= Taylor swimming sheet
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= Taylor's swimming sheet
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The Taylor swimming sheet is an infinite two-dimensional <microswimmer> whose prescribed traveling deformation drives <Stokes flow>. A transverse wave $y_s=\epsilon\sin(x-t)$ of small amplitude swims opposite to its direction of propagation, with speed $U=\epsilon^2/2+O(\epsilon^4)$ when lengths are scaled by inverse wavenumber and velocities by wave speed. Its <biharmonic stream function for planar Stokes flow> has first-order part $\psi_1=(1+y)e^{-y}\sin(x-t)$.
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