesq (NOB) effects arising from variations in thermal expansivity are theoretically and numerically studied in the context of rotating Rayleigh--B\'{e}nard convection in forms of two-dimensional (2D) rolls. The thermal expansivity increases with pressure (depth), and its variation is measured by a dimensionless factor $\epsilon$. Utilizing an asymptotic expansion with weak nonlinearity, we derive an amplitude equation, revealing that NOB effects amplify the magnitude of convection. An $\epsilon^2$-order NOB correction leads to a symmetry breaking about the horizontal mid-plane, manifested in the strengthening of convection near the bottom and its weakening near the top, forming bottom-heavy profiles. At $\epsilon^3$-order, the conjunction of NOB effects and nonlinear advection leads to a horizontal symmetry breaking. The values of Taylor number and Prandlt number determine whether upward or downward plumes are stronger. Numerical calculations validate the theoretical analyses in weakly nonlinear regime. This work advances our understanding of hydrothermal plumes in some winter lakes on Earth, and in the subglacial oceans on icy moons as well as tracer transport from the seafloor to the ice shell.