Relative dispersion with finite inertial ranges

2021 ◽  
Vol 932 ◽  
Author(s):  
J.H. LaCasce ◽  
Thomas Meunier
Keyword(s):  
Three Dimensional ◽  
Planck Equation ◽  
Inertial Range ◽  
Relative Dispersion ◽  
Initial Time ◽  
Local Dispersion ◽  
Theoretical Predictions ◽  
Pair Separation ◽  
Non Local ◽  
And Diffusion

Relative dispersion experiments are often analysed using theoretical predictions from two- and three-dimensional turbulence. These apply to infinite inertial ranges, assuming the same dispersive behaviour over all scales. With finite inertial ranges, the metrics are less conclusive. We examine this using pair separation probability density functions (PDFs), obtained by integrating a Fokker–Planck equation with different diffusivity profiles. We consider time-based metrics, such as the relative dispersion, and separation-based metrics, such as the finite scale Lyapunov exponent (FSLE). As the latter cannot be calculated from a PDF, we introduce a new measure, the cumulative inverse separation time (CIST), which can. This behaves like the FSLE, but advantageously has analytical solutions in the inertial ranges. This allows the establishment of consistency between the time- and space-based metrics, something which has been lacking previously. We focus on three dispersion regimes: non-local spreading (as in a two-dimensional enstrophy inertial range), Richardson dispersion (as in an energy inertial range) and diffusion (for uncorrelated pair motion). The time-based metrics are more successful with non-local dispersion, as the corresponding PDF applies from the initial time. Richardson dispersion is barely observed, because the self-similar PDF applies only asymptotically in time. In contrast, the separation-based CIST correctly captures the dependencies, even with a short (one decade) inertial range, and is superior to the traditional FSLE at large scales. Nevertheless, it is advantageous to use all measures together, to seek consistent indications of the dispersion.

scholarly journals Relative Dispersion in the Antarctic Circumpolar Current

2020 ◽  
Author(s):  
Dhruv Balwada ◽  
Joseph H. LaCasce ◽  
Kevin G. Speer ◽  
Raffaele Ferrari
Keyword(s):  
Southern Ocean ◽  
Finite Size ◽  
Relative Dispersion ◽  
Order Structure ◽  
Dispersion Characteristics ◽  
Local Dispersion ◽  
Relative Diffusivity ◽  
Pair Separation ◽  
Non Local ◽  
Circumpolar Current

AbstractStirring in the subsurface Southern Ocean is examined using RAFOS float trajectories, collected during the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean (DIMES), along with particle trajectories from a regional eddy permitting model. A central question is the extent to which the stirring is local, by eddies comparable in size to the pair separation, or non-local, by eddies at larger scales. To test this, we examine metrics based on averaging in time and in space. The model particles exhibit non-local dispersion, as expected for a limited resolution numerical model that does not resolve flows at scales smaller than ~ 10days or ~ 20–30km. The different metrics are less consistent for the RAFOS floats; relative dispersion, kurtosis and relative diffusivity suggest non-local dispersion as they are consistent with the model within error, while finite size Lyapunov exponents (FSLE) suggests local dispersion. This occurs for two reasons: (i) limited sampling of the inertial length scales and relatively small number of pairs hinder statistical robustness in time-based metrics, and (ii) some space-based metrics (FSLE, 2nd order structure functions), which do not average over wave motions and are reflective of the kinetic energy distribution, are probably unsuitable to infer dispersion characteristics if the flow field includes energetic wave-like flows that do not disperse particles. The relative diffusivity, which is also a space-based metric, allows averaging over waves to infer the dispersion characteristics. Hence, given the error characteristics of the metrics and data used here, the stirring in the DIMES region is likely to be non-local at scales of 5-100km.

