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In undulatory swimming of fish, muscles contract sequentially along the body to generate a bending wave that pushes against the water and produces thrust. Here, we use a 3D computational fluid dynamics model coupled to the motion of the fish with prescribed deformation to study the basic mechanical quantities along the fish's body: force, torque, and power. We find that forces on the bodies of both the anguilliform swimmer and the carangiform swimmer are dominated by reactive forces; furthermore, the force on the caudal fin of the carangiform swimmer is dominated by drag-like forces. The torque exhibits a wave pattern that travels faster than the curvature wave in both the anguilliform and carangiform swimmers, but the wave speed is even higher for the carangiform swimmer. The power output for the anguilliform swimmer is concentrated on the anterior half of the body and is significantly negative on the posterior side of the body. In contrast, most of the power is generated by the posterior part of the body before the peduncle for the carangiform swimmer. The results explain the differences in the observed electromyography patterns in fish with different swimming modes and explain the tendon function in carangiform swimmers.

In undulatory locomotion, torques along the body are required to overcome external forces from the environment and bend the body. Using a resistive force theory model, we find that the torque from external resistive forces has a traveling wave pattern with decreasing speed as the wave number (the number of wavelengths on the locomotor's body) increases from 0.5 to 1.8, and the torque transitions into a two-wave-like pattern and complex patterns as the wave number increases to values of 2 and greater values. Using phasor diagrams analysis, we reveal the formation and transitions of the pattern as the consequences of the integration and cancellation of force phasors.