Fishes regulate tail-beat kinematics to minimize speed-specific cost of transport

Energetic expenditure is an important factor in animal locomotion. Here we test the hypothesis that fishes control tail-beat kinematics to optimize energetic expenditure during undulatory swimming. We focus on two energetic indices used in swimming hydrodynamics, cost of transport and Froude efficiency. To rule out one index in favour of another, we use computational-fluid dynamics models to compare experimentally observed fish kinematics with predicted performance landscapes and identify energy-optimized kinematics for a carangiform swimmer, an anguilliform swimmer and larval fishes. By locating the areas in the predicted performance landscapes that are occupied by actual fishes, we found that fishes use combinations of tail-beat frequency and amplitude that minimize cost of transport. This energy-optimizing strategy also explains why fishes increase frequency rather than amplitude to swim faster, and why fishes swim within a narrow range of Strouhal numbers. By quantifying how undulatory-wave kinematics affect thrust, drag, and power, we explain why amplitude and frequency are not equivalent in speed control, and why Froude efficiency is not a reliable energetic indicator. These insights may inspire future research in aquatic organisms and bioinspired robotics using undulatory propulsion.

Global Satellite-Based Coastal Bathymetry from Waves

The seafloor—or bathymetry—of the world’s coastal waters remains largely unknown despite its primary importance to human activities and ecosystems. Here we present S2Shores (Satellite to Shores), the first sub-kilometer global atlas of coastal bathymetry based on depth inversion from wave kinematics captured by the Sentinel-2 constellation. The methodology reveals coastal seafloors up to a hundred meters in depth which allows covering most continental shelves and represents 4.9 million km2 along the world coastline. Although the vertical accuracy (RMSE 6–9 m) is currently coarser than that of traditional surveying techniques, S2Shores is of particular interest to countries that do not have the means to carry out in situ surveys and to unexplored regions such as polar areas. S2Shores is a major step forward in mitigating the effects of global changes on coastal communities and ecosystems by providing scientists, engineers, and policy makers with new science-based decision tools.

Similarity and Froude Number Similitude in Kinematic and Hydrodynamic Features of Solitary Waves over Horizontal Bed

This study presents, experimentally, similarity and Froude number similitude (FNS) in the dimensionless features of two solitary waves propagating over a horizontal bed, using two wave gauges and a high-speed particle image velocimetry (HSPIV). The two waves have distinct wave heights H0 (2.9 and 5.8 cm) and still water depths h0 (8.0 and 16.0 cm) but identical H0/h0 (0.363). Together with the geometric features of free surface elevation and wavelength, the kinematic characteristics of horizontal and vertical velocities, as well as wave celerity, are elucidated. Illustration of the hydrodynamic features of local and convective accelerations are also made in this study. Both similarity and FNS hold true for the dimensionless free surface elevation (FSE), wavelength and celerity, horizontal and vertical velocities, and local and convective accelerations in the horizontal and vertical directions. The similarities and FNSs indicate that gravity dominates and governs the wave kinematics and hydrodynamics.

AN EXPERIMENTAL STUDY OF A SOLITARY WAVE IMPACTING A VERTICAL SLENDER CYLINDER

Solitary waves can evolve into plunging breakers during shoaling, inducing high wave loads on coastal structures. Meanwhile, plunging waves propagate with rapid spatial-temporal variations both in wave geometry and wave kinematics, causing varying forces on structures for different breaking stages (Chan et al., 1995). Although there have been numerous experiments for wave forces on cylinders, to our knowledge no experiments have studied the forces at different breaking stages of a plunging solitary wave. Thus, in our study, experiments are conducted to investigate the force due to a plunging solitary wave impacting a circular cylinder as a function of the wave's phase. Due to these forces, as expected structural responses are induced (Paulsen et al., 2019); to eliminate the effect of the structural response, the equation of motion is proposed to facilitate extracting only the isolated hydrodynamic forces.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/P07Cdlnxe7s

Rational approximation of P-wave kinematics — Part 2: Orhorhombic media

Orthorhombic anisotropy is a modern standard for 3D seismic studies in complex geologic settings. Several seismic data processing methods and wave propagation modeling algorithms in orthorhombic media rely on phase-velocity, group-velocity, and traveltime approximations. The algebraic simplicity of an approximate equation is an important factor in these media because the governing equations are more complicated than transversely isotropic media. To approximate the P-wave kinematics in acoustic orthorhombic media, we have developed a new 3D general functional equation that has a simple rational form. Using the general form, we adopt two versions of rational approximations for the phase velocity, group velocity, and traveltime. The first version uses a simpler functional form and parameter definition within the orthorhombic symmetry planes. The second version is more accurate, using one parameter that is defined out of the symmetry planes. For the phase velocity, we obtain another approximation that is no longer rational but is still algebraically simple, exact for 3D transversely isotropic media, and it is exact within the symmetry planes of orthorhombic media. We find superior accuracy in our approximations compared with previous ones, using numerical studies on multiple moderately anisotropic orthorhombic models. We investigate the effect of the negative anellipticity parameters on the accuracy and find that, in models in which the error of the existing most accurate approximations exceeds 2%, the error of the new approximations remains below 0.2%. The adopted approximations are algebraically simpler and stably more accurate than existing approximations; therefore, they may be considered as attractive alternatives for the existing approximations in many practical applications. We extend the applicability of our approximations by using them to obtain the equations of group direction as a function of phase direction and vice versa, which are useful in wave propagation modeling methods.

Rational approximation of P-wave kinematics — Part 1: Transversely isotropic media

In seismic data processing and several wave propagation modeling algorithms, the phase velocity, group velocity, and traveltime equations are essential. To have these equations in explicit form, or to reduce algebraic complexity, approximation methods are used. For the approximation of P-wave kinematics in acoustic transversely isotropic media, we have developed a new flexible 2D functional equation in a continued fraction form. Using different orders of the continued fraction, we obtain different approximations for (1) phase velocity as a function of phase direction, (2) group velocity as a function of group direction, and (3) traveltime as a function of offset. Then, we use them in the approximation of the group direction as a function of phase direction, and phase direction as a function of group direction. The proposed approximations have a rational form, which is considered algebraically simple and computationally efficient. The used continued fraction form rapidly converges to exact kinematics. By introducing the optimal ray into our approximations and using it for parameter definition, the convergence becomes faster, so the accuracy of the existing most accurate approximations is available by the third order, and new most accurate approximations are obtained by the fourth order of the proposed general form. The error of the most accurate version of the proposed approximations is below 0.001% for moderate anisotropic models with an anellipticity parameter up to 0.3. This high accuracy is considered to be attractive in practical implementations that use the kinematic equations and their derivatives.