Hydrodynamics of a Flexible Soft-Rayed Caudal Fin

Hydrodynamic stress maps on the surface of a flexible fin-like foil

We determine the time dependence of pressure and shear stress distributions on the surface of a pitching and deforming hydrofoil from measurements of the three dimensional flow field. Period-averaged stress maps are obtained both in the presence and absence of steady flow around the foil. The velocity vector field is determined via volumetric three-component particle tracking velocimetry and subsequently inserted into the Navier-Stokes equation to calculate the total hydrodynamic stress tensor. In addition, we also present a careful error analysis of such measurements, showing that local evaluations of stress distributions are possible. The consistency of the force time-dependence is verified using a control volume analysis. The flapping foil used in the experiments is designed to allow comparison with a small trapezoidal fish fin, in terms of the scaling laws that govern the oscillatory flow regime. As a complementary approach, unsteady Euler-Bernoulli beam theory is employed to derive instantaneous transversal force distributions on the flexible hydrofoil from its deflection and the results are compared to the spatial distributions of hydrodynamic stresses obtained from the fluid velocity field.

In vivo quantification of mechanical properties of caudal fins in adult zebrafish

The caudal fins of adult zebrafish are supported by multiple bony rays that are laterally interconnected by soft interray tissue. Little is known about the fin's mechanical properties that influence bending in response to hydrodynamic forces during swimming. Here, we developed an experimental setup to measure the elastic properties of caudal fins in vivo by applying micro-Newton forces to obtain bending stiffness and a tensional modulus. We detected overall bending moments of 1.5×10⁻⁹–4×10⁻⁹ N m² along the proximal–distal axis of the appendage showing a non-monotonous pattern that was not due to the geometry of the fin itself. Surgical disruption of the interray tissues along the proximal–distal axis revealed no significant changes to the overall bending stiffness, which we confirmed by determining a tensional modulus of the interray tissue. Thus, the biophysical values suggest that the flexibility of the fin during its hydrodynamic performance predominantly relies on the mechanical properties of the rays.

Summary: The quantitative in vivo determination of the zebrafish caudal fin's main constituents (bony rays and interray tissue) shows that flexibility is dominated by the elastic properties of the bony rays, whereas the elastic properties of the interray tissue co-define the fin's complex 3D deformation during swimming and will also be needed as a crucial input for hydrodynamic simulations.

Optimal swimming strategies and behavioral plasticity of oceanic whitetip sharks

Animal behavior should optimize the difference between the energy they gain from prey and the energy they spend searching for prey. This is all the more critical for predators occupying the pelagic environment, as prey is sparse and patchily distributed. We theoretically derive two canonical swimming strategies for pelagic predators, that maximize their energy surplus while foraging. They predict that while searching, a pelagic predator should maintain small dive angles, swim at speeds near those that minimize the cost of transport, and maintain constant speed throughout the dive. Using biologging sensors, we show that oceanic whitetip shark (Carcharhinus longimanus) behavior matches these predictions. We estimate that daily energy requirements of an adult shark can be met by consuming approximately 1-1.5 kg of prey (1.5% body mass) per day; shark-borne video footage shows a shark encountering potential prey numbers exceeding that amount. Oceanic whitetip sharks showed incredible plasticity in their behavioral strategies, ranging from short low-energy bursts on descents, to high-speed vertical surface breaches from considerable depth. Oceanic whitetips live a life of energy speculation with minimization, very different to those of tunas and billfish.