Periodic Orbits as a Basis for Fluid Turbulence

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Turbulence remains one of the outstanding problems of classical physics. Ubiquitous in our every day lives, from weather patterns to agushing water tap, understanding and controlling turbulence continues to be a major international challenge for the scientific community. Despite decades of research we are still without a basic theory which has any proven predictive power. Beyond faithfully simulating thegoverning equations which is prohibitively expensive, the standard approach is to parametrize away temporal variations or small scalesin the flow field neither of which are consistent with the complicated interplay of temporal and spatial scales characterizing turbulence. This proposal seeks to investigate a new dynamical systems approach in which turbulent flows are allowed to select their own `basis functions' in the form of unstable periodic orbits (UPOs) embedded in the turbulence. Each UPO represents the `perfect' balance of somedynamical process which underpins the turbulent state. There are many issues surrounding the construction of a UPO expansion of turbulence which are now eminently addressable due to present-day computer power. This proposal is directed at answering these with the ultimate aim of assessing the practicality and predictive power of a UPO expansion for turbulence.