# Hydrodynamics and Musculture Actuation of Fish during a Fast Start
## 1 Introduction  
The fast start of fish is a critical capability that significantly affects the consequences of hunting prey or escaping from predators [1]. The hydrodynamics of this process feature highly unsteady flows due to its short duration. For the teleost fish, the duration of a fast start is less than 30 ms, with maximum acceleration rates ranging from 22.7 to 39.5 ms\({}^{-2}\)[2]. This short process is divided into three stages, shown in Figure 1: the preparation stage, the propulsion stage, and the completion stage [3]. According to the curvature of the middle line, the fast start of fish can be classified as a C-start or an S-start, with most predatory fish using S-start and herbivorous fish generally using C-start to escape [4, 5]. The fast-start performance of larval fish has been studied, revealing the mechanism for achieving the stunning locomotive performance. Combining flow simulations and an evolutionary optimization algorithm, [PERSON] et al. found that the traveling distance of a fast start is proportional to the bending curvature [6]. [PERSON] et al. reconstructed a larval model with high-fidelity geometry and kinematics and simulated the hydrodynamics. This work not only confirmed the finding of [PERSON] et al., but also revealed that thrust is mainly produced in the posterior part of the body [7]. Following their study, [PERSON] et al. simulated the quick turning of larval fish, finding that the torque from the tail is the primary factor that contributes to the quick rotation [8]. Despite the difference in size, the flow around the larval and adult fish showed no qualitative differences [9]. As the flow around the adult fish is more dominated by inertial force, the fast-start movement of fish induces two types of forces: forces achieved by accelerating the adjacent fluid and lift forces contributing tothrust by the fins [9; 10]. Using digital particle imaging velocimetry (DPIV) technology, [PERSON] et al. measured the flow field evolution during the fast start of the bluegill sunfish [11]. The flow field was characterized by vortex pairs forming local jets that moved opposite to the body movement, which shows that the fast-start agility is directly related to the rapid generation of a vortex through body/tail flexing [12]. Using a geometric model and the kinematics of a fish body in the above experiment as input, the hydrodynamics during the fast-start process with three-dimensional numerical simulation showed details that could not be captured in the experiment: the wake structure of the fast start is a complex vortex structure composed of multiple vortex rings. [PERSON] et al. [13] used numerical simulation to study the hydrodynamics of a virtual swimming C-turn of a tuna-like fish body. The pressure distribution on the swimmer's body surface showed that the thrust is mainly generated by the lunate tail. The vortex ring generated in the propulsion stage is elongated under the backflip of the tail, forming a wide and strong jet, which makes the fish slide forward quickly after the rotation. Similar to cruising swimming, the fast start is powered by the muscles on both sides of the body. In cruising swimming, the torque signal or actuation of the muscle travels posteriorly, but faster than the bending wave of the body; this is called neuromechanical phase lag (NPL). In comparison, studies involving muscle activation and kinematics in the fast-start process show some differences. Although the backward-traveling wave exists during both the cruising and the fast start, the muscle strain during a fast start is much larger than that during cruising swimming and sprinting, resulting in a correspondingly larger torque [14; 15]. During cruising swimming, only the red muscle of the fish is activated, but both the red and white muscles function simultaneously during a fast start. Ignoring the initial brief potentials, the muscles in the concave side are activated in stage 1 and are then followed by another high-amplitude Electromyography (EMG) on the contralateral side [16].