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A certain appeal to the alpha model for turbulence and related viscosity inaccretion disks was that one scales the Reynolds stresses simply on the thermalpressure, assuming that turbulence driven by a certain mechanism will attain acharacteristic Mach number in its velocity fluctuations. Besides the notionthat there are different mechanism driving turbulence and angular momentumtransport in a disk, we also find that within a single instability mechanism,here the Vertical Shear Instability, stresses do not linearly scale withthermal pressure. Here we demonstrate in numerical simulations the effect ofthe gas temperature gradient and the thermal relaxation time on the averagestresses generated in the non-linear stage of the instability. We find that thestresses scale with the square of the exponent of the radial temperatureprofile at least for a range of $d \log T /d \log R = [-0.5, -1]$, beyond whichthe pressure scale height varies too much over the simulation domain, toprovide clear results. Stresses are also dependent on thermal relaxation times,provided they are longer than $10^{-3}$ orbital periods. The strong dependenceof viscous transport of angular momentum on the local conditions in the disk(especially temperature, temperature gradient, and surface density/opticaldepth) challenges the ideas of viscosity leading to smooth densitydistributions, opening a route for structure (ring) formation and time variablemass accretion.

High Resolution Parameter Study of the Vertical Shear Instability II: Dependence on temperature gradient and cooling time