  Vertical convection is the fluid motion that is induced by the heating and
cooling of two opposed vertical boundaries of a rectangular cavity (see e.g.
Wang et al. 2021). We consider the linear stability of the steady
two-dimensional flow reached at Rayleigh numbers of O($10^8$).
  As a function of the Prandtl number, $Pr$, and the height-to-width aspect
ratio of the domain, $A$, the base flow of each case is computed numerically
and linear simulations are used to obtain the properties of the leading linear
instability mode. Flow regimes depend on the presence of a circulation in the
entire cavity, detachment of the thermal layer from the boundary or the corner
regions, and on the oscillation frequency relative to the natural frequency of
oscillation in the stably temperature-stratified interior, allowing for the
presence of internal waves or not. Accordingly the regime is called slow or
fast, respectively. Either the global circulation or internal waves in the
interior may couple the top and bottom buoyancy currents, while their absence
implies asymmetry in their perturbation amplitude.
  Six flow regimes are found in the range of $0.1 \leq Pr \leq 4$ and $0.5 \leq
A \leq 2$. For $Pr \lessapprox 0.4 $ and $A>1$ the base flow is driven by a
large circulation in the entire cavity. For $Pr \gtrapprox 0.7$ the thermal
boundary layers are thin and the instability is driven by the motion along the
wall and the detached boundary layer. A transition between these regimes is
marked by a dramatic change in oscillation frequency at $Pr = 0.55 \pm0.15$ and
$A <2$.
