Edward Redfern
School of Computing and Mathematics
Order from disorder : Chaos , turbulence and recurrent flow
Turbulent fluid phenomena are ubiquitous in nature ; from complex weather systems to pipe flow . Understanding the behaviour of these events has captured the minds of scientists for hundreds of years . We search for a way to reduce the complexity of a turbulent flow by building a skeleton of simple unstable solutions which mimic the characteristics of the full flow . To find the bones of this skeleton we search for periodic behaviour in the system by comparing the flow at different times using a numerical simulation . We then converge these near repeats using a type of Newton- Raphson method . This method requires large computational power and does not always converge to a periodic flow . In order to find away to improve this , we consider using the angle between repeating trajectories ; close and parallel trajectories are necessary for periodic behaviour . We verify the method with a known periodic flow .
Postgraduate Conference 2020 Page 36