A demonstration of the suppression of turbulent cascades by coherent vortices in two‐dimensional turbulence

1990 ◽  
Vol 2 (4) ◽  
pp. 547-552 ◽  
Author(s):  
James C. McWilliams
Keyword(s):  
Two Dimensional ◽  
Coherent Vortices

Coupled systems of two-dimensional turbulence

2013 ◽  
Vol 732 ◽  
Author(s):  
Rick Salmon
Keyword(s):  
Hamiltonian System ◽  
Energy Conservation ◽  
Strong Correlation ◽  
Conservation Law ◽  
Hamiltonian Dynamics ◽  
Coupled Systems ◽  
The Other ◽  
Two Dimensional ◽  
Coherent Vortices ◽  
Fluid Particles

AbstractOrdinary two-dimensional turbulence corresponds to a Hamiltonian dynamics that conserves energy and the vorticity on fluid particles. This paper considers coupled systems of two-dimensional turbulence with three distinct governing dynamics. One is a Hamiltonian dynamics that conserves the vorticity on fluid particles and a quantity analogous to the energy that causes the system members to develop a strong correlation in velocity. The other two dynamics considered are non-Hamiltonian. One conserves the vorticity on particles but has no conservation law analogous to energy conservation; the other conserves energy and enstrophy but it does not conserve the vorticity on fluid particles. The coupled Hamiltonian system behaves like two-dimensional turbulence, even to the extent of forming isolated coherent vortices. The other two dynamics behave very differently, but the behaviours of all four dynamics are accurately predicted by the methods of equilibrium statistical mechanics.

scholarly journals Selective decay and coherent vortices in two-dimensional incompressible turbulence

1991 ◽  
Vol 66 (21) ◽  
pp. 2731-2734 ◽  
Author(s):  
William H. Matthaeus ◽  
W. Troy Stribling ◽  
Daniel Martinez ◽  
Sean Oughton ◽  
David Montgomery
Keyword(s):  
Two Dimensional ◽  
Coherent Vortices ◽  
Selective Decay ◽  
Incompressible Turbulence

Parameterization of dispersion in two-dimensional turbulence

2001 ◽  
Vol 439 ◽  
pp. 279-303 ◽  
Author(s):  
C. PASQUERO ◽  
A. PROVENZALE ◽  
A. BABIANO
Keyword(s):  
Velocity Distribution ◽  
Single Particle ◽  
Stochastic Models ◽  
Particle Dispersion ◽  
Turbulent Dispersion ◽  
Two Dimensional ◽  
Component Process ◽  
Velocity Autocorrelation ◽  
Coherent Vortices ◽  
Non Gaussian

We investigate the performance of standard stochastic models of single-particle dispersion in two-dimensional turbulence. Owing to the presence of coherent vortices, particle dispersion in two-dimensional turbulence is characterized by a non-Gaussian velocity distribution and a non-exponential velocity autocorrelation, and it cannot be properly captured by either linear or nonlinear stochastic models with a single component process. Based on physical and dynamical considerations, we introduce a family of two-process stochastic models that provide a better parameterization of turbulent dispersion in rotating barotropic flows.

Algebraic probability density tails in decaying isotropic two-dimensional turbulence

1996 ◽  
Vol 313 ◽  
pp. 223-240 ◽  
Author(s):  
Javier Jiménez
Keyword(s):  
Isotropic Turbulence ◽  
Cauchy Distribution ◽  
Two Dimensional ◽  
Scaling Properties ◽  
Velocity Gradients ◽  
Random Arrangement ◽  
Coherent Vortices ◽  
Statistical Argument ◽  
Decaying Turbulence ◽  
The One

The p.d.f. of the velocity gradients in two-dimensional decaying isotropic turbulence is shown to approach a Cauchy distribution, with algebraic s−2 tails, as the flow becomes dominated by a large number of compact coherent vortices. The statistical argument is independent of the vortex structure, and depends only on general scaling properties. The same argument predicts a Gaussian p.d.f. for the velocity components. The convergence to these limits as a function of the number of vortices is analysed. It is found to be fast in the former case, but slow (logarithmic) in the latter, resulting in residual u−3 tails in all practical cases. The influence of a spread Gaussian vorticity distribution in the cores is estimated, and the relevant dimensionless parameter is identified as the area fraction covered by the cores. A comparison is made with the result of numerical simulations of two-dimensional decaying turbulence. The agreement of the p.d.f.s is excellent in the case of the gradients, and adequate in the case of the velocities. In the latter case the ratio between energy and enstrophy is computed, and agrees with the simulations. All the one-point statistics considered in this paper are consistent with a random arrangement of the vortex cores, with no evidence of energy screening.

