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The magnetorotational instability (MRI) is a shear instability and thus itssensitivity to the shear parameter $q = - d\ln\Omega/d\ln r $ is of interest toinvestigate. Motivated by astrophysical disks, most (but not all) previous MRIstudies have focused on the Keplerian value of $ q=1.5$. Using simulation with8 vertical density scale heights, we contribute to the subset of studiesaddressing the the effect of varying $q$ in stratified numerical simulations.We discuss why shearing boxes cannot easily be used to study $q>2$ and thusfocus on $q<2$. As per previous simulations, which were either unstratified orstratified with a smaller vertical domain, we find that the $q$ dependence ofstress for the stratified case is not linear, contrary to the Shakura-Sunyaevmodel. We find that the scaling agrees with \cite{1996MNRAS.281L..21A} whofound it to be proportional to the shear to vorticity ratio $q/(2-q)$. We alsofind however, that the shape of the magnetic and kinetic energy spectra arerelatively insensitive to $q$ and that the ratio of Maxwell stress to magneticenergy ratio also remains nearly independent of $q$. This is consistent with atheoretical argument in which the rate of amplification of the azimuthal fielddepends linearly on $q$ and the turbulent correlation time $\tau$ dependsinversely on $q$. As such, we measure the correlation time of the turbulenceand find that indeed it is inversely proportional to $q$.

Sensitivity of the Magnetorotational Instability to the shear parameter in stratified simulations