Turbulence from Earth to Planets, Stars and Galaxies—Commemorative Issue Dedicated to the Memory of Jackson Rea Herring

A special issue of Atmosphere (ISSN 2073-4433).

Deadline for manuscript submissions: closed (25 October 2023) | Viewed by 34548

Special Issue Editors


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Guest Editor
College of Marine Science, University of South Florida, St. Petersburg, FL 33701, USA
Interests: turbulence; turbulence modeling; atmospheric, oceanic, planetary sciences; geophysical fluid dynamics

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Guest Editor
Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80305, USA
Interests: turbulence; atmospheric and oceanic systems; solar and plasma physics; theoretical modeling of nonlinear systems, numerical simulations

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Guest Editor
National Center for Atmospheric Research, Boulder, CO 80301, USA
Interests: turbulence; atmospheric and oceanic boundary layers; air-sea interaction; subgrid-scale modeling; submesoscale dynamics; surface layer observations; high performance computing; large-eddy simulation

Special Issue Information

Dear Colleagues,

This is a Special Issue to honour Dr Jackson Rea Herring who passed away peacefully on May 26, 2022 in Boulder, Colorado after a short illness. Jack was a Senior Scientist at the Mesoscale Microscale Meteorology Division at the National Center for Atmospheric Research (NCAR) at Boulder, Colorado, the position he had held since 1978. Jack earned his B.S. in Physics from Wake Forrest College (1953) and his M.S. and Ph.D., also in Physics, from the University of North Carolina (1956 and 1959). Upon graduating, Jack worked as a physicist at the Theoretical Division, Goddard Space Flight Center, Greenbelt, Md., and Washington, D.C. (1959–1960), the Institute for Space Studies, New York City, N.Y. (1960–1964), and, again, at the Goddard Space Flight Center, Greenbelt, Md. (1964–1972). He was then a Long-Term Visitor and then a Senior Scientist at the Advanced Science Program (ASP) at the National Center for Atmospheric Research (NCAR) at Boulder, Colorado (1972–1978), and starting in 1978, he was a Senior Scientist at the Mesoscale Research Section of Mesoscale Microscale Meteorology Division of NCAR. Jack was Senior Postdoctoral Fellow at the Advanced Study Program at NCAR (1972), Green Scholar at the University of California, San Diego (I.G.P.P.; 1978), and Professeur associé à l'lnstitut de Mécanique de Grenoble (1988). He served on the Advisory Board of Editors for Meteorology and Oceanography, World Scientific Publishing Co., was Associate Editor of Physics of Fluids, was Associate of the La Jolla Institute and served on the Advisory Committee of the NASA-Stanford Center for Turbulence Research (1988-1989).

We welcome papers in all the subject areas that Jack had an interest in and contributed to, and we urge all his colleagues and collaborators over the years to contribute to this Special Issue and thus honor his legacy to the profession and celebrate his life-loving and vivid personality.

Dr. Boris Galperin
Dr. Annick Pouquet
Dr. Peter Sullivan
Guest Editors

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Keywords

  • turbulence, theory and modeling
  • atmospheric and oceanic turbulence
  • planetary and astrophysical turbulence

Published Papers (30 papers)

