examined the effects of using different motions for the left and right pectoral fins and reversing the direction of wave propagation on swimming and showed that they improved turning ability 12. ![]() It has been suggested that the different movements of the left and right pectoral fins affect turning and maneuverability in swimming rays. acutirostra undulates their pectoral fins from front to back (rajiform). In KAIYUKAN, which is one of the biggest aquaria in Japan, pitted stingray Dasyatis matsubarai and sharpnose stingray Dasyatis acutirostra swim with a phase difference between the left and right pectoral fins movements (Supplement Movies 1, 2). In addition, it has been shown that motions vary depending on the species and the depth at which they live 11. It was also clarified that the propulsive efficiency is improved by using the ground effect in both oscillation and undulation 7, 8, 9, 10. The relationship between the aspect ratio of the pectoral fin and swimming performance was investigated, and it was found that thrust and propulsive efficiency increased as the aspect ratio of the pectoral fin increased 6. In a simple model analysis, the ratio of the two methods of thrust generation (added mass and circulation) was examined, and it was found that the ratio of thrust generation by circulation was higher 5. The relationship between swimming speed and the motion of skates was investigated, and it was found that the swimming speed increased as the amplitude and wave number increased 4. The freshwater stingray Potamotrygon orbignyi's swimming behavior was investigated and revealed that a leading-edge vortex highly affects swimming efficiency 3. Previous studies have clarified the swimming methods and mechanisms of undulate rays. Studies on both swimming modes of rays have traditionally been conducted to understand the ecology of rays and apply engineering applications. The ray's motion is divided into two movements: (1) mobuliform oscillation, underwater flapping flight, and (2) rajiform undulation, pectoral fins undulate from anterior to posterior along with pectoral fins 2. Rays use a unique swimming method called the median and paired fin (MPF) mode, while most fishes use the body and/or caudal fin (BCF) mode 1. ![]() 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. The results show that a phase difference between the left and right pectoral fin movements affects swimming stability and maneuverability but not propulsive efficiency. The analysis was performed under four phase difference conditions: 0 \(T\) ( \(T\) is the period), 0.25 \(T\), 0.5 \(T\), and 0.75 \(T\). An overset grid was used to reproduce the ray’s complex motions. ![]() The movement and shape of the ray were made based on previous biological research and pictures. 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. ![]() Moreover, the effects of movements of the left and right pectoral fins on swimming have not been clarified. However, few studies on the swimming of rays have mentioned left and right pectoral fin movements. 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.
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