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Multiresolution analysis for 2D turbulence. Part 2: A physical interpretation
- Discrete and Continuous Dynamical Systems B 2007
"... Abstract. Multiresolution methods like the wavelet packets or the cosine packets are more and more used in physical applications and in particular in two-dimensional turbulence. The theoretical bases of these decompositions have been introduced in the first part of this paper. The numerical results ..."
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Cited by 11 (1 self)
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Abstract. Multiresolution methods like the wavelet packets or the cosine packets are more and more used in physical applications and in particular in two-dimensional turbulence. The theoretical bases of these decompositions have been introduced in the first part of this paper. The numerical results have shown that the wavelet packets decomposition is well suited for studying this kind of problem: the visualization of the vorticity field is better, without any kind of artifacts contrary to the visualization with the cosine packets filtering. The current second part of the paper is devoted to the physical interpretation of the filtering process proposed in the first part. Only the wavelet packets decomposition is considered here since the cosine packets did not give an entire satisfaction. 1. Introduction. We have shown in the first part of this paper [6] that the wavelet packets filtering can be successfully used for analyzing two-dimensional turbulence. This technique allows to separate two kinds of structures, the solid rotations com-posed by the core of the vortices from the background mainly composed by vorticity
Is the subdominant part of the energy spectrum due to downscale energy cascade hidden in quasi-geostrophic turbulence?
, 2006
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Recent developments in understanding two-dimensional turbulence and the Nastrom-Gage spectrum
, 608
"... Two-dimensional turbulence appears to be a more formidable problem than three-dimensional turbulence despite the numerical advantage of working with one less dimension. In the present paper we review recent numerical investigations of the phenomenology of two-dimensional turbulence as well as recent ..."
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Cited by 4 (3 self)
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Two-dimensional turbulence appears to be a more formidable problem than three-dimensional turbulence despite the numerical advantage of working with one less dimension. In the present paper we review recent numerical investigations of the phenomenology of two-dimensional turbulence as well as recent theoretical breakthroughs by various leading researchers. We also review efforts to reconcile the observed energy spectrum of the atmosphere (the spectrum) with the predictions of two-dimensional turbulence and quasigeostrophic turbulence. PACS numbers: 42.68.Bz, 47.27.-i, 47.27.ek, 92.60.hk, 92.10.ak 1.
Remarks on the Frisch framework of hydrodynamic turbulence and the quasi-Lagrangian formulation
, 2008
"... In this paper, we revisit the claim that the Eulerian and quasi-Lagrangian same time correlation tensors are equal. This statement allows us to transform the results of an MSR quasi-Lagrangian statistical theory of hydrodynamic turbulence back to the Eulerian representation. We define a hierarchy of ..."
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Cited by 3 (3 self)
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In this paper, we revisit the claim that the Eulerian and quasi-Lagrangian same time correlation tensors are equal. This statement allows us to transform the results of an MSR quasi-Lagrangian statistical theory of hydrodynamic turbulence back to the Eulerian representation. We define a hierarchy of homogeneity symmetries between the local homogeneity of Frisch and global homogeneity. It is shown that both the elimination of the sweeping interactions and the derivation of the 4/5-law require a homogeneity assumption stronger than local homogeneity but weaker than global homogeneity. The quasi-Lagrangian transformation, on the other hand, requires an even stronger homogeneity assumption which is many-time rather than one-time but still weaker than many-time global homogeneity. We argue that it is possible to relax this stronger assumption and still preserve the conclusions derived from theoretical work based on the quasi-Lagrangian transformation.
On the elimination of the sweeping interactions from theories of hydrodynamic turbulence
, 2006
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The effect of asymmetric large-scale dissipation on energy and potential enstrophy injection in two-layer quasi-geostrophic turbulence
- UNDER CONSIDERATION FOR PUBLICATION IN J. FLUID MECH.
, 2011
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Under consideration for publication in J. Fluid Mech. 1 An Inequality between Fluxes of Energy and Enstrophy in 2D and QG Turbulence
, 2004
"... In systems governing two-dimensional turbulence, surface quasi-geostrophic turbulence, (more generally α-turbulence), two-layer quasi-geostrophic turbulence, etc., there often exist two conservative quadratic quantities, one “energy”-like and one “enstrophy”-like. In a finite inertial range there ar ..."
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In systems governing two-dimensional turbulence, surface quasi-geostrophic turbulence, (more generally α-turbulence), two-layer quasi-geostrophic turbulence, etc., there often exist two conservative quadratic quantities, one “energy”-like and one “enstrophy”-like. In a finite inertial range there are in general two spectral fluxes, one associated with each conserved quantity. The energy spectrum in general has a contribution from each of the fluxes, and our previous work showed that these two contributions to the energy spectrum can be linearly superimposed despite the highly nonlinear nature of the problem. Often, one of the fluxes is dominant and the energy spectrum then has the visual shape of the case with a single flux; the contribution from the subdominant flux is effectively hidden. The relative magnitudes of the spectral fluxes depend on the dissipative sinks in the system, and varies according to the physical/mathematical system under consideration. We derive an important inequality involving the “energy ” and enstrophy ” fluxes for each representative system. This result then allows us to determine the effective energy spectral shape in the general case of double cascades. 1.
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, 2006
"... A new proof on net upscale energy cascade in two-dimensional and quasi-geostrophic turbulence ..."
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A new proof on net upscale energy cascade in two-dimensional and quasi-geostrophic turbulence
unknown title
, 2006
"... On the elimination of the sweeping interactions from theories of hydrodynamic turbulence ..."
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On the elimination of the sweeping interactions from theories of hydrodynamic turbulence