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0 pages, 6116 KiB  
Article
The Intermittency of Turbulence in Magneto-Hydodynamical Simulations and in the Cosmos
by Pierre Lesaffre, Edith Falgarone and Pierre Hily-Blant
Atmosphere 2024, 15(2), 211; https://doi.org/10.3390/atmos15020211 - 08 Feb 2024
Viewed by 593
Abstract
Turbulent dissipation is a central issue in the star and galaxy formation process. Its fundamental property of space–time intermittency, well characterised in incompressible laboratory experiments, remains elusive in cosmic turbulence. Progress requires the combination of state-of-the-art modelling, numerical simulations and observations. The power [...] Read more.
Turbulent dissipation is a central issue in the star and galaxy formation process. Its fundamental property of space–time intermittency, well characterised in incompressible laboratory experiments, remains elusive in cosmic turbulence. Progress requires the combination of state-of-the-art modelling, numerical simulations and observations. The power of such a combination is illustrated here, where the statistical method intended to locate the extrema of velocity shears in a turbulent field, which are the signposts of intense dissipation extrema, is applied to numerical simulations of compressible magneto-hydrodynamical (MHD) turbulence dedicated to dissipation scales and to observations of a turbulent molecular cloud. We demonstrate that increments of several observables computed at the smallest lags can detect coherent structures of intense dissipation. We apply this statistical method to the observations of a turbulent molecular cloud close to the Sun in our galaxy and disclose a remarkable structure of extremely large velocity shear. At the location of the largest velocity shear, this structure is found to foster 10× more carbon monoxide molecules than standard diffuse molecular gas, an enrichment supported by models of non-equilibrium warm chemistry triggered by turbulent dissipation. In our simulations, we also compute structure functions of various synthetic observables and show that they verify Extended Self-Similarity. This allows us to compute their intermittency exponents, and we show how they constrain some properties of the underlying three-dimensional turbulence. The power of the combination of modelling and observations is also illustrated by the observations of the CH+ cation that provide unique quantitative information on the kinetic energy trail in the massive, multi-phase and turbulent circum-galactic medium of a galaxy group at redshift z=2.8. Full article
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13 pages, 2256 KiB  
Article
2D and 3D Properties of Stably Stratified Turbulence
by Yoshifumi Kimura and Peter P. Sullivan
Atmosphere 2024, 15(1), 82; https://doi.org/10.3390/atmos15010082 - 09 Jan 2024
Cited by 1 | Viewed by 677
Abstract
Through interactions between the modes of “waves” and “vortices”, stably stratified turbulence exhibits characteristic features both in 2D and 3D. Using DNS of the Navier–Stokes equations coupled to an equation for temperature (the Bousinessq system), we investigate dynamical properties of stably stratified turbulence. [...] Read more.
Through interactions between the modes of “waves” and “vortices”, stably stratified turbulence exhibits characteristic features both in 2D and 3D. Using DNS of the Navier–Stokes equations coupled to an equation for temperature (the Bousinessq system), we investigate dynamical properties of stably stratified turbulence. After reviewing the importance of three characteristic length scales and their relations in stably stratified turbulence, we present numerical results showing how structures and spectra develop with the growth of the length scales. It is demonstrated that the temperature fluctuations make sharp fronts vertically which result in non-symmetric PDFs of the vertical derivative zθ. Full article
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23 pages, 4823 KiB  
Article
Multi-Scale Reconstruction of Turbulent Rotating Flows with Generative Diffusion Models
by Tianyi Li, Alessandra S. Lanotte, Michele Buzzicotti, Fabio Bonaccorso and Luca Biferale
Atmosphere 2024, 15(1), 60; https://doi.org/10.3390/atmos15010060 - 31 Dec 2023
Viewed by 1150
Abstract
We address the problem of data augmentation in a rotating turbulence set-up, a paradigmatic challenge in geophysical applications. The goal is to reconstruct information in two-dimensional (2D) cuts of the three-dimensional flow fields, imagining spatial gaps present within each 2D observed slice. We [...] Read more.
We address the problem of data augmentation in a rotating turbulence set-up, a paradigmatic challenge in geophysical applications. The goal is to reconstruct information in two-dimensional (2D) cuts of the three-dimensional flow fields, imagining spatial gaps present within each 2D observed slice. We evaluate the effectiveness of different data-driven tools, based on diffusion models (DMs), a state-of-the-art generative machine learning protocol, and generative adversarial networks (GANs), previously considered as the best-performing method both in terms of point-wise reconstruction and the statistical properties of the inferred velocity fields. We focus on two different DMs recently proposed in the specialized literature: (i) RePaint, based on a heuristic strategy to guide an unconditional DM for flow generation by using partial measurements data, and (ii) Palette, a conditional DM trained for the reconstruction task with paired measured and missing data. Systematic comparison shows that (i) DMs outperform the GAN in terms of the mean squared error and/or the statistical accuracy; (ii) Palette DM emerges as the most promising tool in terms of both point-wise and statistical metrics. An important property of DMs is their capacity for probabilistic reconstructions, providing a range of predictions based on the same measurements, enabling uncertainty quantification and risk assessment. Full article
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23 pages, 40051 KiB  
Article
Turbulence Transitions in Kelvin–Helmholtz Instability “Tube” and “Knot” Dynamics: Vorticity, Helicity, and Twist Waves
by David C. Fritts, Thomas S. Lund, Adam C. Lund and Ling Wang
Atmosphere 2023, 14(12), 1770; https://doi.org/10.3390/atmos14121770 - 30 Nov 2023
Viewed by 786
Abstract
We address the sources and dynamics of vorticity and helicity and their relations in transitions to turbulence arising due to Kelvin–Helmholtz instability (KHI) “Tube” and “Knot” (T&K) events. Such events are common in the atmosphere and oceans, and initial numerical simulations reveal that [...] Read more.
We address the sources and dynamics of vorticity and helicity and their relations in transitions to turbulence arising due to Kelvin–Helmholtz instability (KHI) “Tube” and “Knot” (T&K) events. Such events are common in the atmosphere and oceans, and initial numerical simulations reveal that T&K dynamics significantly accelerate turbulence transitions and enhance KHI peak and mean energy dissipation rates. KHI T&K events arise where emerging KH billows exhibit varying wavelengths, phases, amplitudes, and/or discontinuities along their axes. As the KH billows intensify, these regions evolve roughly orthogonal billow cores and induced vortex tubes in close proximity. Their mutual advection as they intensify induces large-amplitude Kelvin vortex waves, or “twist waves”, that arise where locally uniform vortices are distorted by axial or radial advection. The twist waves propagate along, and fragment, the vortex tubes and billow cores, thus accounting for the emergence of helicity and the down-scale energy, enstrophy, and helicity fluxes within the turbulence inertial range. We describe the results of four direct numerical simulations (DNS) addressing KHI T&K dynamics in large and idealized small domains. The large-domain vorticity fields reveal the character and diversity of KHI T&K dynamics, the emergence of twist waves at larger and smaller scales, and their driving of turbulence transitions. Two small-domain DNS exhibit idealized KHI T&K events arising from KH billows that are mis-aligned and that exhibit phase variability along their axes. A third examines the interactions of two vortex tubes in close proximity. These reveal that twist waves drive the character and evolutions of the vorticity and helicity fields. Full article
