The good, the bad and the beautiful. Leonardo's studies of turbulence

Ugo Piomelli

Queen's College, Ontario, Canada

Aspects of fluid dynamics appear often in Leonardo da Vinci's notebooks: sketches of water flow, plans for flying machines, studies of bird flight.  He seemed fascinated by the eddying movement of water, and designed ingenious experiments to try and understand the causes of these complex motions.  He lacked the advanced mathematical tools required to study this subject properly, however, and his attempts to use geometrical reasoning for the analysis of fluid flows were unsuccessful. This limitation is reflected in many of the machines he designed, which we now know cannot work. His observational powers, however, allowed him to make some exceptionally perceptive remarks that foreshadow techniques used today, both in the experimental and the theoretical analysis of flow problems, observations illustrated by striking drawings and sketches.  In this talk, some of Leonardo's reflections on turbulence will be discussed, vis a vis the present understanding of this captivating but baffling subject, perhaps the last unsolved problem in classical physics.