= Transverse mode of a Taylor swimming sheet
{title2=$\psi_1=b(1+ky)e^{-ky}\sin(k(x-t))$}
= Transverse modes of a Taylor swimming sheet
{synonym}
For normal displacement $\epsilon b\sin(k(x-t))$, the first-order decaying <streamfunction> is $b(1+ky)e^{-ky}\sin(k(x-t))$. It obeys zero tangential material velocity and normal velocity $-kb\cos(k(x-t))$ on the reference boundary. Its second-order mean swimming coefficient in the convention of far-field velocity $U\mathbf e_x$ is $k^2b^2/2$.
Back to article page