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19 pages, 757 KiB  
Article
Log-Lattices for Atmospheric Flows
by Quentin Pikeroen, Amaury Barral, Guillaume Costa and Bérengère Dubrulle
Atmosphere 2023, 14(11), 1690; https://doi.org/10.3390/atmos14111690 - 15 Nov 2023
Viewed by 755
Abstract
We discuss how the projection of geophysical equations of motion onto an exponential grid allows the determination of realistic values of parameters at a moderate cost. This allows us to perform many simulations over a wide range of parameters, thereby leading to general [...] Read more.
We discuss how the projection of geophysical equations of motion onto an exponential grid allows the determination of realistic values of parameters at a moderate cost. This allows us to perform many simulations over a wide range of parameters, thereby leading to general scaling laws of transport efficiency that can then be used to parametrize the turbulent transport in general climate models for Earth or other planets. We illustrate this process using the equation describing heat transport in a dry atmosphere to obtain the scaling laws for the onset of convection as a function of rotation. We confirm the theoretical scaling of the critical Rayleigh number, RacE4/3, over a wide range of parameters. We have also demonstrated the existence of two regimes of convection: one laminar regime extending near the convection onset, and one turbulent regime occurring as soon as the vertical Reynolds number reaches a value of 104. We derive general scaling laws for these two regimes, both for the transport of heat and the dissipation of kinetic energy, and values of anisotropy and temperature fluctuations. Full article
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13 pages, 377 KiB  
Article
Dimensional Transitions in Turbulence: The Effects of Rotation and Stratification
by Guido Boffetta
Atmosphere 2023, 14(11), 1688; https://doi.org/10.3390/atmos14111688 - 15 Nov 2023
Viewed by 756
Abstract
The transition from two-dimensional to three-dimensional turbulence is a fascinating problem which finds applications in the study of geophysical flows. This paper briefly reviews the research in this field with emphasis on the role of rotation and stratification, two important ingredients of geophysical [...] Read more.
The transition from two-dimensional to three-dimensional turbulence is a fascinating problem which finds applications in the study of geophysical flows. This paper briefly reviews the research in this field with emphasis on the role of rotation and stratification, two important ingredients of geophysical flows at large scales. By means of direct numerical simulations of the Navier–Stokes equations, the conditions for the emergence of a split cascade, with a simultaneous cascade of energy to both the large and the small scales, are discussed. Full article
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15 pages, 10310 KiB  
Article
Evolution of a Stratified Turbulent Cloud under Rotation
by Tianyi Li, Minping Wan and Shiyi Chen
Atmosphere 2023, 14(10), 1590; https://doi.org/10.3390/atmos14101590 - 22 Oct 2023
Viewed by 978
Abstract
Localized turbulence is common in geophysical flows, where the roles of rotation and stratification are paramount. In this study, we investigate the evolution of a stratified turbulent cloud under rotation. Recognizing that a turbulent cloud is composed of vortices of varying scales and [...] Read more.
Localized turbulence is common in geophysical flows, where the roles of rotation and stratification are paramount. In this study, we investigate the evolution of a stratified turbulent cloud under rotation. Recognizing that a turbulent cloud is composed of vortices of varying scales and shapes, we start our investigation with a single eddy using analytical solutions derived from a linearized system. Compared to an eddy under pure rotation, the stratified eddy shows the physical manifestation of a known potential vorticity mode, appearing as a static stable vortex. In addition, the expected shift from inertial waves to inertial-gravity waves is observed. In our numerical simulations of the turbulent cloud, carried out at a constant Rossby number over a range of Froude numbers, stratification causes columnar structures to deviate from vertical alignment. This deviation increases with increasing stratification, slowing the expansion rate of the cloud. The observed characteristics of these columnar structures are consistent with the predictions of linear theory, particularly in their tilt angles and vertical growth rates, suggesting a significant influence of inertial-gravity waves. Using Lagrangian particle tracking, we have identified regions where wave activity dominates over turbulence. In scenarios of milder stratification, these inertial-gravity waves are responsible for a significant energy transfer away from the turbulent cloud, a phenomenon that attenuates with increasing stratification. Full article
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16 pages, 8519 KiB  
Article
Mean Flow from Phase Averages in the 2D Boussinesq Equations
by Beth A. Wingate, Juliane Rosemeier and Terry Haut
Atmosphere 2023, 14(10), 1523; https://doi.org/10.3390/atmos14101523 - 30 Sep 2023
Viewed by 776
Abstract
The atmosphere and ocean are described by highly oscillatory PDEs that challenge both our understanding of their dynamics and their numerical approximation. This paper presents a preliminary numerical study of one type of phase averaging applied to mean flows in the 2D Boussinesq [...] Read more.
The atmosphere and ocean are described by highly oscillatory PDEs that challenge both our understanding of their dynamics and their numerical approximation. This paper presents a preliminary numerical study of one type of phase averaging applied to mean flows in the 2D Boussinesq equations that also has application to numerical methods. The phase averaging technique, well-known in dynamical systems theory, relies on a mapping using the exponential operator, and then an averaging over the phase. The exponential operator has connections to the Craya–Herring basis pioneered by Jack Herring to study the fluid dynamics of oscillatory, nonlinear fluid dynamics. In this paper, we perform numerical experiments to study the effect of this averaging technique on the time evolution of the solution. We explore its potential as a definition for mean flows. We also show that, as expected from theory, the phase-averaging method can reduce the magnitude of the time rate of change in the PDEs, making them potentially suitable for time stepping methods. Full article
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21 pages, 2147 KiB  
Article
Intermittency Scaling for Mixing and Dissipation in Rotating Stratified Turbulence at the Edge of Instability
