= Linear-drag boundary-current consistency
{title2=$\delta_S=r/\beta$}
If the dimensional <linear drag> acceleration is $-r\mathbf u$, then $r$ has units of inverse time and <Stommel boundary layer> balance $\beta v=-rv_x$ gives $\delta_S=r/\beta$. For returned <volume flux> $Q$ in depth $H$, the boundary speed is $Q/(H\delta_S)$ and <relative vorticity> is of order $Q/(H\delta_S^2)$. A gyre return varying along a distance $B$ has a generic nonlinear-to-planetary <vorticity> advection ratio $V_b/(\beta B\delta_S)$. Large relative vorticity alone does not force nonlinear advection: a perfectly parallel $v=v(x)$, $u=0$ has zero material relative-vorticity advection.
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