Physical Mechanism of the Two-Dimensional Inverse Energy Cascade

Chen, Shiyi; Ecke, Robert E.; Eyink, Gregory L.; Rivera, Michael; Wan, Minping; Xiao, Zuoli

doi:10.1103/physrevlett.96.084502

Cited by 155 publications

(150 citation statements)

References 35 publications

Supporting

Mentioning

126

Contrasting

Order By: Relevance

“…It has been suggested that the Navier-Stokes energy cascade may proceed via aggregation of like-sign vortices (Paret & Tabeling 1997, in which case it might have little to do with shear or strain. Other results (Chen et al 2006;Xiao et al 2009) support the notion that the inverse cascade in forced Navier-Stokes turbulence is due to vortex thinning in eddy-eddy interactions involving comparable scales, but that thinning is due to turbulent stress from small-scale strain rotated by 45…”

Section: Introductionmentioning

confidence: 59%

“…In simulations forced at intermediate scales, and where an inverse energy cascade is present, the spectral slope in the enstrophy cascade is generally steeper than the KLB prediction, although evidence suggests it tends to −3 in the limit of infinite Reynolds number (Boffetta & Musacchio 2010). Farazmand et al (2011) did obtain dual cascades with the KLB spectra, but they used an optimal forcing unlikely to be spontaneously realized.…”

Section: Arguments For Cascade Directionsmentioning

confidence: 99%

See 1 more Smart Citation

Spectral non-locality, absolute equilibria and Kraichnan–Leith–Batchelor phenomenology in two-dimensional turbulent energy cascades

Burgess

Shepherd

2013

J. Fluid Mech.

View full text Add to dashboard Cite

We study the degree to which Kraichnan–Leith–Batchelor (KLB) phenomenology describes two-dimensional energy cascades in $\alpha $ turbulence, governed by $\partial \theta / \partial t+ J(\psi , \theta )= \nu {\nabla }^{2} \theta + f$, where $\theta = {(- \Delta )}^{\alpha / 2} \psi $ is generalized vorticity, and $\hat {\psi } (\boldsymbol{k})= {k}^{- \alpha } \hat {\theta } (\boldsymbol{k})$ in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow ($\alpha = 1$), regular two-dimensional flow ($\alpha = 2$) and rotating shallow flow ($\alpha = 3$), which is the isotropic limit of a mantle convection model. We re-examine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general $\alpha $, and point out their limitations. Using an $\alpha $-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Non-local triads contribute increasingly to the energy flux as $\alpha $ increases. More importantly, the energy cascade is downscale in the self-similar inertial range for $2. 5\lt \alpha \lt 10$. At $\alpha = 2. 5$ and $\alpha = 10$, the KLB spectra correspond, respectively, to enstrophy and energy equipartition, and the triad energy transfers and flux vanish identically. Eddy turnover time and strain rate arguments suggest the inverse energy cascade should obey KLB phenomenology and be self-similar for $\alpha \lt 4$. However, downscale energy flux in the EDQNM self-similar inertial range for $\alpha \gt 2. 5$ leads us to predict that any inverse cascade for $\alpha \geq 2. 5$ will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for $\alpha \geq 2. 5$ is significantly steeper than the KLB prediction, while for $\alpha \lt 2. 5$ we obtain the KLB spectrum.

show abstract

Section: Introductionmentioning

confidence: 59%

Section: Arguments For Cascade Directionsmentioning

confidence: 99%

Spectral non-locality, absolute equilibria and Kraichnan–Leith–Batchelor phenomenology in two-dimensional turbulent energy cascades

Burgess

Shepherd

2013

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…3,10,[16][17][18][19] The result ͑14͒ can be used to construct a simple cartoon of the inverse cascade of freely evolving two-dimensional turbulence. Imagine preparing an initial condition consisting of N ӷ 1 well separated axisymmetric vortices in a large but finite box.…”

Section: ͑23͒mentioning

confidence: 99%

On the energy of elliptical vortices

Vanneste

Young

2010

Physics of Fluids

View full text Add to dashboard Cite

Consider a two-dimensional axisymmetric vortex with circulation Γ. Suppose that this vortex is isovortically deformed into an elliptical vortex. We show that the reduction in energy is ΔE=−Γ2 ln[(q+q−1)/2]/(4π), where q2 is the ratio of the major to the minor axis of any particular elliptical vorticity contour. It is notable that ΔE is independent of the details of vorticity profile of the axisymmetric vortex and, in particular, independent of its average radius. The implications of this result for the two-dimensional inverse cascade are briefly discussed.

show abstract

“…There is no full consent on the physical mechanism behind the inverse energy cascade. In fact, several physical process have been proposed, such as Kraichnan's picture of 'thinning' of small-scale vorticity by strain at large scale [2,3], and the Onsager's picture of clustering of same-signed vortices [4].…”

Section: Introductionmentioning

confidence: 99%

Vortex clustering and universal scaling laws in two-dimensional quantum turbulence

Skaugen

Angheluta

2016

Phys. Rev. E

View full text Add to dashboard Cite

We investigate numerically the statistics of quantized vortices in two-dimensional quantum turbulence using the Gross-Pitaevskii equation. We find that a universal −5/3 scaling law in the turbulent energy spectrum is intimately connected with the vortex statistics, such as number fluctuations and vortex velocity, which is also characterized by a similar scaling behavior. The −5/3 scaling law appearing in the power spectrum of vortex number fluctuations is consistent with the scenario of passive advection of isolated vortices by a turbulent superfluid velocity generated by like-signed vortex clusters. The velocity probability distribution of clustered vortices is also sensitive to spatial configurations, and exhibits a power-law tail distribution with a −5/3 exponent.

show abstract

Physical Mechanism of the Two-Dimensional Inverse Energy Cascade

Cited by 155 publications

References 35 publications

Spectral non-locality, absolute equilibria and Kraichnan–Leith–Batchelor phenomenology in two-dimensional turbulent energy cascades

Spectral non-locality, absolute equilibria and Kraichnan–Leith–Batchelor phenomenology in two-dimensional turbulent energy cascades

On the energy of elliptical vortices

Vortex clustering and universal scaling laws in two-dimensional quantum turbulence

Contact Info

Product

Resources

About