  The linear stability analysis of a stratified rotating fluid (see paper I)
showed that disks with a baroclinic stratification under the influence of
thermal relaxation will become unstable to thermal instabilities. One
instability is the Goldreich-Schubert-Fricke instability (GSF), which is the
local version of the Vertical Shear Instability (VSI) and the other is a
thermal overstability, the Convective Overstability (COS).
  In the present paper we reproduce the analytic predicted growth rates for
both instabilities in numerical experiments of small axisymmetric sections of
vertically isothermal disks with a radial temperature gradient, especially for
cooling times longer than the critical cooling time for VSI. In this cooling
time regime our simulations reveal the simultaneous and independent growth of
both modes: COS and GSF. We consistently observe that GSF modes exhibit a
faster growth rate compared to COS modes. Near the midplane, GSF modes
eventually stop growing, while COS modes continue to grow and ultimately
dominate the flow pattern.
  Away from the midplane, we find GSF modes to saturate, when bands of constant
angular momentum have formed. In these bands we observe the formation and
growth of eddies driven by the baroclinic term, further enhancing the velocity
perturbations. In geophysics this effect is known as horizontal convection or
sea-breeze instability. Three-dimensional simulations will have to show whether
similar effects will occur when axisymmetry is not enforced. Our local
simulations help to reveal the numerical resolution requirements to observe
thermal instabilities in global simulations of disks around young stars.
