= One-third-power similarity of an indented channel boundary layer
{title2=$G'''+\frac23GG''-\frac13(G')^2=\frac23\bar p$}
For indentation $F=bx^{1/3}$, the common layer displacement is $H=bx^{1/3}/2$. The <boundary layer> <stream function> $\psi=x^{2/3}G(zx^{-1/3})$ gives <velocity> $U=x^{1/3}G'$ and <pressure> $P=\bar p x^{2/3}$. Substitution into the <Prandtl boundary-layer equation> yields the displayed equation, with $G(0)=G'(0)=0$ and $G'\sim6\eta+3b$. This is a conditional similarity construction: the constant $\bar p$ must permit a solution of the <boundary value problem>.
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