Different-wavenumber cancellation in sheet swimming
= Different-wavenumber cancellation in sheet swimming
{title2=$U_2=\tfrac12(k_\perp^2b^2-k_\parallel^2a^2)$}
When longitudinal and transverse sheet waves share unit phase speed but have different wavenumbers $k_\parallel,k_\perp$, their second-order swimming coefficient is $(k_\perp^2b^2-k_\parallel^2a^2)/2$. Thus their leading propulsion cancels at $b/a=k_\parallel/k_\perp$. This statement concerns the small-amplitude leading order.