6,060 research outputs found
Energy Spectrum of Quasi-Geostrophic Turbulence
We consider the energy spectrum of a quasi-geostrophic model of forced,
rotating turbulent flow. We provide a rigorous a priori bound E(k) <= Ck^{-2}
valid for wave numbers that are smaller than a wave number associated to the
forcing injection scale. This upper bound separates this spectrum from the
Kolmogorov-Kraichnan k^{-{5/3}} energy spectrum that is expected in a
two-dimensional Navier-Stokes inverse cascade. Our bound provides theoretical
support for the k^{-2} spectrum observed in recent experiments
Algebraic constructions in the category of vector bundles
The category of generalized Lie algebroids is presented. We obtain an
exterior differential calculus for generalized Lie algebroids. In particular,
we obtain similar results with the classical and modern results for Lie
algebroids. So, a new result of Maurer-Cartan type is presented. Supposing that
any vector subbundle of the pullback vector bundle of a generalized Lie
algebroid is called interior differential system (IDS) for that generalized Lie
algebroid, a theorem of Cartan type is obtained. Extending the classical notion
of exterior differential system (EDS) to generalized Lie algebroids, a theorem
of Cartan type is obtained. Using the theory of linear connections of Ehresmann
type presented in the paper [1], the identities of Cartan and Bianchi type are
presented.Comment: 29 page
Mechanical Systems in the Generalized Lie Algebroids Framework
\emph{Mechanical systems} called by use, \emph{mechanical}\emph{-systems, Lagrange mechanical}\emph{-systems} or \emph{Finsler mechanical}\emph{-systems} are presented. The canonical \emph{-}semi(spray) associated to a mechanical -system is obtained. New and important results are obtained in the particular
case of Lie algebroids. The Lagrange mechanical % -systems are
the spaces necessary to develop a new Lagrangian formalism. We obtain the
-semispray associated to a regular Lagrangian and external
force and we derive the equations of Euler-Lagrange type. So, a new
solution for the Weinstein's Problem in the general framework of generalized
Lie algebroids is presented.Comment: 43 pages International journal of Geometric Methods in Modern
Physics, 2013. arXiv admin note: substantial text overlap with
arXiv:1108.2844, arXiv:1007.1541, arXiv:1109.1242, arXiv:1101.0960,
arXiv:1108.505
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