= Stress-driven stagnation-point boundary layer
{title2=$f'''+ff''+1-(f')^2=0$}
For a fluid occupying $z<0$, match an outer <stagnation point> flow $u=x,w=-z$ to a flat impermeable interface with dimensionless <shear stress> $\beta x$. With <boundary layer thickness> $\delta=\mathrm{Re}^{-1/2}$, <inner variable> $\zeta=z/\delta$ and $\gamma=\delta\beta$, the leading <boundary-layer equation> admits $u=xf'(\zeta)$ and $w=-\delta f(\zeta)$. <Incompressibility> is automatic, and tangential <momentum conservation> gives the displayed <ordinary differential equation>, with $f(0)=0$, $f''(0)=\gamma$ and $f'\to1$ at $\zeta\to-\infty$. The sign of this far-field endpoint is fixed by the fluid domain. This is a prescribed-<traction> interface; it does not impose a <no-slip boundary condition>.
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