Cluster Size Distributions in Different Temperature Regimes: The System Ga on GaAs(001)

1991 ◽  
Vol 237 ◽  
Author(s):  
Y. Ren ◽  
M. Zinke-Allmang ◽  
L. C. Feldman ◽  
W. Van Saarloos
Keyword(s):  
Cluster Size ◽  
Ostwald Ripening ◽  
Three Dimensional ◽  
Size Distributions ◽  
Limited Growth ◽  
Deposition Rates ◽  
Diffusion Limited ◽  
Temperature Regimes ◽  
Theoretical Predictions ◽  
And Diffusion

ABSTRACTIn this paper we discuss results for the clustering of Ga on GaAs(001). The dominant dynamic process which drives this system toward this three dimensional equilibrium changes from Ostwald ripening at low deposition rates to coalescence at higher deposition rates. The experimental data allow us to test several theoretical predictions for cluster size distributions based on a detailed study of the microscopic processes. These include, at higher deposition rates, the observation of local ripening effects and diffusion limited growth.

scholarly journals Intermittency in the relative separations of tracers and of heavy particles in turbulent flows

2014 ◽  
Vol 757 ◽  
pp. 550-572 ◽  
Author(s):  
L. Biferale ◽  
A. S. Lanotte ◽  
R. Scatamacchia ◽  
F. Toschi
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Isotropic Turbulence ◽  
Exit Time ◽  
Three Dimensional ◽  
Stokes Number ◽  
Inertial Range ◽  
Relative Dispersion ◽  
Heavy Particles ◽  
Self Similar

AbstractResults from direct numerical simulations (DNS) of particle relative dispersion in three-dimensional homogeneous and isotropic turbulence at Reynolds number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\mathit{Re}}_{\lambda } \sim 300$ are presented. We study point-like passive tracers and heavy particles, at Stokes number $\mathit{St}=0.6,1$ and 5. Particles are emitted from localised sources, in bunches of thousands, periodically in time, allowing an unprecedented statistical accuracy to be reached, with a total number of events for two-point observables of the order of ${10^{11}}$. The right tail of the probability density function (PDF) for tracers develops a clear deviation from Richardson’s self-similar prediction, pointing to the intermittent nature of the dispersion process. In our numerical experiment, such deviations are manifest once the probability to measure an event becomes of the order of – or rarer than – one part over one million, hence the crucial importance of a large dataset. The role of finite-Reynolds-number effects and the related fluctuations when pair separations cross the boundary between viscous and inertial range scales are discussed. An asymptotic prediction based on the multifractal theory for inertial range intermittency and valid for large Reynolds numbers is found to agree with the data better than the Richardson theory. The agreement is improved when considering heavy particles, whose inertia filters out viscous scale fluctuations. By using the exit-time statistics we also show that events associated with pairs experiencing unusually slow inertial range separations have a non-self-similar PDF.

scholarly journals Adaptive Chaotic Image Encryption Algorithm Based on RNA and Pixel Depth

Electronics ◽  
2021 ◽  
Vol 10 (15) ◽  
pp. 1770
Author(s):  
Xiaoqiang Zhang ◽  
Xuangang Yan
Keyword(s):  
Image Encryption ◽  
Three Dimensional ◽  
Encryption Algorithm ◽  
Current Time ◽  
Plain Image ◽  
Scope Of Application ◽  
Selective Diffusion ◽  
Chaotic Image Encryption ◽  
And Diffusion ◽  
Image Encryption Algorithm

To prevent the leakage of image content, image encryption technology has received increasing attention. Most current algorithms are only suitable for the images of certain types and cannot update keys in a timely manner. To tackle such problems, we propose an adaptive chaotic image encryption algorithm based on RNA and pixel depth. Firstly, a novel chaotic system, two-dimensional improved Logistic-adjusted-Sine map is designed. Then, we propose a three-dimensional adaptive Arnold transform for scrambling. Secondly, keys are generated by the hash values of the plain image and current time to achieve one-image, one-key, and one-time pad simultaneously. Thirdly, we build a pre-permuted RNA cube for 3D adaptive scrambling by pixel depth, chaotic sequences, and adaptive RNA coding. Finally, selective diffusion combined with pixel depth and RNA operations is performed, in which the RNA operators are determined by the chemical structure and properties of amino acids. Pixel depth is integrated into the whole procedure of parameter generation, scrambling, and diffusion. Experiments and algorithm analyses show that our algorithm has strong security, desirable performance, and a broader scope of application.

