Marston, JB, Chini, GP and Tobias, SM (2016) Generalized Quasilinear Approximation: Application to Zonal Jets. Physical Review Letters, 116 (21). 214501. ISSN 0031-9007
Abstract
Quasilinear theory is often utilized to approximate the dynamics of fluids exhibiting significant interactions between mean flows and eddies. We present a generalization of quasilinear theory to include dynamic mode interactions on the large scales. This generalized quasilinear (GQL) approximation is achieved by separating the state variables into large and small zonal scales via a spectral filter rather than by a decomposition into a formal mean and fluctuations. Nonlinear interactions involving only small zonal scales are then removed. The approximation is conservative and allows for scattering of energy between small-scale modes via the large scale (through nonlocal spectral interactions). We evaluate GQL for the paradigmatic problems of the driving of large-scale jets on a spherical surface and on the beta plane and show that it is accurate even for a small number of large-scale modes. As GQL is formally linear in the small zonal scales, it allows for the closure of the system and can be utilized in direct statistical simulation schemes that have proved an attractive alternative to direct numerical simulation for many geophysical and astrophysical problems.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 American Physical Society. This is an author produced version of a paper published in Physical Review Letters. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 12 May 2016 15:49 |
Last Modified: | 13 Mar 2020 13:23 |
Published Version: | https://dx.doi.org/10.1103/PhysRevLett.116.214501 |
Status: | Published |
Publisher: | American Physical Society |
Identification Number: | 10.1103/PhysRevLett.116.214501 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:99466 |