Chris Leipold

 
Chris Leipold

University of New Hampshire

Mathematics


2015

Mentor: Dr. John Gibson, Department of Mathematics

Patterns in Chaos: Periodic Solutions to Turbulent Flow

Fluid flow is prominent in the physical world and many engineering models rely on an accurate representation of it. However, as seen in the current of the ocean or dust swirling in the wind, fluid can behave in a very complex way. This complexity is known as turbulence and has been the main hurdle in creating an accurate model for fluid flow. Historically turbulence was treated as a random, but more recently the notion of bridging the gap to dynamical systems theory has arose. The research proposed here aims to help connect the two by calculating solutions to turbulence, specifically in plane Coquette flow (PCF). By performing time-integrations of simulated PCF, good initial guesses for the Newton-Kyrlov-hookstep algorithm will be derived. Then using the same algorithm we will calculate equilibria, traveling wave, periodic, and most importantly and the least studied relative periodic solutions. The objective of this research is to build upon the library of turbulence solutions for future research in connecting turbulence and dynamical systems theory.

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