scholarly journals An ‘ideal’ form of decaying two-dimensional turbulence

2002 ◽  
Vol 456 ◽  
pp. 183-198 ◽  
Author(s):  
TAKAHIRO IWAYAMA ◽  
THEODORE G. SHEPHERD ◽  
TAKESHI WATANABE
Keyword(s):  
Navier Stokes ◽  
Two Dimensional ◽  
Similarity Hypothesis ◽  
Ideal Form ◽  
Coherent Vortices ◽  
Wave Numbers

In decaying two-dimensional Navier–Stokes turbulence, Batchelor's similarity hypothesis fails due to the existence of coherent vortices. However, it is shown that decaying two-dimensional turbulence governed by the Charney–Hasegawa–Mima (CHM) equation(∂/∂t)(∇2φ−λ2φ) +J(φ, ∇2φ) = D,where D is a damping, is described well by Batchelor's similarity hypothesis for wave numbers k [Lt ] λ (the so-called AM regime). It is argued that CHM turbulence in the AM regime is a more ‘ideal’ form of two-dimensional turbulence than is Navier–Stokes turbulence itself.

scholarly journals Velocity statistics inside coherent vortices generated by the inverse cascade of 2-D turbulence

2016 ◽  
Vol 809 ◽  
Author(s):  
I. V. Kolokolov ◽  
V. V. Lebedev
Keyword(s):  
Velocity Profile ◽  
Structure Function ◽  
Correlation Functions ◽  
Two Dimensional ◽  
Strong Anisotropy ◽  
Velocity Fluctuations ◽  
Inverse Cascade ◽  
Velocity Statistics ◽  
Flow Fluctuations ◽  
Coherent Vortices

We analyse velocity fluctuations inside coherent vortices generated as a result of the inverse cascade in the two-dimensional (2-D) turbulence in a finite box. As we demonstrated in Kolokolov & Lebedev (Phys. Rev. E, vol. 93, 2016, 033104), the universal velocity profile, established in Laurie et al. (Phys. Rev. Lett., vol. 113, 2014, 254503), corresponds to the passive regime of the flow fluctuations. This property enables one to calculate correlation functions of the velocity fluctuations in the universal region. We present the results of the calculations that demonstrate a non-trivial scaling of the structure function. In addition the calculations reveal strong anisotropy of the structure function.

Coherent vortices and tracer cascades in two-dimensional turbulence

2007 ◽  
Vol 574 ◽  
pp. 429-448 ◽  
Author(s):  
ARMANDO BABIANO ◽  
ANTONELLO PROVENZALE
Keyword(s):  
Inertial Range ◽  
Two Dimensional ◽  
Passive Tracer ◽  
Simultaneous Presence ◽  
Inverse Cascade ◽  
Coherent Vortices ◽  
Small Scales ◽  
Elliptic Regions ◽  
Enstrophy Cascade

We study numerically the scale-to-scale transfers of enstrophy and passive-tracer variance in two-dimensional turbulence, and show that these transfers display significant differences in the inertial range of the enstrophy cascade. While passive-tracer variance always cascades towards small scales, enstrophy is characterized by the simultaneous presence of a direct cascade in hyperbolic regions and of an inverse cascade in elliptic regions. The inverse enstrophy cascade is particularly intense in clusters of small-scales elliptic patches and vorticity filaments in the turbulent background, and it is associated with gradient-decreasing processes. The inversion of the enstrophy cascade, already noticed by Ohkitani (Phys. Fluids A, vol. 3, 1991, p. 1598), appears to be the main difference between vorticity and passive-tracer dynamics in incompressible two-dimensional turbulence.

