  Ray-finned fish are able to adapt the curvature of their fins through
musculature at the base of the fin. In this work we numerically investigate the
effects of such leading-edge curvature actuation on the hydrodynamic
performance of a heaving and pitching fin. We present a geometric and numerical
framework for constructing the shape of ray-membrane type fins with imposed
leading-edge curvatures, under the constraint of membrane inextensibility. This
algorithm is coupled with a 3D Navier-Stokes solver, enabling us to assess the
hydrodynamic performance of such fins. To determine the space of possible
shapes, we present a simple model for leading-edge curvature actuation through
two coefficients that determine chordwise and spanwise curvature, respectively.
We systematically vary these two parameters through regimes that mimic both
passive elastic deformations and active curvatures against the hydrodynamic
loading, and compute thrust and power coefficients, as well as hydrodynamic
efficiency. Our results demonstrate that both thrust and efficiency are
predominantly affected by chordwise curvature, with some small additional
benefits of spanwise curvature on efficiency. The main improvements in
performance are explained by the altered trailing-edge kinematics arising from
leading-edge curvature actuation, which can largely be reproduced by a rigid
fin whose trailing-edge kinematics follow that of the curving fin. Changes in
fin camber, for fixed trailing-edge kinematics, mostly benefit efficiency.
Based on our results, we discuss the use of leading-edge curvature actuation as
a robust and versatile way to improve flapping fin performance.
