= Optimal transient amplification of a viscous shearing wave
{title2=$G_{\max}\sim(2\mathrm{Re}/e)^{2/3}$}
For the shearing-wave <energy> profile, stationary points satisfy $-2\mathrm{Re}\,T=(1+T^2)^2$. At large <Reynolds number>, the initial minimum is at $T_-\sim-(2\mathrm{Re})^{1/3}$ and the subsequent maximum is at $T_+\sim-1/(2\mathrm{Re})$. Their <energy> ratio is $G_{\max}\sim(2\mathrm{Re})^{2/3}e^{-2/3}$. The <Reynolds number> here uses $A$, half the background shear rate; using $2A$ instead changes the coefficient convention.
// Target: astrophysics.bigb
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