scholarly journals Transmission and diffusion: Linguistic change in the regional French of Béarn

2015 ◽  
Vol 26 (3) ◽  
pp. 327-352
Author(s):  
DAMIEN MOONEY
Keyword(s):  
Individual Change ◽  
Vowel Quality ◽  
Linguistic Change ◽  
Local Varieties ◽  
Transmission Process ◽  
Non Local ◽  
Diffusion Interface ◽  
Successive Generations ◽  
And Diffusion ◽  
Shed Light

ABSTRACTThis article examines the seemingly dichotomous linguistic processes of transmission and diffusion (Labov, 2007) in the regional variety of French spoken in Béarn, southwestern France. Using a sociophonetic apparent time methodology, an analysis of nasal vowel quality provides evidence for the advancement of linguistic changes from below taking place between successive generations during the transmission process, as well as for change from above taking place in the variety as a result of exposure to diffusing non-local varieties of French. The results address Labov's (2007) assertion that it is rare to investigate incremental changes occurring from below in European dialectological studies and shed light on the transmission–diffusion interface by showing the adoption of an individual change from above to instigate a faithfully-transmitted counterclockwise chain shift in the regional French nasal vowel system.

scholarly journals Reflection-driven magnetohydrodynamic turbulence in the solar atmosphere and solar wind

2019 ◽  
Vol 85 (4) ◽  
Author(s):  
Benjamin D. G. Chandran ◽  
Jean C. Perez
Keyword(s):  
Solar Wind ◽  
Heating Rate ◽  
Three Dimensional ◽  
Power Spectra ◽  
Inertial Range ◽  
Magnetic Flux Tube ◽  
Analytic Model ◽  
Mhd Turbulence ◽  
Background Magnetic Field ◽  
Turbulent Heating

We present three-dimensional direct numerical simulations and an analytic model of reflection-driven magnetohydrodynamic (MHD) turbulence in the solar wind. Our simulations describe transverse, non-compressive MHD fluctuations within a narrow magnetic flux tube that extends from the photosphere, through the chromosphere and corona and out to a heliocentric distance  $r$ of 21 solar radii  $(R_{\odot })$ . We launch outward-propagating ‘ $\boldsymbol{z}^{+}$ fluctuations’ into the simulation domain by imposing a randomly evolving photospheric velocity field. As these fluctuations propagate away from the Sun, they undergo partial reflection, producing inward-propagating ‘ $\boldsymbol{z}^{-}$ fluctuations’. Counter-propagating fluctuations subsequently interact, causing fluctuation energy to cascade to small scales and dissipate. Our analytic model incorporates dynamic alignment, allows for strongly or weakly turbulent nonlinear interactions and divides the $\boldsymbol{z}^{+}$ fluctuations into two populations with different characteristic radial correlation lengths. The inertial-range power spectra of $\boldsymbol{z}^{+}$ and $\boldsymbol{z}^{-}$ fluctuations in our simulations evolve toward a $k_{\bot }^{-3/2}$ scaling at $r>10R_{\odot }$ , where $k_{\bot }$ is the wave-vector component perpendicular to the background magnetic field. In two of our simulations, the $\boldsymbol{z}^{+}$ power spectra are much flatter between the coronal base and $r\simeq 4R_{\odot }$ . We argue that these spectral scalings are caused by: (i) high-pass filtering in the upper chromosphere; (ii) the anomalous coherence of inertial-range $\boldsymbol{z}^{-}$ fluctuations in a reference frame propagating outwards with the $\boldsymbol{z}^{+}$ fluctuations; and (iii) the change in the sign of the radial derivative of the Alfvén speed at $r=r_{\text{m}}\simeq 1.7R_{\odot }$ , which disrupts this anomalous coherence between $r=r_{\text{m}}$ and $r\simeq 2r_{\text{m}}$ . At $r>1.3R_{\odot }$ , the turbulent heating rate in our simulations is comparable to the turbulent heating rate in a previously developed solar-wind model that agreed with a number of observational constraints, consistent with the hypothesis that MHD turbulence accounts for much of the heating of the fast solar wind.