by Annick Pouquet, Duane Rosenberg, Raffaele Marino and Pablo Mininni
Atmosphere 2023, 14(9), 1375; https://doi.org/10.3390/atmos14091375 - 31 Aug 2023
Viewed by 1046
Abstract
Many issues pioneered by Jackson Herring deal with how nonlinear interactions shape atmospheric dynamics. In this context, we analyze new direct numerical simulations of rotating stratified flows with a large-scale forcing, which is either random or quasi-geostrophic (QG). Runs were performed at a [...] Read more.
Many issues pioneered by Jackson Herring deal with how nonlinear interactions shape atmospheric dynamics. In this context, we analyze new direct numerical simulations of rotating stratified flows with a large-scale forcing, which is either random or quasi-geostrophic (QG). Runs were performed at a moderate Reynolds number Re and up to 1646 turn-over times in one case. We found intermittent fluctuations of the vertical velocity w and temperature θ in a narrow domain of parameters as for decaying flows. Preliminary results indicate that parabolic relations between normalized third- and fourth-order moments of the buoyancy flux wθ and of the energy dissipation emerge in this domain, including for passive and active scalars, with or without rotation. These are reminiscent of (but not identical to) previous findings for other variables and systems such as oceanic and atmospheric flows, climate re-analysis data, fusion plasmas, the Solar Wind, or galaxies. For QG forcing, sharp scaling transitions take place once the Ozmidov length scale Oz is resolved—Oz being the scale after which a turbulent Kolmogorov energy spectrum likely recovers at high Re. Full article
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13 pages, 973 KiB  
Article
Exact Intermittent Solutions in a Turbulence Multi-Branch Shell Model
by Ben Ajzner and Alexandros Alexakis
Atmosphere 2023, 14(8), 1316; https://doi.org/10.3390/atmos14081316 - 20 Aug 2023
Viewed by 823
Abstract
Reproducing complex phenomena with simple models marks our understanding of the phenomena themselves, and this is what Jack Herring’s work demonstrated multiple times. In that spirit, this work studies a turbulence shell model consisting of a hierarchy of structures of different scales [...] Read more.
Reproducing complex phenomena with simple models marks our understanding of the phenomena themselves, and this is what Jack Herring’s work demonstrated multiple times. In that spirit, this work studies a turbulence shell model consisting of a hierarchy of structures of different scales n such that each structure transfers its energy to two substructures of scale n+1=n/λ. For this model, we construct exact inertial range solutions that display intermittency, i.e., absence of self-similarity. Using a large ensemble of these solutions, we investigate how the probability distributions of the velocity modes change with scale. It is demonstrated that, while velocity amplitudes are not scale-invariant, their ratios are. Furthermore, using large deviation theory, we show how the probability distributions of the velocity modes can be re-scaled to collapse in a scale-independent form. Finally, we discuss the implications the present results have for real turbulent flows. Full article
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19 pages, 1226 KiB  
Article
Modal Projection for Quasi-Homogeneous Anisotropic Turbulence
by Ying Zhu and Claude Cambon
Atmosphere 2023, 14(8), 1215; https://doi.org/10.3390/atmos14081215 - 28 Jul 2023
Viewed by 711
Abstract
This article, or essay, addresses the anisotropic structure and the dynamics of quasi-homogeneous, incompressible turbulence. Modal projection and expansions in terms of spherical harmonics in three-dimensional Fourier space are in line with a seminal study by Jack Herring, around the so-called Craya–Herring frame [...] Read more.
This article, or essay, addresses the anisotropic structure and the dynamics of quasi-homogeneous, incompressible turbulence. Modal projection and expansions in terms of spherical harmonics in three-dimensional Fourier space are in line with a seminal study by Jack Herring, around the so-called Craya–Herring frame of reference, with a large review of the related approaches to date. The research part is focused on structure and dynamics of rotating sheared turbulence, including a description of both directional and polarization anisotropy with a minimal number of modes. Effort is made to generalize expansions in terms of scalar spherical harmonics (SSHs) to vector spherical harmonics (VSHs). Looking at stochastic fields, for possibly intermittent vector fields, some directions are explored to reconcile modal projection, firstly used for smooth vector fields, and multifractal approaches for internal intermittency but far beyond scalar correlations, such as structure functions. In order to illustrate turbulence from Earth to planets, stars, and galaxies, applications to geophysics and astrophysics are touched upon, with generalization to coupled vector fields (for kinetic, magnetic, and potential energies), possibly dominated by waves (Coriolis, gravity, and Alfvén). Full article
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20 pages, 13271 KiB  
Article
Velocity Fluctuations Spectra in Experimental Data on Rayleigh–Taylor Mixing
by Kurt C. Williams and Snezhana I. Abarzhi
Atmosphere 2023, 14(7), 1178; https://doi.org/10.3390/atmos14071178 - 21 Jul 2023
Viewed by 794
Abstract
Rayleigh–Taylor (RT) interfacial mixing plays an important role in nature and technology, including atmospheric flows. In this work, we identify the physics properties of Rayleigh–Taylor mixing through the analysis of unprocessed experimental data. We consider the fluctuations spectra of the specific kinetic energy [...] Read more.
Rayleigh–Taylor (RT) interfacial mixing plays an important role in nature and technology, including atmospheric flows. In this work, we identify the physics properties of Rayleigh–Taylor mixing through the analysis of unprocessed experimental data. We consider the fluctuations spectra of the specific kinetic energy of each of the velocity components, and identify their spectral shapes, by employing the group theory guided foundations and the rigorous statistical method. We find the spectral shape parameters, including their mean values and relative errors, and apply the Anderson–Darling test to inspect the residuals and the goodness-of-fit. We scrupulously study the effect of the fitting window and identify, for each velocity component, the best fit interval, where the relative errors are small and the goodness of fit is excellent. We reveal that the fluctuations spectra in RT mixing experiments can be described by a compound function, being a product of a power-law and an exponential. The data analysis results unambiguously discovered the dynamic anisotropy and the dynamic bias of RT mixing and displayed the necessity to improve the design of experiments on RT mixing. Full article
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15 pages, 3997 KiB  
Article
Segregation of Fast-Reactive Species in Atmospheric Turbulent Flow
by Guy P. Brasseur, Mary Barth, Jan Kazil, Edward G. Patton and Yuting Wang
Atmosphere 2023, 14(7), 1136; https://doi.org/10.3390/atmos14071136 - 11 Jul 2023
Cited by 2 | Viewed by 881
Abstract
Atmospheric turbulence, which produces chaotic motions in the planetary boundary layer, can inhibit mixing between fast-reacting species produced or released at different locations. This segregation process modifies the effective rate at which reactions occur between these species and is not appropriately accounted for [...] Read more.
