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Swimming motions of rays that swim using undulation locomotion are not always symmetrical; there may be a phase difference between the left and right pectoral fins. However, few studies on the swimming of rays have mentioned left and right pectoral fin movements. Moreover, the effects of movements of the left and right pectoral fins on swimming have not been clarified. This paper describes a computational study of phase differences of pectoral fin movements in the swimming of rays with the validity of fluid analysis methods. The movement and shape of the ray were made based on previous biological research and pictures. An overset grid was used to reproduce the ray’s complex motions. The analysis was performed under four phase difference conditions: 0 $$T$$ T ($$T$$ T is the period), 0.25 $$T$$ T , 0.5 $$T$$ T , and 0.75 $$T$$ T . The results show that a phase difference between the left and right pectoral fin movements affects swimming stability and maneuverability but not propulsive efficiency. We suggest that the phase difference in pectoral fin movements is essential for the swimming of rays, and rays adjust the phase difference between the movement of the left and right pectoral fins to suit their purpose.

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