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For a Keplerian shearing sheet, the shear rate is $S=3\Omega /2$ and the shearing-sheet tidal potential isA uniform steady solution isThe Coriolis acceleration of this linear shear flow balances the radial tidal acceleration. The only nonzero background component of the viscous stress tensor that matters is $T_{xy}=-\nu ({\Sigma }_0){\Sigma }_{0}S$, which is spatially constant. Hence $\nabla \cdot \mathbf{T}=0$: a local uniform patch has no stress gradient or torque divergence to drive an accretion flow.

Let $D/Dt={\partial }_t-Sx{\partial }_y$ be the material derivative along the background linear shear flow ${\mathbf{u}}_0=-Sx{\mathbf{e}}_y$. Linearizing about constant $\Sigma$ givesThe coefficient $2\Omega -S$ includes the contribution $\mathbf{v}\cdot \nabla {\mathbf{u}}_0=-S{v}_x{\mathbf{e}}_y$ from perturbation advection of the background shear.