scholarly journals Simulations of Nearshore Particle-Pair Dispersion in Southern California

2013 ◽  
Vol 43 (9) ◽  
pp. 1862-1879 ◽  
Author(s):  
Leonel Romero ◽  
Yusuke Uchiyama ◽  
J. Carter Ohlmann ◽  
James C. McWilliams ◽  
David A. Siegel
Keyword(s):  
Kinetic Energy ◽  
Southern California ◽  
Separation Distance ◽  
Horizontal Resolution ◽  
Particle Dispersion ◽  
Eddy Kinetic Energy ◽  
Relative Dispersion ◽  
Numerical Resolution ◽  
Relative Diffusivity ◽  
Pair Separation

Abstract Knowledge of horizontal relative dispersion in nearshore oceans is important for many applications including the transport and fate of pollutants and the dynamics of nearshore ecosystems. Two-particle dispersion statistics are calculated from millions of synthetic particle trajectories from high-resolution numerical simulations of the Southern California Bight. The model horizontal resolution of 250 m allows the investigation of the two-particle dispersion, with an initial pair separation of 500 m. The relative dispersion is characterized with respect to the coastal geometry, bathymetry, eddy kinetic energy, and the relative magnitudes of strain and vorticity. Dispersion is dominated by the submesoscale, not by tides. In general, headlands are more energetic and dispersive than bays. Relative diffusivity estimates are smaller and more anisotropic close to shore. Farther from shore, the relative diffusivity increases and becomes less anisotropic, approaching isotropy ~10 km from the coast. The degree of anisotropy of the relative diffusivity is qualitatively consistent with that for eddy kinetic energy. The total relative diffusivity as a function of pair separation distance R is on average proportional to R5/4. Additional Lagrangian experiments at higher horizontal numerical resolution confirmed the robustness of these results. Structures of large vorticity are preferably elongated and aligned with the coastline nearshore, which may limit cross-shelf dispersion. The results provide useful information for the design of subgrid-scale mixing parameterizations as well as quantifying the transport and dispersal of dissolved pollutants and biological propagules.

Fast (non-)diffusive Quasi-Geostrophic Magneto-Coriolis Modes in the Earth's core

2021 ◽  
Author(s):  
Felix Gerick ◽  
Dominique Jault ◽  
Jerome Noir
Keyword(s):  
Magnetic Field ◽  
Magnetic Energy ◽  
Three Dimensional ◽  
Outer Core ◽  
Equatorial Region ◽  
Earth’S Core ◽  
Earth's Core ◽  
Strong Focusing ◽  
Geomagnetic Observations ◽  
And Diffusion

<p> Fast changes of Earth's magnetic field could be explained by inviscid and diffusion-less quasi-geostrophic (QG) Magneto-Coriolis modes. We present a hybrid QG model with columnar flows and three-dimensional magnetic fields and find modes with periods of a few years at parameters relevant to Earth's core. These fast Magneto-Coriolis modes show strong focusing of their kinetic and magnetic energy in the equatorial region, while maintaining a relatively large spatial structure along the azimuthal direction. Their properties agree with some of the observations and inferred core flows. We find additionally, in contrast to what has been assumed previously, that these modes are not affected significantly by magnetic diffusion. The model opens a new way of inverting geomagnetic observations to the flow and magnetic field deep within the Earth's outer core.</p>

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