Abstract
This paper describes topological kinematics associated with the stirring by rods of a two-dimensional fluid. The main tool is theThurston-Nielsen (TN) theory which implies that depending on the stirring protocol the essential topological length of material lines grows either exponentially or linearly. We give an application to the growth of the gradient of a passively advected scalar, the Helmholtz-Kelvin Theorem then yields applications to Euler flows. The main theorem shows that there are periodic stirring protocols for which generic initial vorticity yields a solution to Euler's equations which is not periodic and further, the L∞ and L1-norms of the gradient of its vorticity grow exponentially in time.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
