Periodic Orbits as a Basis for Fluid Turbulence
Lead Research Organisation:
University of Bristol
Department Name: Mathematics
Abstract
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.
Organisations
People |
ORCID iD |
Richard Kerswell (Principal Investigator) |
Publications
Chandler G
(2013)
Invariant recurrent solutions embedded in a turbulent two-dimensional Kolmogorov flow
in Journal of Fluid Mechanics
Lucas D
(2014)
Spatiotemporal dynamics in two-dimensional Kolmogorov flow over large domains
in Journal of Fluid Mechanics
Lucas D
(2017)
Layer formation in horizontally forced stratified turbulence: connecting exact coherent structures to linear instabilities
in Journal of Fluid Mechanics
Lucas D
(2015)
Recurrent flow analysis in spatiotemporally chaotic 2-dimensional Kolmogorov flow
in Physics of Fluids
Lucas D
(2017)
Sustaining processes from recurrent flows in body-forced turbulence
in Journal of Fluid Mechanics
Description | We tested and confirmed that a novel technique to extract exact simple solutions to the Navier-Stokes equations from direct numerical simulations of turbulent flows works. An alphabet of such solutions was found and then an attempt was made to a posteriori predict some statistical properties of the turbulence. This worked reasonably but not compellingly well. The next challenge is to devise a more systematic search for these simple solutions (which are the periodic orbits of the grant title) and a better way to weight them in any expansion of the turbulence. This is under investigation. |
Exploitation Route | People can see this approach works in some sense but can also see the shortcomings. The challenges are now clear to make further progress |
Sectors | Aerospace, Defence and Marine,Energy |