Screened first-order transverse sheet flow
= Screened first-order transverse sheet flow
{title2=$\psi_1=f(y)\sin(x-t)$}
With $s=\sqrt{1+A^2}$, a dimensionless decaying first-order transverse sheet has $f=(s e^{-y}-e^{-sy})/(s-1)$, $f(0)=1$, $f'(0)=0$, and <pressure> $-s(s+1)e^{-y}\cos(x-t)$. The coincident-root limit is $(1+y)e^{-y}$, the ordinary <transverse mode of a Taylor swimming sheet>.