Unifying Scaling Theory for Vortex Dynamics in Two-Dimensional Turbulence

Dritschel, David G.; Scott, R. K.; Macaskill, C.; Gottwald, Georg A.; Tran, Chuong V.

doi:10.1103/physrevlett.101.094501

Cited by 51 publications

(67 citation statements)

References 20 publications

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“…His model does not take into account the effect of coherent vortices, which are localised in physical space and therefore are widely distributed in spectral space. This was argued previously by Dritschel et al 32 in the case of freely-decaying turbulence, for which it was shown that vortices are responsible for the (there strong) deviation between their numerical results and Batchelor's theory. In forced turbulence, Danilov & Gurarie 12 and Vallgren 20 also found that the effect of coherent vortices is significant, and, in particular, that the dominant triad interactions are highly nonlocal.…”

Section: Vortex Population Characteristicssupporting

confidence: 57%

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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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Section: Vortex Population Characteristicssupporting

confidence: 57%

“…To define the coherent part we first identify contiguous regions of vorticity whose magnitude is above the rms value, following the method described in Dritschel et al 32 for the freely decaying case. We then consider the shape of each contiguous region.…”

Section: Vortex Population Characteristicsmentioning

confidence: 99%

Vortical control of forced two-dimensional turbulence

2013

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“…The continuum case is particularly interesting because universal scaling laws have been proposed for distributions of vortex sizes in decaying two-dimensional turbulence (Dritschel et al 2008). …”

Section: The Fixed Ratio Neutral Vortex Gas and Its Continuum Limitmentioning

confidence: 99%

Universal statistics of point vortex turbulence

Esler

Ashbee

2015

J. Fluid Mech.

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A new methodology, based on the central limit theorem, is applied to describe the statistical mechanics of two-dimensional point vortex motion in a bounded container D, as the number of vortices N tends to infinity. The key to the approach is the identification of the normal modes of the system with the eigenfunction solutions of the so-called hydro- The pdf of the leading vorticity projection is of particular interest because it has a unimodal distribution at low energy and a bimodal distribution at high energy. This behaviour is indicative of a phase transition, known as Onsager-Kraichnan condensation in the literature, between low energy states with no mean flow in the domain and high energy states with a coherent mean flow. The critical temperature for the phase transition, which depends on the shape but not the size of D, and the associated critical energy are found. Finally the accuracy and the extent of the validity of the theory, at finite N , are explored using a Markov chain phase-space sampling method.

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“…CLAM was developed originally to better model both unforced and forced 2D turbulence at ultra-high Reynolds numbers (Dritschel et al, 2008Fontane & Dritschel, 2009). It is an extension of the recent HyperCASL algorithm (Fontane & Dritschel, 2009), which introduced the idea of using point vortices or particles to represent a residual tracer field q d (e.g.…”

Section: The Methodsmentioning

confidence: 99%

The combined Lagrangian advection method

Dritschel

Fontane

2010

Journal of Computational Physics

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International audienceWe present and test a new hybrid numerical method for simulating layerwise-two-dimensional geophysical flows. The method radically extends the original Contour-Advective Semi-Lagrangian (CASL) algorithm by combining three computational elements for the advection of general tracers (e.g. potential vorticity, water vapor, etc.): (1) a pseudospectral method for large scales, (2) Lagrangian contours for intermediate to small scales, and (3) Lagrangian particles for the representation of general forcing and dissipation. The pseudo-spectral method is both efficient and highly accurate at large scales, while contour advection is efficient and accurate at small scales, allowing one to simulate extremely finescale structure well below the basic grid scale used to represent the velocity field. The particles allow one to efficiently incorporate general forcing and dissipation

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Unifying Scaling Theory for Vortex Dynamics in Two-Dimensional Turbulence

Cited by 51 publications

References 20 publications

Vortical control of forced two-dimensional turbulence

Vortical control of forced two-dimensional turbulence

Universal statistics of point vortex turbulence

The combined Lagrangian advection method

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