Carangiform fish, like mackerel, saithe and bass, swim forward by rhythmically passing body waves from the head to the tail. In this paper, the undulating motions are decomposed into the travelling part and the standing part by complex orthogonal decomposition (COD), and the ratio between these two parts, i.e., the travelling index, is proposed to analyse the waveform of fish-like movements. To further study the relative influences of the waveform on swimming performance, a self-propelled model of carangiform fish is developed by the level set/immersed boundary (LS-IB) method, and the in-house code is tested by two cases of flow past a sphere and an oscillating cylinder, respectively. In this study, the travelling index is varied in ranges up to 50% larger or smaller than the biological data. The results show that carangiform fish seem to favour a fast and efficient swimming motion with a travelling index of around 0.6. Meanwhile, we study several numerical cases with different amplitude coefficients (0.5~1.1) and tail-beat frequency (2 Hz~5 Hz), and then compare their swimming performance with each other. We found that the forward speed is closely related to the travelling index and tail-beat frequency, while the swimming efficiency is increased with the tail-beat frequency and amplitude coefficient. These results are also consistent with biological observations, and they might provide beneficial guidance with respect to the future design of robotic fish.

A second order finite-difference numerical method is used to solve the Navier–Stokes equations of incompressible flow, in which the solid body with complex geometry is immersed into the fluid domain with orthogonal Cartesian meshes. To account for influences of the solid body, interactive forces are applied as boundary conditions at Cartesian grid nodes located in the exterior but in the immediate vicinity of the solid body. Fluid flow velocities in these nodes are reconstructed to track and control the deformation of the solid body, in which the local direction normal to the body surface is employed using the level-set function. The capabilities of this method are demonstrated by the application to fish swimming, and the computed behaviors of swimming fish agree well with experimental ones. The results elucidate that the ability of swimming fish to produce more thrust and high efficiency is closely related to the Reynolds number. The single reverse Kármán street tends to appear when both the Strouhal number and tail-beating frequency are small, otherwise the double-row reverse Kármán street appears. The algorithm can capture the geometry of a deformable solid body accurately, and performs well in simulating interactions between fluid flow and the deforming and moving body.

Biological evidence demonstrates that fish can tune their body stiffness to improve thrust and efficiency during swimming locomotion. However, the stiffness-tuning strategies that maximize swimming speed or efficiency are still unclear. In the present study, a musculo-skeletal model of anguilliform fish is developed to study the properties of variable stiffness, in which the planar serial-parallel mechanism is used to model the body structure. The calcium ion model is adopted to simulate muscular activities and generate muscle force. Further, the relations among the forward speed, the swimming efficiency, and Young’s modulus of the fish body are investigated. The results show that for certain body stiffness, the swimming speed and efficiency are increased with the tail-beat frequency until reaching the maximum value and then decreased. The peak speed and efficiency are also increased with the amplitude of muscle actuation. Anguilliform fish tend to vary their body stiffness to improve the swimming speed and efficiency at a high tail-beat frequency or small amplitude of muscle actuation. Furthermore, the midline motions of anguilliform fish are analyzed by the complex orthogonal decomposition (COD) method, and the discussions of fish motions associated with the variable body stiffness and the tail-beat frequency are also presented. Overall, the optimal swimming performance of anguilliform fish benefits from the matching relationships among the muscle actuation, the body stiffness, and the tail-beat frequency.

In nature, most fish undulate their body and/or caudal fin togenerate thrust and swim forward.

A novel numerical framework is developed for large-eddy simulation (LES) of interactions among air, water, and solid bodies. The motions of air and water are solved on a fixed block-structured mesh, with the air–water interface captured using the volume-of-fluid method. A new sub-grid scale stress model based on the vortex identifier is used to improve the robustness and efficiency of the simulation flows with air–water interface. The new framework is tested in the context of bow waves and Kelvin waves generated by a water-surface vehicle. Wave breaking at the bow of the vehicle is captured in LES. The LES results of wave geometry approaches the measurements progressively as the grid resolution is refined. The simulation results indicate that LES is a useful tool for studying wave dynamics of water-surface vehicles.