The zebrafish C-start occurs not only in the escape response (C-escape), but also in the non-escape response (C-turn). They have different deforming modes and durations, and put in distinct kinematics performances. With the same bending amplitude, C-turns achieve larger turning angles, while C-escapes have higher velocities. However, little is known about their hydrodynamic mechanisms and energetics features. We proposed two novel curvature models based on the deformation characteristics of C-turn and C-escape, respectively. An optimization algorithm was used to determine the model parameters according to experimental data. Through self-propelled numerical simulation, we found that the positive moment at stage 1 of C-turn was large and the negative moment at stage 2 was small. So C-turn achieved a large turning angle. However, C-escape had a large thrust at stage 2, which led to the negative moment increasing and the turning angle reducing. We also found that the duration had little effect on the turning angle, but had a significant influence on escape velocity and energy consumption. Therefore, in order to save energy the duration of C-turn is usually over 100 ms, and the duration of C-escape is near 50 ms in order to pursue high speed.
WANG Zhongwei
,
YU Yongliang
. Energetics comparison between zebrafish C-shaped turning and escape: self-propelled simulation with novel curvature models[J]. Journal of University of Chinese Academy of Sciences, 2019
, 36(4)
: 467
-480
.
DOI: 10.7523/j.issn.2095-6134.2019.04.005
[1] Domenici P, Blake R. The kinematics and performance of fish fast-start swimming[J]. Journal of Experimental Biology, 1997, 200(8):1165-1178.
[2] Triantafyllou M S. Survival hydrodynamics[J]. Journal of Fluid Mechanics, 2012, 698:1-4.
[3] Domenici P, Blake R W. The kinematics and performance of the escape response in the angelfish (Pterophyllum eimekei)[J]. Journal of Experimental Biology, 1991, 156(1):187-205.
[4] Harper D G, Blake R W. Fast-start performance of rainbow trout Salmo gairdneri and northern pike Esox lucius[J]. Journal of Experimental Biology, 1990, 150(1):321-342.
[5] Zhang B B, Yu Y L. Living body experimental study of dynamic characteristics of zebrafish C-start swimming[J]. Journal of Expermental Mechanics, 2014, 29(6):727-736(in Chinese).
[6] Hu W R, Yu Y L, Tong B G, et al. A numerical and analytical study on a tail-flapping model for fish fast C-start[J]. Acta Mechanica Sinica, 2004, 20(1):16-23.
[7] Jing J, Yin X Z, Lu X Y. Hydrodynamic analysis of C-start in crucian carp[J]. Journal of Bionic Engineering, 2004, 1(2):102-107.
[8] Jing J, Yin X Z, Lu X Y. Observation and hydrodynamic analysis of fast-start of yellow catfish (Pelteobagrus fulvidraco)[J]. Progress in Natural Science, 2005, 15(1):34-40.
[9] Tytell E D, Lauder G V. Hydrodynamics of the escape response in bluegill sunfish, Lepomis macrochirus[J]. Journal of Experimental Biology, 2008, 211(21):3359-3369.
[10] Witt W C, Wen L, Lauder G V. Hydrodynamics of C-start escape responses of fish as studied with simple physical models[J]. Integrative and comparative biology, 2015, 55(4):728-739.
[11] Liu G, Yu Y L, Tong B G. Flow control by means of a traveling curvature wave in fishlike escape responses[J]. Physical Review E, 2011, 84(5):56312.
[12] Gazzola M, Van Rees W M, Koumoutsakos P. C-start:optimal start of larval fish[J]. Journal of Fluid Mechanics, 2012, 698:5-18.
[13] Li G, Müller U K, Van Leeuwen J L, et al. Body dynamics and hydrodynamics of swimming fish larvae:a computational study[J]. Journal of Experimental Biology, 2012, 215(22):4015-4033.
[14] Li G, Müller U K, Van Leeuwen J L, et al. Escape trajectories are deflected when fish larvae intercept their own C-start wake[J]. Journal of The Royal Society Interface, 2014, 11(101):20140848.
[15] Borazjani I, Sotiropoulos F, Tytell E D, et al. Hydrodynamics of the bluegill sunfish C-start escape response:three-dimensional simulations and comparison with experimental data[J]. Journal of Experimental Biology, 2012, 215(4):671-684.
[16] Borazjani I. The functional role of caudal and anal/dorsal fins during the C-start of a bluegill sunfish[J]. Journal of Experimental Biology, 2013, 216(9):1658-1669.
[17] Song J L, Zhong Y, Luo H X, et al. Hydrodynamics of larval fish quick turning:a computational study[J/OL]. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science, (2017-12-01)[2018-03-05]. http://journals.sagepub.com/doi/10.1177/0954406217743271. DOI:10.1177/0954406217743271.
[18] Carling J, Williams T L, Bowtell G. Self-propelled anguilliform swimming:simultaneous solution of the two-dimensional Navier-Stokes equations and Newton's laws of motion[J]. Journal of experimental biology, 1998, 201(23):3143-3166.
[19] Kern S, Koumoutsakos P. Simulations of optimized anguilliform swimming[J]. Journal of Experimental Biology, 2006, 209(24):4841-4857.
[20] Xin Z Q, Wu C J. Numerical simulations and vorticity dynamics of self-propelled swimming of 3D bionic fish[J]. Science China:Physics, Mechanics & Astronomy, 2012, 55(2):272-283.
[21] Su Z S, Yu J Z, Tan M, et al. Implementing flexible and fast turning maneuvers of a multijoint robotic fish[J]. IEEE/ASME Transactions on Mechatronics, 2014, 19(1):329-338.
[22] Yang Y, Wu G H, Yu Y L, et al. Two-dimensional self-propelled fish motion in medium:an integrated method for deforming body dynamics and unsteady fluid dynamics[J]. Chinese Physics Letters, 2008, 25(2):597-600.
[23] Wang Z W, Yu Y L, Tong B G. An energetics analysis of fish self-propelled swimming[J]. Science China:Physics, Mechanics & Astronomy, 2018, 61(7):74721.
