Drag reduction by elastic reconfiguration of non-uniform beams in non-uniform flows

• We use self-similarity arguments to predict the scaling of drag with flow velocity.
• These findings extend to more general non-uniform systems.
• The Vogel exponent of actual systems should never change appreciably from −1.

Flexible systems bending in steady flows are known to experience a lesser drag compared to their rigid counterpart. Through a careful dimensional analysis, an analytical expression of the Vogel exponent quantifying this reduction of drag is derived for cantilever beams, within a framework based on spatial self-similar modelling of the flow and structural properties at the clamped edge of the structure. Numerical computations are performed on various situations, including systems involving more complex distributions of the flow or structural parameters. The scaling of drag versus flow velocity for large loadings is shown to be well predicted by fitting the system properties by simple power laws at the scale of the length on which significant bending occurs. Ultimately, the weak sensitivity of the Vogel exponent to the parameters of the system provides an explanation to the rather reduced scattering of the Vogel exponents around −1−1 observed on most natural systems in aquatic or aerial vegetation.