Larger wavelengths suit hydrodynamics of carangiform swimmers

The wavelength of undulatory kinematics of fish is an important parameter to determine their hydrodynamic performance. This study focuses on numerical examination of this feature by reconstructing the real physiological model and kinematics of steadily swimming Jack Fish. We perform three-dimensional numerical simulations for flows over these models composed of the trunk, and dorsal, anal, and caudal fins. Moreover, we prescribe the carangiform-like motion for its undulation for a range of wavelengths. Undulation with larger wavelengths improves the hydrodynamic performance of the carangiform swimmer in terms of better thrust production by the caudal fin, lower drag production on the trunk, and reduced power consumption by the trunk. This coincides with the formation of stronger posterior body vortices and leading-edge vortices with more circulation on the caudal fin. The real kinematics of Jack Fish surpasses the performance of those with prescribed motion owing to the flexibility of the caudal fin.

Figure 1

(a) Virtual tunnel for simulating flows over Jack Fish with its dimensions and (b) the physiological model of Jack Fish covered with a mesh to indicate marker points to track their motion.

Figure 2

Comparison of the real and prescribed kinematics (${\lambda }^{★}=1.05$ and $\varphi =-5.5^{\circ }$) through temporal histories of displacements for four distinct points on the trunk and dorsal, anal, and caudal fins.

Figure 3

Comparison of the real and prescribed (${\lambda }^{★}=1.05$) motion of Jack Fish (with models in dark and light colors, respectively) at two time instants.

Figure 4

Time-averaged thrust coefficient ($\overline{C_T}$) for an undulating foil as the function of Strouhal number for (a) $\text{Re}=100$, (b) 1000, and (c) 5000 [34].

Figure 5

(a) Thrust coefficient of the caudal fin, (b) drag coefficient of the trunk, and (c) drag coefficient of the anal and dorsal fins, where each cycle-averaged coefficient is normalized by its respective value for the real fish kinematics.

Figure 6

Cycle-averaged power coefficient of (a) the caudal fin, (b) trunk, and (c) anal and dorsal fins, where each coefficient is normalized by its respective value for the real fish kinematics.

Figure 7

(a) Hydrodynamic efficiency of the caudal fin of Jack Fish as a function of undulatory wavelength where $\eta$ is normalized by its value for the real fish kinematics and (b) temporal histories of $C_T$ of the caudal fin for the real and prescribed motion.

Figure 8

Top views of 3D vortex structures around Jack Fish undulating with ${\lambda }^{★}=$ (a) 0.80, (b) 1.05, (c) 1.25, and (d) real kinematics where the coherent structures are identified by the isosurface of the $Q$-criterion. The isosurface $Q=5$ is in gray and $Q=30$ is in green. Two-dimensional blue and red vortices, with negative and positive vorticity, respectively, are also shown on the midplane of these flow fields.

Figure 9

Vortex topology around Jack Fish for originally recorded kinematics, where coherent structures are colored by the isosurface of the $Q$-criterion. The isosurface $Q=5$ is in light-gray color, whereas inner vortex cores with $Q=30$ are colored by the nondimensional $x$-component of vorticity (${\omega }_x$).

Figure 10

Vortex dynamics in the vicinity of the caudal fin of Jack Fish undulating with the prescribed motion at ${\lambda }^{★}=0.80$, 1.05, 1.25, and the real kinematics in the first, second, third, and fourth columns, respectively, and the top and bottom rows show flow states at their respective beginning of rightwards stroke and in its middle stage, respectively. Here wake structures are colored by the isosurface of the $Q$-criterion. The isosurface $Q=5$ is in gray and $Q=30$ is in blue. The latter highlights the vortex core.

Figure 11

Vortex dynamics with contours of ${\omega }_x^{★}={\omega }_{x}L/U_{\infty }$ in a vertical plane located at $0.90L$ on the caudal fin of Jack Fish undulating with the prescribed motion at ${\lambda }^{★}=0.80$, 1.05, 1.25, and the real kinematics in the first, second, third, and fourth columns, respectively.

Figure 12

Circulation of $\text{LEVs}$ that remain attached with the caudal fin throughout its rightward flapping stroke.

Figure 13

Vortex dynamics with contours of ${\omega }_y^{★}={\omega }_{y}L/U_{\infty }$ in a lateral plane located on the dorsal side of Jack Fish undulating with the prescribed motion at ${\lambda }^{★}=0.80$, 1.05, 1.25, and the real kinematics in the first, second, third, and fourth columns, respectively.