Self-propelled anguilliform swimming: Simultaneous solution of the two-dimensional Navier-Stokes equations and Newton's laws of motion

Anguilliform swimming has been investigated by using a computational model combining the dynamics of both the creature's movement and the two-dimensio nal fluid flow of the surrounding water. The model creature is self-propell ed; it follows a path determined by the forces acting upon it, as generated by its prescribed changing shape. The numerical solution has been obtained by applying coordinate transformations and then using finite difference me thods. Results are presented showing the flow around the creature as it acc elerates from rest in an enclosed tank. The kinematics and dynamics associa ted with the creature's centre of mass are also shown. For a particular set of body shape parameters, the final mean swimming speed is found to be 0.7 7 times the speed of the backward-travelling wave. The corresponding moveme nt amplitude envelope is shown. The magnitude of oscillation in the net for ward force has been shown to be approximately twice that in the lateral for ce. The importance of allowing for acceleration and deceleration of the cre ature's body (rather than imposing a constant swimming speed) has been demo nstrated. The calculations of rotational movement of the body and the assoc iated moment of forces about the centre of mass have also been included in the model. The important role of viscous forces along and around the creatu re's body and in the growth and dissolution of the vortex structures has be en illustrated.