Atmospheric turbulence, which produces chaotic motions in the planetary boundary layer, can inhibit mixing between fast-reacting species produced or released at different locations. This segregation process modifies the effective rate at which reactions occur between these species and is not appropriately accounted for in coarse-resolution models, since these models assume complete mixing of tracers within each grid box. Here, we present a few examples of large-eddy simulations (LES) applied to chemically reactive species in a forested area with high emissions of biogenic hydrocarbons, an urban area rich in anthropogenic emissions, and a maritime area with high emissions of reduced sulfur species. Full article
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12 pages, 282 KiB  
Article
Average Turbulence Dynamics from a One-Parameter Kinetic Theory
by Hudong Chen, Ilya Staroselsky, Katepalli R. Sreenivasan and Victor Yakhot
Atmosphere 2023, 14(7), 1109; https://doi.org/10.3390/atmos14071109 - 04 Jul 2023
Cited by 1 | Viewed by 842
Abstract
We show theoretically that the mean turbulent dynamics can be described by a kinetic theory representation with a single free relaxation time that depends on space and time. A proper kinetic equation is constructed from the Klimontovich-type kinetic equation for fluid elements, which [...] Read more.
We show theoretically that the mean turbulent dynamics can be described by a kinetic theory representation with a single free relaxation time that depends on space and time. A proper kinetic equation is constructed from the Klimontovich-type kinetic equation for fluid elements, which satisfies the Navier–Stokes hydrodynamics exactly. In a suitably averaged form, the turbulent kinetic energy plays the role of temperature in standard molecular thermodynamics. We show that the dynamics of turbulent fluctuations resembles a collision process that asymptotically drives the mean distribution towards a Gaussian (Maxwell–Boltzmann) equilibrium form. Non-Gaussianity arises directly from non-equilibrium shear effects. The present framework overcomes the bane of most conventional turbulence models and theoretical frameworks arising from the lack of scale separation between the mean and fluctuating scales of the Navier-Stokes equation with an eddy viscous term. An averaged turbulent flow in the present framework behaves more like a flow of finite Knudsen number with finite relaxation time, and is thus more suitably described in a kinetic theory representation. Full article
26 pages, 6216 KiB  
Article
Stable Boundary Layers and Subfilter-Scale Motions
by James C. McWilliams, Charles Meneveau, Edward G. Patton and Peter P. Sullivan
Atmosphere 2023, 14(7), 1107; https://doi.org/10.3390/atmos14071107 - 04 Jul 2023
Viewed by 1195
Abstract
Recent high-resolution large-eddy simulations (LES) of a stable atmospheric boundary layer (SBL) with mesh sizes N=(5123,10243,20483) or mesh spacings =(0.78,0.39,0.2) m are analyzed. The [...] Read more.
Recent high-resolution large-eddy simulations (LES) of a stable atmospheric boundary layer (SBL) with mesh sizes N=(5123,10243,20483) or mesh spacings =(0.78,0.39,0.2) m are analyzed. The LES solutions are judged to be converged based on the good collapse of vertical profiles of mean winds, temperature, and low-order turbulence moments, i.e., fluxes and variances, with increasing N. The largest discrepancy is in the stably stratified region above the low-level jet. Subfilter-scale (SFS) motions are extracted from the LES with N=20483 and are compared to sonic anemometer fields from the horizontal array turbulence study (HATS) and its sequel over the ocean (OHATS). The results from the simulation and observations are compared using the dimensionless resolution ratio Λw/f where f is the filter width and Λw is a characteristic scale of the energy-containing eddies in vertical velocity. The SFS motions from the observations and LES span the ranges 0.1<Λw/f<20 and are in good agreement. The small, medium, and large range of Λw/f correspond to Reynolds-averaged Navier–Stokes (RANS), the gray zone (a.k.a. “Terra Incognita”), and fine-resolution LES. The gray zone cuts across the peak in the energy spectrum and then flux parameterizations need to be adaptive and account for partially resolved flux but also “stochastic” flux fluctuations that represent the turbulent correlation between the fluctuating rate of strain and SFS flux tensors. LES data with mesh 20483 will be made available to the research community through the web and tools provided by the Johns Hopkins University Turbulence Database. Full article
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22 pages, 655 KiB  
Article
Realizable Eddy Damped Markovian Anisotropic Closure for Turbulence and Rossby Wave Interactions
by Jorgen S. Frederiksen and Terence J. O’Kane
Atmosphere 2023, 14(7), 1098; https://doi.org/10.3390/atmos14071098 - 30 Jun 2023
Viewed by 694
Abstract
A realizable Eddy Damped Markovian Anisotropic Closure (EDMAC) is presented for the interaction of two-dimensional turbulence and transient waves such as Rossby waves. The structure of the EDMAC ensures that it is as computationally efficient as the eddy damped quasi normal Markovian (EDQNM) [...] Read more.
A realizable Eddy Damped Markovian Anisotropic Closure (EDMAC) is presented for the interaction of two-dimensional turbulence and transient waves such as Rossby waves. The structure of the EDMAC ensures that it is as computationally efficient as the eddy damped quasi normal Markovian (EDQNM) closure but, unlike the EDQNM, is guaranteed to be realizable in the presence of transient waves. Jack Herring’s important contributions to laying the foundations of statistical dynamical closure theories of fluid turbulence are briefly reviewed. The topics covered include equilibrium statistical mechanics, Eulerian and quasi-Lagrangian statistical dynamical closure theories, and the statistical dynamics of interactions of turbulence with topography. The impact of Herring’s work is described and placed in the context of related developments. Some of the further works that have built upon Herring’s foundations are discussed. The relationships between theoretical approaches employed in statistical classical and quantum field theories, and their overlap, are outlined. The seminal advances made by the pioneers in strong interaction fluid turbulence theory are put in perspective by comparing related developments in strong interaction quantum field theory. Full article
11 pages, 363 KiB  
Article
Statistics of the Inertial Energy Transfer Range in d-Dimensional Turbulence (2 ≤ d ≤ 3) in a Lagrangian Renormalized Approximation
by Toshiyuki Gotoh and Yukio Kaneda
Atmosphere 2023, 14(6), 1053; https://doi.org/10.3390/atmos14061053 - 20 Jun 2023
Viewed by 858
Abstract
Statistics in the inertial energy transfer range (IETR) of d-dimensional turbulence ( 2d3) are studied using a Lagrangian renormalized approximation (LRA). The LRA suggests that the energy spectrum in the IETR is given by [...] Read more.
Statistics in the inertial energy transfer range (IETR) of d-dimensional turbulence ( 2d3) are studied using a Lagrangian renormalized approximation (LRA). The LRA suggests that the energy spectrum in the IETR is given by Kd|ε¯|2/3k5/3, where Kd is a constant and ε¯ is the energy flux across wave-number k; the energy transfer is forward for dc<d3 but inverse for 2d<dc, where dc2.065; at d=dc, Kd diverges and the skewness of the longitudinal velocity difference vanishes; and the d-dependence of the two-time Lagrangian velocity correlation spectra under appropriate normalization is weak in the IETR. Full article
