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dc.contributor.authorBurgess, B. H.
dc.contributor.authorShepherd, T. G.
dc.date.accessioned2017-01-06T16:30:13Z
dc.date.available2017-01-06T16:30:13Z
dc.date.issued2013-06
dc.identifier.citationBurgess , B H & Shepherd , T G 2013 , ' Spectral non-locality, absolute equilibria and Kraichnan-Leith-Batchelor phenomenology in two-dimensional turbulent energy cascades ' , Journal of Fluid Mechanics , vol. 725 , pp. 332-371 . https://doi.org/10.1017/jfm.2013.192en
dc.identifier.issn0022-1120
dc.identifier.otherPURE: 248699890
dc.identifier.otherPURE UUID: a639a5d9-0f4c-4101-9e41-b87f7bcf205f
dc.identifier.otherWOS: 000319511200013
dc.identifier.otherScopus: 84880238483
dc.identifier.otherORCID: /0000-0001-9297-8003/work/54516625
dc.identifier.urihttp://hdl.handle.net/10023/10062
dc.description.abstractWe study the degree to which Kraichnan-Leith-Batchelor (KLB) phenomenology describes two-dimensional energy cascades in alpha turbulence, governed by δθ/δt + J(ψ, θ) = ν ∇2θ + f, where θ = (-Δ)α/2ψ is generalized vorticity, and ψ over bar (k)= k-α θ over bar (k) in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow (alpha = 1), regular two-dimensional flow (α = 2) and rotating shallow flow (α = 3), which is the isotropic limit of a mantle convection model. We re-examine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general α, and point out their limitations. Using an α-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Non-local triads contribute increasingly to the energy flux as α increases. More importantly, the energy cascade is downscale in the self-similar inertial range for 2.5 <α <10. At α = 2.5 and α = 10, the KLB spectra correspond, respectively, to enstrophy and energy equipartition, and the triad energy transfers and flux vanish identically. Eddy turnover time and strain rate arguments suggest the inverse energy cascade should obey KLB phenomenology and be self-similar for α <4. However, downscale energy flux in the EDQNM self-similar inertial range for α > 2.5 leads us to predict that any inverse cascade for α ≥ 2.5 will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for α ≥ 2.5 is significantly steeper than the KLB prediction, while for α <2.5 we obtain the KLB spectrum.
dc.format.extent40
dc.language.isoeng
dc.relation.ispartofJournal of Fluid Mechanicsen
dc.rights© 2013 Cambridge University Press. The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution-NonCommercial-ShareAlike licence <http://creativecommons.org/licenses/by-nc-sa/3.0/>. The written permission of Cambridge University Press must be obtained for commercial re-use.en
dc.subjectIsotropic turbulenceen
dc.subjectTurbulent flowsen
dc.subjectTurbulence theoryen
dc.subjectQC Physicsen
dc.subject.lccQCen
dc.titleSpectral non-locality, absolute equilibria and Kraichnan-Leith-Batchelor phenomenology in two-dimensional turbulent energy cascadesen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews.Applied Mathematicsen
dc.identifier.doihttps://doi.org/10.1017/jfm.2013.192
dc.description.statusPeer revieweden


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