  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 under two-dimensional (2D)
configuration. 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
order-$\epsilon^2$ 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 a bottom-heavy profiles. At
order $\epsilon^3$, the conjunction of NOB effects and nonlinear advection
leads to a horizontal symmetry breaking. The downward cold plumes become
stronger and more concentrated compared to the upward warm plumes. Numerical
simulations validate the theoretical analyses in the weak nonlinear regime and
confirm robust horizontal asymmetry and stronger downward plumes at very large
Rayleigh numbers. 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.
