  This paper presents a method to stabilise oscillations occurring in a mixed
convective flow in a nearly hemispherical cavity, using an actuation modelled
on the receptivity map of the unstable mode underpinning these oscillations.
This configuration represents a simplified model inspired from the continuous
casting of metallic alloys where hot liquid metal is poured at the top of a hot
sump with cold walls pulled in a solid phase at the bottom. The model focuses
on the underlying fundamental thermo-hydrodynamic processes without dealing
with the complexity inherent to the real configuration (Flood & Davidson 1994).
This flow exhibits three branches of instability (Kumar & Poth{\'e}rat 2020).
By solving the adjoint eigenvalue problem for the convective flow equations, we
find that the region of the highest receptivity for the unstable modes of each
branch tends to concentrate near the inflow upper surface. Simulations of the
linearised governing equations then reveal that a thermo-mechanical actuation
modelled on the adjoint eigenmode suppresses the unstable mode over a finite
time, after which it becomes destabilising. Based on this phenomenology, we
apply the same actuation for the duration of the the stabilising phase only in
the nonlinear evolution of the unstable mode. It turns out that the
stabilisation persists, even when the unstable mode is left to evolve freely
after the actuation period. Besides demonstrating the effectiveness of
receptivity-informed actuation for the purpose of stabilising convective
oscillations, these results potentially open the way to a simple strategy to
control them during arbitrarily long periods of time.
