Nonlinear transfer and spectral distribution of energy in $α$ turbulence

dc.creatorTran, Chuong V.
dc.date2004-03-03
dc.date.accessioned2026-07-07T05:35:23Z
dc.date.available2026-07-07T05:35:23Z
dc.descriptionTwo-dimensional turbulence governed by the so-called $α$ turbulence equations, which include the surface quasi-geostrophic equation ($α=1$), the Navier--Stokes system ($α=2$), and the governing equation for a shallow flow on a rotating domain driven by a uniform internal heating ($α=3$), is studied here in both the unbounded and doubly periodic domains. This family of equations conserves two inviscid invariants (energy and enstrophy in the Navier--Stokes case), the dynamics of which are believed to undergo a dual cascade. It is shown that an inverse cascade can exist in the absence of a direct cascade and that the latter is possible only when the inverse transfer rate of the inverse-cascading quantity approaches its own injection rate. Constraints on the spectral exponents in the wavenumber ranges lower and higher than the injection range are derived. For Navier--Stokes turbulence with moderate Reynolds numbers, the realization of an inverse energy cascade in the complete absence of a direct enstrophy cascade is confirmed by numerical simulations.
dc.description5 figures, 28 pages
dc.identifierhttps://arxiv.org/abs/nlin/0403002
dc.identifierhttp://arxiv.org/abs/nlin/0403002
dc.identifierdoi:10.1016/j.physd.2003.11.005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80680
dc.subjectChaotic Dynamics
dc.titleNonlinear transfer and spectral distribution of energy in $α$ turbulence
dc.typetext

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