Sine-cosine cellular Euler flow ($\psi =\sin x\cos y,{\omega }_z=2\psi$)

With $u={\psi }_y$ and $v=-{\psi }_x$, this steady incompressible solution of the Euler equations has velocity $(-\sin x\sin y,-\cos x\cos y)$ and vorticity $2\psi$. Its pressure is $C+\rho (\cos 2x-\cos 2y)/4$. The Bernoulli function is $C_0-{\psi }^2$, so it is constant along streamlines but generally varies between them.