Longitudinal mode of a Taylor swimming sheet
= Longitudinal mode of a Taylor swimming sheet
{title2=$\psi_1=-ka\,ye^{-ky}\cos(k(x-t))$}
= Longitudinal modes of a Taylor swimming sheet
{synonym}
For tangential displacement $\epsilon a\sin(k(x-t))$, the first-order decaying <streamfunction> is $-ka\,ye^{-ky}\cos(k(x-t))$. It obeys tangential material velocity $-ka\cos(k(x-t))$ and zero normal velocity on the reference boundary. Its second-order mean swimming coefficient is $-k^2a^2/2$.