3.3 Friday, Jan. 4 On the interpretation of swimming as a limit cycle JACOBS, H.O.; Imperial College London firstname.lastname@example.org
When the wind blows through the venetian blinds in your house, it is not uncommon for them to flutter. The next time this happens, note two things. Firstly, the fluttering is really the sound of a periodic oscillation at a fixed frequency. Secondly, if you hold one of the blinds between your fingers and then releases it, the fluttering will stop and then restore itself. This stable oscillatory behavior is known by mathematicians as a limit cycle. Given the complex dynamics which are possible in fluids, it is remarkable that fish, frogs, tadpoles, and humans can obtain regular motion in a given direction by periodically flexing muscles. Perhaps motion in a fixed direction is stable under the influence of a periodic force. In other words, perhaps swimming is a limit cycle. The stability of a limit cycle implies that locomotion in a fixed direction can be achieved by exploiting passive physical dynamics and relatively simple motor patterns. In this talk I will provide a sketch of the physics and mathematical proofs which suggest this to be the case for neutrally buoyant bodies of arbitrary shape immersed in a Newtonian fluid in the middle Reynolds number regime (Re ~ 100 to 10,000). The theory should be of interest to those wishing to understand and mimic the orderliness of swimming in this regime or understand the robustness of fluid locomotion across body type and size.