= Rapid-rotation mean gyrotactic orientation
{title2=$\langle\mathbf p\rangle=-2\mathbf e_1/(3B\Omega)$}
For rigid fluid rotation with <vorticity> $-2\Omega\mathbf e_2$, $B\Omega\gg1$, and $BD_R$ of order one, the normalized steady density is $f=(4\pi)^{-1}[1-2p_1/(B\Omega)]+O((B\Omega)^{-2})$. The result follows by acting with the rotation generator on $p_1$ and using $\int p_i p_jd\Omega=4\pi\delta_{ij}/3$. Reversing the imposed rotation reverses the mean horizontal swimming direction.
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