On Lighthill's elongated-body theory

In 1971, Lighthill published a paper entitled "Large-amplitude elongated-body theory of fish locomotion". In this paper, he derived a potential flow theory for the undulatory locomotion of an elongated swimmer. He showed, in particular, that the average thrust force due to the undulatory motion only depends on the kinematics of the tail. To this day, it has been the only theory for undulatory locomotion derived from first principles.

During this talk, we will revisit Lighthill's elongated-body theory. We will show in particular how it can be used to derive the time-dependent force along the backbone at any instant. We will also show the potential flow associated with this theory and compare it with numerical simulations.