Preliminary investigation of yaw stability in undulatory fish propulsion using stability derivatives

Fish are capable of maintaining a stable forward direction without yawing during long-distance movements. This long-term yaw stability has been investigated using static derivatives, revealing that undulatory locomotion is highly unstable. However, the present simulation of the perturbation development process shows that the yaw perturbation growth rate of the undulatory fish is an order of magnitude smaller than that of non-undulatory one. This study investigates the yaw stability of two-dimensional fish body undergoing the carangiform undulatory deformation by considering both the mean static and dynamic derivatives method. The results indicate that the yaw instability always occurs when the fish body is in undulatory propulsion or coasting model, and the undulation has stabilizing effect compared with the body straight in the uniform incoming flow. Analysis of the mean derivatives reveals that the stabilizing effect is due to the negative value of the dynamic derivative, which plays the role of damping, although the static derivative indicates that the yaw is unstable. Utilizing mean derivatives method can analyze qualitatively the linear stability at the equilibrium point, which cannot provide an assessment of overall stability.