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22 pages, 6522 KiB  
Article
Non-Equilibrium Turbulent Transport in Convective Plumes Obtained from Closure Theory
by Nobumitsu Yokoi
Atmosphere 2023, 14(6), 1013; https://doi.org/10.3390/atmos14061013 - 12 Jun 2023
Cited by 2 | Viewed by 729
Abstract
The non-equilibrium property of turbulence modifies the characteristics of turbulent transport. With the aid of response function formalism, such non-equilibrium effects in turbulent transport can be represented by the temporal variation of the turbulent energy (K) and its dissipation rate ( [...] Read more.
The non-equilibrium property of turbulence modifies the characteristics of turbulent transport. With the aid of response function formalism, such non-equilibrium effects in turbulent transport can be represented by the temporal variation of the turbulent energy (K) and its dissipation rate (ε) along the mean stream through the advective derivatives of K and ε. Applications of this effect to the turbulent convection with plumes are considered for the first time in this work. The non-equilibrium transport effects associated with plumes are addressed in two aspects. Firstly, the effect associated with a single plume is evaluated using data measured in the recent plume/jet experiments. The second argument is developed for the collective turbulent transport associated with multiple plumes mimicking the stellar convection zone. In this second case, for the purpose of capturing the plume motions into the advective derivatives, use has to be made of the time–space double-averaging procedure, where the turbulent fluctuations are divided into the coherent or dispersion component (which represents plume motions) and the incoherent or random component. With the aid of the transport equations of the coherent velocity stress and the incoherent counterpart, the interaction between the dispersion and random fluctuations are also discussed in the context of convective turbulent flows with plumes. It is shown from these analyses that the non-equilibrium effect associated with plume motions is of a great deal of relevance in the convective turbulence modeling. Full article
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17 pages, 2067 KiB  
Article
Turbulence with Magnetic Helicity That Is Absent on Average
by Axel Brandenburg and Gustav Larsson
Atmosphere 2023, 14(6), 932; https://doi.org/10.3390/atmos14060932 - 26 May 2023
Cited by 3 | Viewed by 1010
Abstract
Magnetic helicity plays a tremendously important role when it is different from zero on average. Most notably, it leads to the phenomenon of an inverse cascade. Here, we consider decaying magnetohydrodynamic (MHD) turbulence as well as some less common examples of magnetic evolution [...] Read more.
Magnetic helicity plays a tremendously important role when it is different from zero on average. Most notably, it leads to the phenomenon of an inverse cascade. Here, we consider decaying magnetohydrodynamic (MHD) turbulence as well as some less common examples of magnetic evolution under the Hall effect and ambipolar diffusion, as well as cases in which the magnetic field evolution is constrained by the presence of an asymmetry in the number density of chiral fermions, whose spin is systematically either aligned or anti-aligned with its momentum. In all those cases, there is a new conserved quantity: the Hosking integral. We present quantitative scaling results for the magnetic integral scale as well as the magnetic energy density and its spectrum. We also compare with cases were a magnetic version of the Saffman integral is initially finite. Rotation in MHD turbulence tends to suppress nonlinearity and thereby also inverse cascading. Finally, the role of the Hosking and magnetic Saffman integrals in shell models of turbulence is examined. Full article
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11 pages, 1176 KiB  
Article
Small-Scale Anisotropy in Stably Stratified Turbulence; Inferences Based on Katabatic Flows
by Eliezer Kit and Harindra J. S. Fernando
Atmosphere 2023, 14(6), 918; https://doi.org/10.3390/atmos14060918 - 24 May 2023
Cited by 1 | Viewed by 846
Abstract
The focus of the current study is on the anisotropy of stably stratified turbulence that is not only limited to large scales and an inertial subrange but also penetrates to small-scale turbulence in the viscous/dissipation subrange on the order of the Kolmogorov scale. [...] Read more.
The focus of the current study is on the anisotropy of stably stratified turbulence that is not only limited to large scales and an inertial subrange but also penetrates to small-scale turbulence in the viscous/dissipation subrange on the order of the Kolmogorov scale. The anisotropy of buoyancy forces is well-known, including ensuing effects such as horizontal layering and pancakes structures. Laboratory experiments in the nineties by Van Atta and his students showed that the anisotropy penetrates to very small scales, but their experiments were performed only at a relatively low Reλ (i.e., at Taylor Reynolds numbers) and, therefore, did not provide convincing evidence of anisotropy penetration into viscous sublayers. Nocturnal katabatic flows having configurations of stratified parallel shear flows and developing on mountain slopes provide high Reynolds number data for testing the notion of anisotropy at viscous scales, but obtaining appropriate time series of the data representing stratified shear flows devoid of unwarranted atmospheric factors is a challenge. This study employed the “in situ” calibration of multiple hot-film-sensors collocated with a sonic anemometer that enabled obtaining a 90 min continuous time series of a “clean” katabatic flow. A detailed analysis of the structure functions was conducted in the inertial and viscous subranges at an Reλ around 1250. The results of DNS simulations by Kimura and Herring were employed for the interpretation of data. Full article
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6 pages, 1585 KiB  
Article
Review of Jackson Herring’s Early Work on Thermal Convection
by Robert M. Kerr
Atmosphere 2023, 14(6), 907; https://doi.org/10.3390/atmos14060907 - 23 May 2023
Viewed by 777
Abstract
Jack Herring had three mid-1960s numerical papers on Rayleigh-Bénard thermal convection that might seem primitive by today’s standards, but already encapsulated many of the questions that are still being asked. All of them use severely truncated versions of the incompressible Navier–Stokes–Boussinesq equations with [...] Read more.
Jack Herring had three mid-1960s numerical papers on Rayleigh-Bénard thermal convection that might seem primitive by today’s standards, but already encapsulated many of the questions that are still being asked. All of them use severely truncated versions of the incompressible Navier–Stokes–Boussinesq equations with only one, or just a few, horizontal Fourier modes. In the first two papers, 1963 and 1964, the presented results used only one Fourier mode α and three variables. The single mode’s variables are its vertical velocity profile wα(z,t), its temperature profile θα(z,t) and the horizontally uniform vertical profile of the background temperature ψ(z,t). All of the second- and third-order terms are ignored except the convective heat flux wθ¯. The objective was to find asymptotic steady-state solutions. Each paper found evidence for the one-third Nusselt versus Rayleigh scaling of NuRa1/3, originally derived from Malkus’ maximum flux principle. The 1963 paper uses free-slip upper and lower boundaries, with magnitudes of Nu that are a factor of three larger than the experiments. In the 1964 paper, by introducing no-slip/rigid boundary conditions, the magnitude of Nu dropped to within 20% of the experimental values. Both Nu(Ra) relations are in good agreement with circa-1990 direct numerical simulations (DNS). This dependence upon the boundary condition at the walls suggests that to obtain physically realistic scaling, no-slip boundary conditions are necessary. The third paper is discussed only in terms of what it might have been aiming to accomplish and its relation to the earlier free-slip results. Full article
