How flexibility induces streamlining in a two-dimensional flow

Recent work in bio-fluid dynamics has studied the relation of fluid drag to flow speed for flexible organic structures, such as tree leaves, seaweed, and coral beds, and found a reduction in drag growth due to body reconfiguration with increasing flow speed. Our theoretical and experimental work isolates the role of elastic bending in this process. Using a flexible glass fiber wetted into a vertical soap-film flow, we identify a transition in flow speed beyond which fluid forces dominate the elastic response, and yield large deformations of the fiber that greatly reduce drag. We construct free-streamline models that couple fluid and elastic forces and solve them in an efficient numerical scheme. Shape self-similarity emerges, with a scaling set by the balance of forces in a small "tip region" about the flow's stagnation point. The result is a transition from the classical U² drag scaling of rigid bodies to a new U^4/3 drag law. We derive an asymptotic expansion for the fiber shape and flow, based on the length-scale of similarity. This analysis predicts that the fiber and wake are quasiparabolic at large velocities, and obtains the new drag law in terms of the drag on the tip region. Under variations of the model suggested by the experiment-the addition of flow tunnel walls, and a back pressure in the wake-the drag law persists, with a simple modification.