= Quasistatic gyrotactic balance with half-rate reorientation
{title2=$0=\frac{\mathbf e_z-p_z\mathbf p}{2B}+\frac12\boldsymbol\omega\times\mathbf p$}
This convention defines the <gyrotactic reorientation time> by an aligning rate $1/(2B)$. Multiplying the <torque> balance by $2B$ and perturbing about the upward direction gives $\mathbf p_\perp=B\boldsymbol\omega\times\mathbf e_z$. For an <incompressible flow>, its horizontal <divergence> is $-B\nabla^2w$, because $\nabla\times\boldsymbol\omega=-\nabla^2\mathbf u$. The parameter $B$ is half the reorientation parameter used in the convention with aligning rate $1/B$; writing the governing equation prevents a factor-of-two ambiguity.
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