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Number of degrees of freedom and energy spectrum of surface quasi-geostrophic turbulence

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Date
10/2011
Author
Tran, Chuong Van
Blackbourn, Luke Austen Kazimierz
Scott, Richard Kirkness
Keywords
Geostrophic turbulence
Quasi-geostrophic flows
QA Mathematics
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Abstract
We study both theoretically and numerically surface quasi-geostrophic turbulence regularized by the usual molecular viscosity, with an emphasis on a number of classical predictions. It is found that the system's number of degrees of freedom N, which is defined in terms of local Lyapunov exponents, scales as Re-3/2, where R e is the Reynolds number expressible in terms of the viscosity, energy dissipation rate and system's integral scale. For general power-law energy spectra k(-alpha), a comparison of N with the number of dynamically active Fourier modes, i.e. the modes within the energy inertial range, yields alpha = 5/3. This comparison further renders the scaling Re-1/2 for the exponential dissipation rate at the dissipation wavenumber. These results have been predicted on the basis of Kolmogorov's theory. Our approach thus recovers these classical predictions and is an analytic alternative to the traditional phenomenological method. The implications of the present findings are discussed in conjunction with related results in the literature. Support for the analytic results is provided through a series of direct numerical simulations.
Citation
Tran , C V , Blackbourn , L A K & Scott , R K 2011 , ' Number of degrees of freedom and energy spectrum of surface quasi-geostrophic turbulence ' , Journal of Fluid Mechanics , vol. 684 , pp. 427-440 . https://doi.org/10.1017/jfm.2011.310
Publication
Journal of Fluid Mechanics
Status
Peer reviewed
DOI
https://doi.org/10.1017/jfm.2011.310
ISSN
0022-1120
Type
Journal article
Rights
Copyright © Cambridge University Press 2011
Description
L.A.K.B. was supported by an EPSRC post-graduate studentship.
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/3377

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