= Sinusoidal cellular flow
{title2=$\psi_0=-\sin x\sin y$}
Using $\mathbf u=(-\psi_y,\psi_x)$, the displayed <stream function> gives $\mathbf u_0=(\sin x\cos y,-\cos x\sin y)$. Its <streamlines> are level sets of $\psi_0$. At $(n\pi,m\pi)$, the <Jacobian matrix> is $\operatorname{diag}((-1)^{n+m},-(-1)^{n+m})$, so the points are <saddle equilibria>. At $(\pi/2+n\pi,\pi/2+m\pi)$ the eigenvalues are $\pm i$, giving <center equilibria> surrounded by closed <streamlines>. The grid lines $x=n\pi$ and $y=m\pi$ form <heteroclinic orbits> between adjacent saddles; circulation alternates between cells.
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