Forced 2D Turbulence: Experimental Evidence of Simultaneous Inverse Energy and Forward Enstrophy Cascades

Rutgers, M. A.

doi:10.1103/physrevlett.81.2244

Cited by 174 publications

(158 citation statements)

References 17 publications

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“…Several of these studies have been reported in the literature. [8][9][10] Besides the experiments on soap films, it is also possible to study Q2D flows in a thin layer of fluid inside a container, for example, the experiments on vortex interactions performed by Antonova et al 11 and the experiments on freely decaying Q2D turbulence by Tabeling et al 12 In the latter experiment, but also in several other studies of this type, the flow is forced electromagnetically. Other examples are the experiments on the interaction of allocated vortices performed by Danilov et al 13 and the experimental study of Q2D shear flows by Dolzhan-skii et al 14,15 In the experimental studies on thin-layer flows of this type, usually a single layer of fluid is used.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional structure and decay properties of vortices in shallow fluid layers

et al. 2001

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Recently, several laboratory experiments on vortex dynamics and quasi-two-dimensional turbulence have been performed in thin (stratified) fluid layers. Commonly, it is tacitly assumed that vertical motions, giving rise to a three-dimensional character of the flow, are inhibited by the limited vertical dimension. However, shallow water flows, which are vertically bounded by a no-slip bottom and a free surface, necessarily possess a three-dimensional structure due to the shear in the vertical direction. This shear may lead to significant secondary circulations. In this paper, the three-dimensional (3D) structure and the decay properties of vortices in shallow layers of fluid, both homogeneous and stratified, have been studied in detail by 3D direct numerical simulations. The quasi-two-dimensionality of these flows is an important issue if one is interested in a comparison of experiments of this type with purely two-dimensional theoretical models. The influence of several flow parameters, like the depth of the fluid and the Reynolds number, has been investigated. In general, it can be concluded that the flow loses its two-dimensional character for larger fluid depth and larger Reynolds number. Furthermore, it is possible to construct a regime diagram that allows the assessment of the parameter regime, where the flow can be considered as quasi-two-dimensional. It is found that the presence of secondary circulations within a planar vortex flow results in a deformation of the radial profile of axial vorticity. In the limiting case of quasi-two-dimensional flow, the vorticity profiles can be scaled according to a simple diffusion model. In a two-layer stratified system, the decay is reduced and three-dimensional motions are significantly inhibited compared to the corresponding flows in a homogeneous layer.

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Section: Introductionmentioning

confidence: 99%

Three-dimensional structure and decay properties of vortices in shallow fluid layers

et al. 2001

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“…As concluded by Danilov & Gurarie 12 , the universal k −5/3 seems 'exceptional and unstable'. But all of these studies [6][7][8][9][10][11][12][13][14][15][16][17][18] suffer from at least one of the two following issues that have a strong influence on both cascades, which put in question the reliability of their results.…”

Section: Introductionmentioning

confidence: 99%

“…Since then, a substantial number of studies have been carried out to validate the Kraichnan-Batchelor theory by means of numerical simulations [6][7][8][9][10][11][12][13][14] and physical experiments [15][16][17][18] . While most of them have confirmed the Kraichnan-Batchelor theory, three numerical works found a deviation from the k −5/3 spectrum in the inverse energy cascade range where a steeper slope was measured: Borue 11 observed spectra as steep as k −3 while Smith & Yakhot 9 and Danilov & Gurarie 12 observed spectra of the form k −n with 2 < n < 2.3 and 2.2 < n < 2.5 respectively -even in special cases with no large-scale energy dissipation.…”

Section: Introductionmentioning

confidence: 99%

Vortical control of forced two-dimensional turbulence

2013

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A new numerical technique for the simulation of forced two-dimensional turbulence [D. Dritschel and J. Fontane, “The combined Lagrangian advection method,” J. Comput. Phys. 229, 5408–5417 (2010)10.1016/j.jcp.2010.03.048] is used to examine the validity of Kraichnan-Batchelor scaling laws at higher Reynolds number than previously accessible with classical pseudo-spectral methods, making use of large simulation ensembles to allow a detailed consideration of the inverse cascade in a quasi-steady state. Our results support the recent finding of Scott [R. Scott, “Nonrobustness of the two-dimensional turbulent inverse cascade,” Phys. Rev. E 75, 046301 (2007)10.1103/PhysRevE.75.046301], namely that when a direct enstrophy cascading range is well-represented numerically, a steeper energy spectrum proportional to k−2 is obtained in place of the classical k−5/3 prediction. It is further shown that this steep spectrum is associated with a faster growth of energy at large scales, scaling like t−1 rather than Kraichnan's prediction of t−3/2. The deviation from Kraichnan's theory is related to the emergence of a population of vortices that dominate the distribution of energy across scales, and whose number density and vorticity distribution with respect to vortex area are related to the shape of the enstrophy spectrum. An analytical model is proposed which closely matches the numerical spectra between the large scales and the forcing scale.

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“…in a variety of laboratory experiments (Couder [12], Kellay et al [13], Martin et al [14], Rutgers [15], Rivera et al [16], Vorobieff et al [17], Rivera et al [18] and [19]). However, the BatchelorKraichnan theory for the enstrophy cascade in 2D FDT (with the energy spectrum E(k) ∼ k −3 ) 4 has essential differences with the Kolmogorov theory for the energy cascade in 3D FDT.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, the consequent statistical dependence between the vorticity and the vorticity gradient at a point may be expected in turn to lead to non-gaussian statistics. Indeed, probability density functions (PDF) of enstrophy flux was measured in a freely-decaying 2D FDT by Kellay et al [47] which was found to be highly [53], Martin et al [14], Rutgers [15]), electromagnetically driven flow experiments (Paret al [54])…”

Section: Introductionmentioning

confidence: 99%

Intermittency in the enstrophy cascade of two-dimensional fully developed turbulence: Universal features

Shivamoggi

2008

Annals of Physics

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Intermittency (externally induced) in the two-dimensional (2D) enstrophy cascade is shown to be able to maintain a finite enstrophy along with a vorticity conservation anomaly. Intermittency mechanisms of three-dimensional (3D) energy cascade and 2D enstrophy cascade in fully-developed turbulence (FDT) seem to have some universal features. The parabolic-profile approximation (PPA) for the singularity spectrum f (α) in multi-fractal model is used and extended to the appropriate microscale regimes to exhibit these features. The PPA is also shown to afford, unlike the generic multi-fractal model, an analytical calculation of probability distribution functions (PDF) of flowvariable gradients in these FDT cases and to describe intermittency corrections that complement those provided by the homogeneous fractal model.

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Forced 2D Turbulence: Experimental Evidence of Simultaneous Inverse Energy and Forward Enstrophy Cascades

Cited by 174 publications

References 17 publications

Three-dimensional structure and decay properties of vortices in shallow fluid layers

Three-dimensional structure and decay properties of vortices in shallow fluid layers

Vortical control of forced two-dimensional turbulence

Intermittency in the enstrophy cascade of two-dimensional fully developed turbulence: Universal features

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