The dependence of propulsive performance on the slip number in an undulatory swimming fish

•A detouring proto-vortex shed around the fish tail produces a low-pressure kernel.•A low-pressure kernel leads to an increase in form drag of a swimming fish.•A low-pressure kernel is able to cause a decrease in swimming power of a fish.

To investigate the dependence of propulsive performance on the slip number (signifying the ratio of swimming velocity to the phase velocity of body wave undulation) in an undulatory swimming fish, we performed two-dimensional numerical simulations for a fish swimming at various slip numbers, addressing the hydrodynamic correlation between slip number and propulsive performance. The amounts of power consumption evaluated from the numerical simulation increases for a decreasing slip number. The simulated flow fields reveal that vortex shedding has a substantial impact on the force and power consumption of a fish swimming at various slip numbers. A detouring proto-vortex shed around the fish tail produces a low- pressure kernel that beneficially results in decreased power consumption but also detrimentally causes an increased anterior–posterior pressure drag. A decreased slip number strengthens the effect of the low-pressure kernel, consequently causing an increased power consumption.