= Lighthill elongated-body theory
{c}
= Elongated-body theory
{synonym}
In the small-amplitude <slender-body theory> approximation, an undulating swimmer accelerates an <added mass> of fluid per unit length $m(x)$. With $\mathcal D=\partial_t+U\partial_x$ and transverse displacement $h$, the lateral <force> on the body is $-\mathcal D(m\mathcal Dh)$. Its reaction on the fluid has the opposite sign. For a periodic stroke and the usual negligible leading-edge added-mass contribution, the mean trailing-edge thrust is $m\langle h_t^2-U^2h_x^2\rangle/2$. This is a reactive inertial model, distinct from viscous <resistive-force theory>.
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