Sine-cosine cellular Euler flow
= Sine-cosine cellular Euler flow
{c}
{title2=$\psi=\sin x\cos y,\quad\omega_z=2\psi$}
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 $C+\rho(\cos2x-\cos2y)/4$. The Bernoulli function is $C_0-\psi^2$, so it is constant along streamlines but generally varies between them.