Self-propelled anguilliform swimming: simultaneous solution of the two-dimensional navier–stokes equations and Newton’s laws of motion

ABSTRACT Anguilliform swimming has been investigated by using a computational model combining the dynamics of both the creature’s movement and the two-dimensional fluid flow of the surrounding water. The model creature is self-propelled; 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 methods. Results are presented showing the flow around the creature as it accelerates from rest in an enclosed tank. The kinematics and dynamics associated 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 0.77 times the speed of the backward-travelling wave. The corresponding movement amplitude envelope is shown. The magnitude of oscillation in the net forward force has been shown to be approximately twice that in the lateral force. The importance of allowing for acceleration and deceleration of the creature’s body (rather than imposing a constant swimming speed) has been demonstrated. The calculations of rotational movement of the body and the associated 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 creature’s body and in the growth and dissolution of the vortex structures has been illustrated.