Abstract: 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.

Key words: C-start, turning, curvature model, self-propelled swimming, energetics