The forces exerted on a body moving through a fluid depend strongly on the local dynamic processes and structures generated by the body motion, such as flow separation, vortices, etc. A detailed and quantitative understanding of the effects of these processes and structures on the instantaneous overall force characteristics is of fundamental significance, and may improve our capabilities for flow analysis and control. In the present study, some unconventional force expressions based on ‘derivative-moment transformations’, which can have a rich variety of forms for the same flow field, are used to provide better insight into local dynamics. In particular, we apply jointly three alternative unconventional force expressions to analyse two numerical solutions of unsteady and viscous circular-cylinder flows. The results confirm the exactness of the expressions and, more importantly, provide a unified understanding of the specific influence on the force of each individual flow structure at its different evolution stages.

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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SUMMARYA numerical simulation is performed to investigate the ow induced by a sphere moving along the axis of a rotating cylindrical container ÿlled with the viscous uid. Three-dimensional incompressible Navier-Stokes equations are solved using a ÿnite element method. The objective of this study is to examine the feature of waves generated by the Coriolis force at moderate Rossby numbers and that to what extent the Taylor-Proudman theorem is valid for the viscous rotating ow at small Rossby number and large Reynolds number. Calculations have been undertaken at the Rossby numbers (Ro) of 1 and 0.02 and the Reynolds numbers (Re) of 200 and 500. When Ro = O(1), inertia waves are exhibited in the rotating ow past a sphere. The e ects of the Reynolds number and the ratio of the radius of the sphere and that of the rotating cylinder on the ow structure are examined. When Ro 1, as predicted by the Taylor-Proudman theorem for inviscid ow, the so-called 'Taylor column' is also generated in the viscous uid ow after an evolutionary course of vortical ow structures. The initial evolution and ÿnal formation of the 'Taylor column' are exhibited. According to the present calculation, it has been veriÿed that major theoretical statement about the rotating ow of the inviscid uid may still approximately predict the rotating ow structure of the viscous uid in a certain regime of the Reynolds number.