Vorticity and passive-scalar dynamics in two-dimensional turbulence

1987 ◽  
Vol 183 ◽  
pp. 379-397 ◽  
Author(s):  
Armando Babiano ◽  
Claude Basdevant ◽  
Bernard Legras ◽  
Robert Sadourny
Keyword(s):  
Similarity Theory ◽  
Physical Space ◽  
Passive Scalar ◽  
Inertial Range ◽  
Flow Dynamics ◽  
Two Dimensional ◽  
Closure Model ◽  
Coherent Vortices ◽  
Vorticity Transport ◽  
Kolmogorov Theory

The dynamics of vorticity in two-dimensional turbulence is studied by means of semi-direct numerical simulations, in parallel with passive-scalar dynamics. It is shown that a passive scalar forced and dissipated in the same conditions as vorticity, has a quite different behaviour. The passive scalar obeys the similarity theory à la Kolmogorov, while the enstrophy spectrum is much steeper, owing to a hierarchy of strong coherent vortices. The condensation of vorticity into such vortices depends critically both on the existence of an energy invariant (intimately related to the feedback of vorticity transport on velocity, absent in passive-scalar dynamics, and neglected in the Kolmogorov theory of the enstrophy inertial range); and on the localness of flow dynamics in physical space (again not considered by the Kolmogorov theory, and not accessible to closure model simulations). When space localness is artificially destroyed, the enstrophy spectrum again obeys a k−1 law like a passive scalar. In the wavenumber range accessible to our experiments, two-dimensional turbulence can be described as a hierarchy of strong coherent vortices superimposed on a weak vorticity continuum which behaves like a passive scalar.

Kraichnan–Leith–Batchelor similarity theory and two-dimensional inverse cascades

2015 ◽  
Vol 767 ◽  
pp. 467-496 ◽  
Author(s):  
B. H. Burgess ◽  
R. K. Scott ◽  
T. G. Shepherd
Keyword(s):  
Large Scale ◽  
Similarity Theory ◽  
Vortex Formation ◽  
Turbulence Models ◽  
Two Dimensional ◽  
Scaling Properties ◽  
Inverse Cascade ◽  
Coherent Vortices ◽  
Coherent Vortex ◽  
Non Gaussian

AbstractWe study the scaling properties and Kraichnan–Leith–Batchelor (KLB) theory of forced inverse cascades in generalized two-dimensional (2D) fluids (${\it\alpha}$-turbulence models) simulated at resolution $8192^{2}$. We consider ${\it\alpha}=1$ (surface quasigeostrophic flow), ${\it\alpha}=2$ (2D Euler flow) and ${\it\alpha}=3$. The forcing scale is well resolved, a direct cascade is present and there is no large-scale dissipation. Coherent vortices spanning a range of sizes, most larger than the forcing scale, are present for both ${\it\alpha}=1$ and ${\it\alpha}=2$. The active scalar field for ${\it\alpha}=3$ contains comparatively few and small vortices. The energy spectral slopes in the inverse cascade are steeper than the KLB prediction $-(7-{\it\alpha})/3$ in all three systems. Since we stop the simulations well before the cascades have reached the domain scale, vortex formation and spectral steepening are not due to condensation effects; nor are they caused by large-scale dissipation, which is absent. One- and two-point p.d.f.s, hyperflatness factors and structure functions indicate that the inverse cascades are intermittent and non-Gaussian over much of the inertial range for ${\it\alpha}=1$ and ${\it\alpha}=2$, while the ${\it\alpha}=3$ inverse cascade is much closer to Gaussian and non-intermittent. For ${\it\alpha}=3$ the steep spectrum is close to that associated with enstrophy equipartition. Continuous wavelet analysis shows approximate KLB scaling $\mathscr{E}(k)\propto k^{-2}~({\it\alpha}=1)$ and $\mathscr{E}(k)\propto k^{-5/3}~({\it\alpha}=2)$ in the interstitial regions between the coherent vortices. Our results demonstrate that coherent vortex formation (${\it\alpha}=1$ and ${\it\alpha}=2$) and non-realizability (${\it\alpha}=3$) cause 2D inverse cascades to deviate from the KLB predictions, but that the flow between the vortices exhibits KLB scaling and non-intermittent statistics for ${\it\alpha}=1$ and ${\it\alpha}=2$.

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