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