Relative dispersion in generalized two-dimensional turbulence

2017 ◽  
Vol 821 ◽  
pp. 358-383 ◽  
Author(s):  
Alexis Foussard ◽  
Stefano Berti ◽  
Xavier Perrot ◽  
Guillaume Lapeyre
Keyword(s):  
Probability Distributions ◽  
Turbulence Models ◽  
Relative Displacement ◽  
Relative Dispersion ◽  
Spectral Energy ◽  
Two Dimensional ◽  
Energy Transfers ◽  
Non Local ◽  
Turbulent Cascade ◽  
Non Locality

The statistical properties of turbulent fluids depend on how local the energy transfers among scales are, i.e. whether the energy transfer at some given scale is due to the eddies at that particular scale, or to eddies at larger (non-local) scale. This locality in the energy transfers may have consequences for the relative dispersion of passive particles. In this paper, we consider a class of generalized two-dimensional flows (produced by the so-called $\unicode[STIX]{x1D6FC}$-turbulence models), theoretically possessing different properties in terms of locality of energy transfers. It encompasses the standard barotropic quasi-geostrophic (QG) and the surface quasi-geostrophic (SQG) models as limiting cases. The relative dispersion statistics are examined, both as a function of time and as a function of scale, and compared to predictions based on phenomenological arguments assuming the locality of the cascade. We find that the dispersion statistics follow the predicted values from local theories, as long as the parameter $\unicode[STIX]{x1D6FC}$ is small enough (dynamics close to that of the SQG model), for sufficiently small initial pair separations. In contrast, non-local dispersion is observed for the QG model, a robust result when looking at relative displacement probability distributions. However, we point out that spectral energy transfers do have a non-local contribution for models with different values of $\unicode[STIX]{x1D6FC}$, including the SQG case. This indicates that locality/non-locality of the turbulent cascade may not always imply locality/non-locality in the relative dispersion of particles and that the self-similar nature of the turbulent cascade is more appropriate for determining the relative dispersion locality.

scholarly journals Non-local energy transfers in rotating turbulence at intermediate Rossby number

2011 ◽  
Vol 690 ◽  
pp. 129-147 ◽  
Author(s):  
L. Bourouiba ◽  
D. N. Straub ◽  
M. L. Waite
Keyword(s):  
Turbulent Flows ◽  
Scaling Law ◽  
Three Dimensional ◽  
Rossby Number ◽  
Local Energy ◽  
Two Dimensional ◽  
Horizontal Scale ◽  
Energy Transfers ◽  
Non Local ◽  
Non Locality

AbstractTurbulent flows subject to solid-body rotation are known to generate steep energy spectra and two-dimensional columnar vortices. The localness of the dominant energy transfers responsible for the accumulation of the energy in the two-dimensional columnar vortices of large horizontal scale remains undetermined. Here, we investigate the scale-locality of the energy transfers directly contributing to the growth of the two-dimensional columnar structures observed in the intermediate Rossby number ($\mathit{Ro}$) regime. Our approach is to investigate the dynamics of the waves and vortices separately: we ensure that the two-dimensional columnar structures are not directly forced so that the vortices can result only from association with wave to vortical energy transfers. Detailed energy transfers between waves and vortices are computed as a function of scale, allowing the direct tracking of the role and scales of the wave–vortex nonlinear interactions in the accumulation of energy in the large two-dimensional columnar structures. It is shown that the dominant energy transfers responsible for the generation of a steep two-dimensional spectrum involve direct non-local energy transfers from small-frequency small-horizontal-scale three-dimensional waves to large-horizontal-scale two-dimensional columnar vortices. Sensitivity of the results to changes in resolution and forcing scales is investigated and the non-locality of the dominant energy transfers leading to the emergence of the columnar vortices is shown to be robust. The interpretation of the scaling law observed in rotating flows in the intermediate-$\mathit{Ro}$ regime is revisited in the light of this new finding of dominant non-locality.

Numerical simulation of relative dispersion in two-dimensional, homogeneous, decaying turbulence

1981 ◽  
Vol 109 ◽  
pp. 45-61 ◽  
Author(s):  
A. D. Kowalski ◽  
R. L. Peskin
Keyword(s):  
Single Particle ◽  
Large Scale ◽  
Local Strain ◽  
Relative Dispersion ◽  
Two Dimensional ◽  
Temporal Behaviour ◽  
Relative Separation ◽  
Non Local ◽  
Decaying Turbulence ◽  
Enstrophy Cascade

