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

Thermal instabilities in accretion disks II: Numerical Experiments for  the Goldreich-Schubert-Fricke Instability and the Convective Overstability in  disks around young stars