= Linear planar flow with strain and rotation
{title2=$\psi=\epsilon xy-\frac{\gamma}{2}(x^2+y^2)$}
The incompressible linear flow $(u,v)=(\epsilon x-\gamma y,\gamma x-\epsilon y)$ has <streamfunction> $\psi=\epsilon xy-\gamma(x^2+y^2)/2$. Its velocity matrix squares to $(\epsilon^2-\gamma^2)I$. Thus strain-dominated flow has saddle trajectories, rotation-dominated flow has closed elliptical trajectories, and equal nonzero strain and rotation gives <simple shear flow> along parallel lines with a stationary line. Pure rotation is counterclockwise for positive $\gamma$.
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