= Slip-enhanced swimming speed of a transverse sheet
{title2=$U^*=\tfrac12\epsilon^2(1+2\delta)+O(\epsilon^4)$}
At second order, the displaced-boundary <Navier slip boundary condition> gives $(\psi_2)_Y-\delta[(\psi_2)_{YY}-(\psi_2)_{XX}]=(1+2\delta)\sin^2(X-\tau)$ at $Y=0$. Its mean shear is zero in a bounded half-space flow, so the <Navier-slip Taylor swimming sheet> dimensionless speed is $U^*=\epsilon^2(1+2\delta)/2+O(\epsilon^4)$. The sheet travels opposite to the wave. This fixed-slip <asymptotic expansion> predicts a speed enhancement factor $1+2\delta$.
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