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13 pages, 22229 KiB  
Article
Potential Vorticity Generation in Breaking Gravity Waves
by Michael L. Waite and Nicholas Richardson
Atmosphere 2023, 14(5), 881; https://doi.org/10.3390/atmos14050881 - 18 May 2023
Cited by 1 | Viewed by 1216
Abstract
Potential vorticity (PV) is an important quantity in stratified flows because it is conserved following the flow in the absence of forcing and viscous and diffusive effects. However, as shown by previous work for unstratified turbulence, viscosity and diffusion, when present, are not [...] Read more.
Potential vorticity (PV) is an important quantity in stratified flows because it is conserved following the flow in the absence of forcing and viscous and diffusive effects. However, as shown by previous work for unstratified turbulence, viscosity and diffusion, when present, are not purely dissipative and can create potential vorticity even when none is present initially. In this work, we use direct numerical simulations to investigate the viscous and diffusive generation of potential vorticity and potential enstrophy (integrated square PV) in stratified turbulence. Simulations are initialized with a two-dimensional standing internal gravity wave, which has no potential vorticity apart from some low-level random noise; as a result, all potential vorticity and enstrophy comes from viscous and diffusive effects. Significant potential enstrophy is found when the standing wave breaks, and the maximum potential enstrophy increases with increasing Reynolds number. The mechanism for the initial PV generation is spanwise diffusion of buoyancy perturbations, which grow as the standing wave three-dimensionalizes, into the direction of spanwise vorticity. The viscous and diffusive terms responsible are small-scale and are sensitive to under-resolution, so high resolution is required to obtain robust results. Full article
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20 pages, 1917 KiB  
Article
Fog Intermittency and Critical Behavior
by Kelly Y. Huang, Gabriel G. Katul, Thomas J. Hintz, Jesus Ruiz-Plancarte, Qing Wang and Harindra J. S. Fernando
Atmosphere 2023, 14(5), 875; https://doi.org/10.3390/atmos14050875 - 17 May 2023
Viewed by 1112
Abstract
The intermittency of fog occurrence (the switching between fog and no-fog) is a key stochastic feature that plays a role in its duration and the amount of moisture available. Here, fog intermittency is studied by using the visibility time series collected during the [...] Read more.
The intermittency of fog occurrence (the switching between fog and no-fog) is a key stochastic feature that plays a role in its duration and the amount of moisture available. Here, fog intermittency is studied by using the visibility time series collected during the month of July 2022 on Sable Island, Canada. In addition to the visibility, time series of air relative humidity and turbulent kinetic energy, putative variables akin to the formation and breakup conditions of fog, respectively, are also analyzed in the same framework to establish links between fog intermittency and the underlying atmospheric variables. Intermittency in the time series is quantified with their binary telegraph approximations to isolate clustering behavior from amplitude variations. It is shown that relative humidity and turbulent kinetic energy bound many stochastic features of visibility, including its spectral exponent, clustering exponent, and the growth of its block entropy slope. Although not diagnostic, the visibility time series displays features consistent with Pomeau–Manneville Type-III intermittency in its quiescent phase duration PDF scaling (3/2), power spectrum scaling (1/2), and signal amplitude PDF scaling (2). The binary fog time series exhibits properties of self-organized criticality in the relation between its power spectrum scaling and quiescent phase duration distribution. Full article
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10 pages, 372 KiB  
Article
Turbulent Convection at Very High Rayleigh Numbers and the Weakly Nonlinear Theory
by Katepalli R. Sreenivasan and Joseph J. Niemela
Atmosphere 2023, 14(5), 826; https://doi.org/10.3390/atmos14050826 - 04 May 2023
Viewed by 1300
Abstract
To provide insights into the challenging problem of turbulent convection, Jack Herring used a greatly truncated version of the complete Boussinesq equations containing only one horizontal wavenumber. In light of later observations of a robust large-scale circulation sweeping through convecting enclosures at high [...] Read more.
To provide insights into the challenging problem of turbulent convection, Jack Herring used a greatly truncated version of the complete Boussinesq equations containing only one horizontal wavenumber. In light of later observations of a robust large-scale circulation sweeping through convecting enclosures at high Rayleigh numbers, it is perhaps not an implausible point of view from which to reexamine high-Rayleigh-number data. Here we compare past experimental data on convective heat transport at high Rayleigh numbers with predictions from Herring’s model and, in fact, find excellent agreement. The model has only one unknown parameter compared to the two free parameters present in the lowest-order least-squares power-law fit. We discuss why the underlying simplistic physical picture, meant to work at Rayleigh numbers slightly past the critical value of a few thousand, is consistent with the data when the single free parameter in it is revised, over some eleven decades of the Rayleigh number—stretching from about a million to about 1017. Full article
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24 pages, 3919 KiB  
Article
Two-Dimensional Flow on the Sphere
by Rick Salmon and Nick Pizzo
Atmosphere 2023, 14(4), 747; https://doi.org/10.3390/atmos14040747 - 20 Apr 2023
Cited by 1 | Viewed by 1488
Abstract
Equilibrium statistical mechanics predicts that inviscid, two-dimensional, incompressible flow on the sphere eventually reaches a state in which spherical harmonic modes of degrees n=1 and n=2 hold all the energy. By a separate theory, such flow is static in [...] Read more.
Equilibrium statistical mechanics predicts that inviscid, two-dimensional, incompressible flow on the sphere eventually reaches a state in which spherical harmonic modes of degrees n=1 and n=2 hold all the energy. By a separate theory, such flow is static in a reference frame rotating at angular speed 2Ω/3 with respect to the inertial frame. The vorticity field in the static frame is an accident of the initial conditions, but, once established, it lasts forever under the stated assumptions. We investigate the possibility of such behavior with a stereographic-coordinate model that conserves energy and enstrophy when the viscosity vanishes. Full article
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Review

