| EPSRC Reference: |
EP/H051295/1 |
| Title: |
Wave Turbulence in the Strongly Nonlinear Regime: Theory and Applications |
| Principal Investigator: |
Connaughton, Professor C |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Mathematics |
| Organisation: |
University of Warwick |
| Scheme: |
First Grant - Revised 2009 |
| Starts: |
01 May 2011 |
Ends: |
30 April 2013 |
Value (£): |
101,311
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| EPSRC Research Topic Classifications: |
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| EPSRC Industrial Sector Classifications: |
| Aerospace, Defence and Marine |
Energy |
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| Related Grants: |
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| Panel History: |
| Panel Date | Panel Name | Outcome |
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22 Apr 2010
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Process Environment & Sustainability Panel
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Announced
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Summary on Grant Application Form |
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Wave turbulence is a mathematical theory which aims to describe the average behaviour of wave fields containing large numbers of interacting waves such as might occur, for example, on the surface of the ocean on a windy day. Less obvious examples include the large scale planetary waves (Rossby waves) in our atmosphere which play an important role in generating the weather or the density waves (drift waves) which propagate in strongly magnetised plasmas and present a key engineering challenge in the design of future fusion reactors. An elegant mathematical theory exists which predicts the average behaviour of wave fields in the weakly nonlinear limit. In essence, this weakly nonlinear theory works by first determining the behaviour of a system of non-interacting (linear) waves, which is mathematically straightforward, and then analysing interacting (nonlinear) waves by treating the effect of the wave interactions as a small correction to the non-interacting case. In many applications, however, the interactions between waves are sufficiently strong that they cannot be treated as a small correction. This proposal aims, firstly, to extend the theory to allow cases with strong nonlinearity to be studied mathematically and, secondly, to determine the extent to which these new theoretical results are relevant to applications. There will be particular focus on the ocean wave and Rossby wave examples.The theoretical results will be obtained by exploiting the constraints imposed on the wave field by fundamental conservation laws, such as conservation of energy, which remain true even when wave interactions are strong. The established theory of hydrodynamic turbulence, for which nonlinearity is always strong, will provide some indication of how to develop the analogous theory for strong wave turbulence although there are essential differences. The most important difference is the existence of a weakly nonlinear limit for wave turbulence which has no analogue for classical turbulence and will provide, to some extent, a starting point for an analytical description of strong wave turbulence. Nevertheless, computer simulations will be necessary to complement the theoretical study. The application of the results to real wave problems will be guided by the establishment of new collaborations with interested researchers expert in atmospheric dynamics and wave forecasting.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.warwick.ac.uk |