Lagrangian statistical results are presented from numerical simulations of an ensemble of fluid particles which were generated from a two-dimensional pseudospectral code. The single-particle results are in qualitative agreement with previous simulations on a lower-resolution grid. The two-particle, relative velocity correlations were found to fall off more rapidly than the single-particle correlations for short to intermediate times due to large-scale eddy advection in the single-particle case. The temporal behaviour of the mean square relative separation, 〈rl2〉, is analysed for short to intermediate times and is found to be consistent with scaling arguments based on Kraichnan's expression for the non-local strain acting in the high-wavenumber enstrophy cascade spectral range. For longer times, 〈rl2〉 exhibits tn behaviour. The power-law region is associated with the locally determined strain rates which characterize a backward energy-cascade spectrum.

scholarly journals Patterns of water in light

2019 ◽  
Vol 475 (2227) ◽  
pp. 20190110 ◽  
Author(s):  
Theodoros P. Horikis ◽  
Dimitrios J. Frantzeskakis
Keyword(s):  
Liquid Crystals ◽  
Water Waves ◽  
Soliton Solutions ◽  
Direct Numerical Simulations ◽  
Two Dimensional ◽  
Shallow Water Waves ◽  
Soliton Interactions ◽  
Non Local ◽  
Local Nonlinearity ◽  
Non Locality

The intricate patterns emerging from the interactions between soliton stripes of a two-dimensional defocusing nonlinear Schrödinger (NLS) model with a non-local nonlinearity are considered. We show that, for sufficiently strong non-locality, the model is asymptotically reduced to a Kadomtsev–Petviashvilli-II (KPII) equation, which is a common model arising in the description of shallow water waves, as such patterns of water may indeed exist in light (this non-local NLS finds applications in nonlinear optics, modelling beam propagation in media featuring thermal nonlinearities, in plasmas, and in nematic liquid crystals). This way, approximate antidark soliton solutions of the NLS model are constructed from the stable KPII line solitons. By means of direct numerical simulations, we demonstrate that non-resonant and resonant two- and three-antidark NLS stripe soliton interactions give rise to wave configurations that are found in the context of the KPII equation. Thus, our study indicates that patterns which are usually observed in water can also be found in optics.

scholarly journals Evaluating probabilistic forecasts of football matches: the case against the ranked probability score

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Edward Wheatcroft
Keyword(s):  
Scoring Rules ◽  
Brier Score ◽  
Sporting Events ◽  
Forecast Performance ◽  
Scoring Rule ◽  
Probability Score ◽  
Probabilistic Forecasts ◽  
Non Local ◽  
Evaluating Forecasts ◽  
Non Locality

Abstract A scoring rule is a function of a probabilistic forecast and a corresponding outcome used to evaluate forecast performance. There is some debate as to which scoring rules are most appropriate for evaluating forecasts of sporting events. This paper focuses on forecasts of the outcomes of football matches. The ranked probability score (RPS) is often recommended since it is ‘sensitive to distance’, that is it takes into account the ordering in the outcomes (a home win is ‘closer’ to a draw than it is to an away win). In this paper, this reasoning is disputed on the basis that it adds nothing in terms of the usual aims of using scoring rules. A local scoring rule is one that only takes the probability placed on the outcome into consideration. Two simulation experiments are carried out to compare the performance of the RPS, which is non-local and sensitive to distance, the Brier score, which is non-local and insensitive to distance, and the Ignorance score, which is local and insensitive to distance. The Ignorance score outperforms both the RPS and the Brier score, casting doubt on the value of non-locality and sensitivity to distance as properties of scoring rules in this context.

scholarly journals Non-local regularisation and two-dimensional induced actions

1992 ◽  
Vol 288 (1-2) ◽  
pp. 47-53 ◽  
Author(s):  
F. De Jonghe ◽  
R. Siebelink ◽  
W. Troost
Keyword(s):  
Two Dimensional ◽  
Non Local

scholarly journals Diluted mass gap in strongly coupled non-local Yang-Mills

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Marco Frasca ◽  
Anish Ghoshal
Keyword(s):  
Field Theory ◽  
Particle Physics ◽  
Mass Scale ◽  
Local Theory ◽  
Quantum Field ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Mass Gap ◽  
Non Local ◽  
Non Locality

Abstract We investigate the non-perturbative regimes in the class of non-Abelian theories that have been proposed as an ultraviolet completion of 4-D Quantum Field Theory (QFT) generalizing the kinetic energy operators to an infinite series of higher-order derivatives inspired by string field theory. We prove that, at the non-perturbative level, the physical spectrum of the theory is actually corrected by the “infinite number of derivatives” present in the action. We derive a set of Dyson-Schwinger equations in differential form, for correlation functions till two-points, the solution for which are known in the local theory. We obtain that just like in the local theory, the non-local counterpart displays a mass gap, depending also on the mass scale of non-locality, and show that it is damped in the deep UV asymptotically. We point out some possible implications of our result in particle physics and cosmology and discuss aspects of non-local QCD-like scenarios.

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