Jump to: Research

12 pages, 538 KiB  
Review
Vectorial EM Propagation Governed by the 3D Stochastic Maxwell Vector Wave Equation in Stratified Layers
by Bryce M. Barclay, Eric J. Kostelich and Alex Mahalov
Atmosphere 2023, 14(9), 1451; https://doi.org/10.3390/atmos14091451 - 18 Sep 2023
Viewed by 858
Abstract
The modeling and processing of vectorial electromagnetic (EM) waves in inhomogeneous media are important problems in physics and engineering, and new methods need to be developed to incorporate novel vector sensor technology. Vectorial phenomena of EM waves in stratified atmospheric layers can be [...] Read more.
The modeling and processing of vectorial electromagnetic (EM) waves in inhomogeneous media are important problems in physics and engineering, and new methods need to be developed to incorporate novel vector sensor technology. Vectorial phenomena of EM waves in stratified atmospheric layers can be incorporated into governing equations by retaining the gradient of the refractive index when deriving the Maxwell Vector Wave Equation (MVWE) from Maxwell’s equations. The MVWE, as opposed to the scalar wave, Helmholtz, and paraxial equations, couples the EM field components in inhomogeneous media and thus captures important physics phenomena such as depolarization. Here, recent developments are reviewed on using sensor time series data to reconstruct electromagnetic waves that propagate through stratified media. In modern applications, often many sensors can be deployed simultaneously to observe electromagnetic waves. These networks of sensors can be used to improve the quality of the reconstructed EM wave fields and cross-validate the observed sensor time series. Lastly, the effects of noisy current densities on sensor time series are considered. Generally, as the sensor observes for longer periods of time, the variance of estimates of the wave field obtained from sensor time series data increases. As a result, longer sensor observation times do not always result in better estimates of the EM wave fields, and an optimal observation time can be obtained. Full article
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12 pages, 5733 KiB  
Review
The Surprising Roles of Turbulence in Tropical Cyclone Physics
by Kerry Emanuel, Martin Velez-Pardo and Timothy W. Cronin
Atmosphere 2023, 14(8), 1254; https://doi.org/10.3390/atmos14081254 - 07 Aug 2023
Cited by 2 | Viewed by 1721
Abstract
Tropical cyclones have long been known to be powered by turbulent enthalpy fluxes from the ocean’s surface and slowed by turbulent momentum fluxes into the surface. Here, we review evidence that the development and structure of these storms are also partially controlled by [...] Read more.
Tropical cyclones have long been known to be powered by turbulent enthalpy fluxes from the ocean’s surface and slowed by turbulent momentum fluxes into the surface. Here, we review evidence that the development and structure of these storms are also partially controlled by turbulence in the outflow near the storm’s top. Finally, we present new research that shows that tropical cyclone-like, low-aspect-ratio vortices are most likely in systems in which the bottom heat flux is controlled by mechanical turbulence, and the top boundary is insulating. Full article
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13 pages, 274 KiB  
Review
The Decay of Energy and Scalar Variance in Axisymmetric Turbulence
by Peter A. Davidson
Atmosphere 2023, 14(6), 1019; https://doi.org/10.3390/atmos14061019 - 13 Jun 2023
Viewed by 654
Abstract
We review the recent progress in our understanding of the large scales in homogeneous (but anisotropic) turbulence. We focus on turbulence which emerges from Saffman-like initial conditions, in which the vortices possess a finite linear impulse. Such turbulence supports long-range velocity correlations of [...] Read more.
We review the recent progress in our understanding of the large scales in homogeneous (but anisotropic) turbulence. We focus on turbulence which emerges from Saffman-like initial conditions, in which the vortices possess a finite linear impulse. Such turbulence supports long-range velocity correlations of the form uiuj=O(r3), where u and u are separated by a distance r, and these long-range interactions dominate the dynamics of large eddies. We show that, for axisymmetric turbulence, the energy and integral scales evolve as u2~u//2~t6/5 and l~l//~t2/5, where and // indicate directions that are perpendicular and parallel to the symmetry axis, respectively. These predictions are consistent with the evidence of direct numerical simulations. Similar results are obtained for the passive scalar variance, where we find that θ2~t6/5. The primary point of novelty in our discussion of passive scalar decay is that it is based in real (rather than spectral) space, making use of an integral invariant which is a generalization of the isotropic Corrsin integral. Full article
23 pages, 366 KiB  
Review
Jackson R. Herring and the Statistical Closure Problem of Turbulence: A Review of Renormalized Perturbation Theories
by David McComb
Atmosphere 2023, 14(5), 827; https://doi.org/10.3390/atmos14050827 - 04 May 2023
Cited by 1 | Viewed by 1179
Abstract
The pioneering applications of the methods of theoretical physics to the turbulence statistical closure problem are summarised. These are: the direct-interaction approximation (DIA) of Kraichnan, the self-consistent-field theory of Edwards, and the self-consistent-field theory of Herring. Particular attention is given to the latter, [...] Read more.
The pioneering applications of the methods of theoretical physics to the turbulence statistical closure problem are summarised. These are: the direct-interaction approximation (DIA) of Kraichnan, the self-consistent-field theory of Edwards, and the self-consistent-field theory of Herring. Particular attention is given to the latter, in terms of its elegance and its pedagogical value. We then concentrate on the assessment of these theories and take the historical route of Kraichnan’s diagnosis of the failure of DIA, followed by Edwards’s analysis of the failure of his self-consistent theory, when compared to the Kolmogorov spectrum. As all three theories are closely related, these analyses also shed light on Herring’s theory. The second-generation theories that grew out of this assessment are then discussed. First, there were the Lagrangian theories, initially stemming from the work of Kraichnan and Herring, and later the purely Eulerian local energy-transfer (LET) theory. The latter is significant because its development exposes the underlying problems with the pioneering theories in terms of the basic physics of the inertial energy transfer. In particular, later work allows us to assign a unified explanation of the incompatibility of all three pioneering theories with the Kolmororov spectrum, in that they are all Markovian approximations (in wavenumber) to the non-Markovian phenomenon of fluid turbulence. In the interests of completeness, we briefly review the formalisms of Wyld and Martin, Siggia, and Rose. More recent developments are also discussed, in order to bring the subject up to the present day. Full article
8 pages, 230 KiB  
Review
Beyond Scale-by-Scale Equilibrium
by John C. Vassilicos
Atmosphere 2023, 14(4), 736; https://doi.org/10.3390/atmos14040736 - 19 Apr 2023
Cited by 2 | Viewed by 1251
Abstract
Homogeneous turbulence and turbulence in scale-by-scale equilibrium, played a leading role in the turbulence research of the second half of the twentieth century, and Jack Herring was an important contributor to these developments. The research activity which has followed these developments over the [...] Read more.
Homogeneous turbulence and turbulence in scale-by-scale equilibrium, played a leading role in the turbulence research of the second half of the twentieth century, and Jack Herring was an important contributor to these developments. The research activity which has followed these developments over the past ten to fifteen years concerns turbulence, which is out of scale-by-scale equilibrium either because it is non-stationary or because it is non-homogeneous or both. This paper is a short review of recent progress in this relatively new direction of turbulence research. Full article
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