= Rotating-frame reduction of circular viscoelastic shear
{title2=$L_{\rm eff}=\begin{pmatrix}0&0\\v'-v/r&0\end{pmatrix}$}
For azimuthal velocity $v(r)e_\theta$, the <velocity gradient> in the rotating polar basis is $\begin{pmatrix}0&-v/r\\v'&0\end{pmatrix}$. The basis rotates along a particle at angular speed $v/r$. Accounting for that rotation in the <material derivative> replaces $L$ by $L-(v/r)\begin{pmatrix}0&-1\\1&0\end{pmatrix}$ in the <upper-convected derivative>. Its remaining shear rate is $v'-v/r$, so the local viscoelastic <normal-stress difference> follows the same constitutive algebra as <simple shear flow>.
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