  The flapping states of a flexible fiber fully coupled to a three-dimensional
turbulent flow are investigated via state-of-the-art numerical methods. Two
distinct flapping regimes are predicted by the phenomenological theory recently
proposed by Rosti et al. [Phys. Rev. Lett. 121, 044501, 2018]: the under-damped
regime, where the elasticity strongly affects the fiber dynamics, and the
over-damped regime, where the elastic effects are strongly inhibited. In both
cases we can identify a critical value of the bending rigidity of the fiber by
a resonance condition, which further provides a distinction between different
flapping behaviors, especially in the under-damped case. We validate the theory
by means of direct numerical simulations and find that, both for the
over-damped regime and for the under-damped one, fibers are effectively slaved
to the turbulent fluctuations and can therefore be used as a proxy to measure
various two-point statistics of turbulence. Finally, we show that this holds
true also in the case of a passive fiber, without any feedback force on the
fluid.
