= Mean boundary velocity determines Taylor-sheet swimming speed
A <Taylor expansion> of the <no-slip boundary condition> about the flat sheet makes the second-order mean tangential velocity $\langle u_2(0)\rangle=-\langle y_1\partial_yu_1(0)\rangle$. The mean mode of <Stokes flow> is linear in height when no pressure gradient is imposed. In an unbounded fluid, bounded velocity excludes mean shear; in a confined fluid, the <force-free> condition excludes it. The remaining mean velocity is uniform and equals the swimming speed in the sheet frame. Thus the leading speed can be found from the first-order field without solving the oscillatory second-order field.
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