Analysis of swimming three-dimensional waving plates

Abstract

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.

A continuous dynamic beam model for swimming fish

“…According to the 3D £exible plate model of ¢sh swimming (Cheng et al 1991), the total thrust due to pressure di¡erences on the plate, the hydrodynamic power to maintain the movement of the plate in water, and the lateral force can be derived, and their coe¤cients can be written as Figure 11. The time-courses of the onset and end of EMG activity on the left side of a swimming mackerel or saithe (Wardle & Videler 1993), and of the muscle bending moment (M m ) along the body length calculated by the present theory for saithe.…”

“…As in almost all studies of ¢sh hydrodynamics (Lighthill 1960(Lighthill , 1971(Lighthill , 1975Wu 1971a;Cheng et al 1991), we conceptually separate the production of thrust, by the essentially non-viscous reaction of the water to lateral movements of the body, from the countervailing drag generated by longitudinal inertia (mass Âacceleration), so if we can use the observed motions to calculate the thrust and longitudinal acceleration, we can infer the drag. However, in this paper we are concerned not with the overall thrust and drag but with the time-varying distribution of lateral forces along the body, because it is these that are generated by the bending of the body and that contribute to the distribution of bending moment.…”

“…Although the calculated thrust varies during`steady' swimming, from close to zero to about twice its mean value, the corresponding £uctuations in velocity have been estimated by , taking into account body inertia as well as drag, as only AE 2%, so we neglect them. We use the 3D waving plate theory of Cheng et al (1991), rather than Lighthill's elongated-body theory (1975), because, although it is as yet restricted to small amplitude displacement waves, it does not neglect the feedback from the vortex wake onto the ¢sh and appears to be more accurate in the sense that it requires less`recoil correction' (see ½ 3; Cheng et al 1991).…”

Mechanisms underlying rhythmic locomotion: body–fluid interaction in undulatory swimming

“…Classical works by Taylor (Taylor, 1952) and Lighthill (Lighthill, 1960;Lighthill, 1969;Lighthill, 1970;Lighthill, 1971) and their extensions (Cheng et al, 1991) provide analytical models of fluid forces acting on the body during undulatory swimming. The fluid forces were modeled as static functions of kinematic variables: velocity-dependent resistive force (Taylor, 1952) for low Reynolds number (Re) swimming or acceleration-dependent reactive force (Lighthill, 1960) for high Re swimming.…”

Thrust generation and wake structure of wiggling hydrofoil

“…The finding is supported by the experiments on oscillating foils [3][4][5] . However, such theoretical analyses made by Lighthill [1,2,6] , Wu [7] , Newman [8] , and Cheng et al [9] are limited to inviscid flows. In some recent experimental and numerical studies [10][11][12][13][14][15][16] , the propulsive efficiency is found to be related to the wiggling frequency and wavelength, and the vortex structure is related to the propulsive performance.…”