When a ¢sh swims in water, muscle contraction, controlled by the nervous system, interacts with the body tissues and the surrounding £uid to yield the observed movement pattern of the body. A continuous dynamic beam model describing the bending moment balance on the body for such an interaction during swimming has been established. In the model a linear visco-elastic assumption is made for the passive behaviour of internal tissues, skin and backbone, and the unsteady £uid force acting on the swimming body is calculated by the 3D waving plate theory. The body bending moment distribution due to the various components, in isolation and acting together, is analysed. The analysis is based on the saithe (Pollachius virens), a carangiform swimmer. The £uid reaction needs a bending moment of increasing amplitude towards the tail and nearstanding wave behaviour on the rear-half of the body. The inertial movement of the ¢sh results from a wave of bending moment with increasing amplitude along the body and a higher propagation speed than that of body bending. In particular, the £uid reaction, mainly designed for propulsion, can provide a considerable force to balance the local momentum change of the body and thereby reduce the power required from the muscle. The wave of passive visco-elastic bending moment, with an amplitude distribution peaking a little before the mid-point of the ¢sh, travels with a speed close to that of body bending. The calculated muscle bending moment from the whole dynamic system has a wave speed almost the same as that observed for electromyogram-onset and a starting instant close to that of muscle activation, suggesting a consistent matching between the muscle activation pattern and the dynamic response of the system in steady swimming. A faster wave of muscle activation, with a variable phase relation between the strain and activation cycle, appears to be designed to ¢t the £uid reaction and, to a lesser extent, the body inertia, and is limited by the passive internal tissues. Higher active stress is required from caudal muscle, as predicted from experimental studies on ¢sh muscle. In general, the active force development by muscle does not coincide with the propulsive force generation on the tail. The sti¡er backbone may play a role in transmitting force and deformation to maintain and adjust the movement of the body and tail in water.

The three-dimensional waving plate theory is developed to investigate the swimming performance of fish undulatory motion. In particular, the propulsive effectiveness is discussed. The unsteady potential flow over model rectangular and triangular flexible plates performing a motion which consists of a progressing wave with variable amplitudes is calculated by the vortex ring panel method. It is found that the undulatory motion can reduce three-dimensional effects. It is this important hydrodynamic phenomenon that may be one of the main reasons why such undulation is widely used as the swimming method by a large number of aquatic animals. When the span of the undulating plate is nearly unchanged and the wave amplitude is constant or increases slightly along the chord, and the wavelength is close to the body length, theoretical results show that the swimming performance is best and the flow around the plate has a quasi-two-dimensional property. This swimming method may be observed in many fishes, especially those with an anguilliform mode of propulsion. The modification of the anguilliform mode of propulsion to the carangiform mode is also discussed. It is confirmed that the pronounced necking of the body anterior to the tail, which acts to improve the propulsive performance, is a major morphological adaptation of fishes using the carangiform mode, in which the characteristic nature of flexural movement confined to the rear part of the body is that the amplitude of undulation increases posteriorly and no complete wavelength is at any time apparent.

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Scallop locomotion was investigated on the basis of an analysis of fluid forces acting on the body and the balance of the forces during swimming. A hydrodynamic model for unsteady jet propulsion was developed in which propulsion performance is characterized by three nondimensional parameters: the storage/discharge volume ratio, reduced clapping frequency, and reduced discharge frequency. Pulsed jet propulsion is designed to achieve high thrust, although not necessarily with low hydrodynamic propulsive efficiency, as was previously widely considered. Swimming in scallops is realized by orientating the body at a certain angle of attack and maintaining a minimum swimming speed to prevent sinking. The working frequency of the locomotor system is determined and adjusted by the swimming strategy (angle of attack, swimming speed, and trajectory angle). For Placopecten magellanicus, the optimum angle of attack is about 6° – 12°, at which swimming requires the lowest energy input (lowest frequency) and hydrodynamic behaviour is ideal (without severe separation and stall). To maintain level swimming, P. magellanicus, during almost all their life, must swim at 5 – 7 body lengths per second if postured at a 6° – 12° angle of attack. The estimated Froude efficiency decreases during growth from about 0.5 to 0.3 for level swimming and from about 0.4 to 0.2 for climbing at an angle of 25°. It is suggested that the heavy body and inferior hydrodynamic characteristics (low aspect ratio and imperfect planform shape) have prevented scallops from becoming good swimmers. These problems are enhanced as the animals grow.