Breadcrumb
Periodic Orbits as a Basis for Fluid Turbulence
EPSRC
Principal Investigator: Rich Kerswell, FRS
Starts: May 2010
Ends: April 2013
Description
Turbulence remains one of the outstanding problems of classical physics. Ubiquitous in our every day lives, from weather patterns to a gushing 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 the governing equations which is prohibitively expensive, the standard approach is to parametrize away temporal variations or small scales in 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 some dynamical 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.