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Atmosphere
Special Issues
Isotropic Turbulence: Recent Advances and Current Challenges
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Isotropic Turbulence: Recent Advances and Current Challenges

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

Deadline for manuscript submissions: 30 June 2024 | Viewed by 1689

Special Issue Editor

Prof. David McComb

E-Mail Website
Guest Editor
School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, UK
Interests: phenomenology of isotropic turbulence; statistical closure theory; renormalized perturbation theory; renormalization group; drag reduction

Special Issue Information

Dear Colleagues,

We have seen an enormous increase in the attention paid to isotropic turbulence in recent years. However, research in this field is divided into many different topics, each with its own group of adherents, which leads to a lack of informed consensus. In fact, it could be said that, when considered overall, the subject lacks both focus and direction. Of course, this is not really surprising, given the heterogeneous nature of the community studying it, which ranges from applied scientists and applied mathematicians to theoretical physicists and, more recently, pure mathematicians. Naturally, the topics studied exhibit a similar diversity, and, for this reason, we think that it will be helpful to divide them up into three broad strands. These are as follows:

  1. Fundamentals (thermodynamic aspects, validity of equations and the continuum limit, Taylor’s dissipation surrogate, Onsager’s conjecture and related physics, limit of infinite Reynolds numbers, Euler and Navier–Stokes equations driven by random inputs, and the relevance of intermittency).
  2. Phenomenology (conservation of energy, asymptotic behaviour with increasing Reynolds number, Kolmogorov (1941) theory, Onsager’s model and scale invariance of the energy flux, dimensionless dissipation, two-time correlations and temporal spectra, and finite Reynolds number effects).
  3. Statistical Theory (Eddy viscosity models, renormalized perturbation theories, Eulerian DIA and LET theories, Lagrangian theories, single-time Markovian models, mode elimination and sub-grid models, and renormalization group).

The aim of this Special Issue is to publish papers which can help to identify the most recent advances and what the current challenges are. Thus, we ask for submissions which have both a pedagogical and a review perspective. That is, they should be written to be intelligible to those outside your own subject area, and they should eschew experimental details and mathematical derivations alike, as these may be covered by references to your other published work.

Prof. David McComb
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Atmosphere is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • dissipation anomaly
  • Onsager’s conjecture
  • infinite Reynolds number limit
  • intermittency
  • scale-invariance of the inertial flux
  • temporal spectra
  • sweeping effects
  • finite Reynolds number effects
  • infrared divergence
  • Galilean invariance

Published Papers (3 papers)

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Review

12 pages, 317 KiB  
Review
Unsteady and Inhomogeneous Turbulent Fluctuations around Isotropic Equilibrium
by Wouter J. T. Bos
Atmosphere 2024, 15(5), 547; https://doi.org/10.3390/atmos15050547 - 29 Apr 2024
Viewed by 216
Abstract
Extracting statistics for turbulent flows directly from the Navier–Stokes equations poses a formidable challenge, particularly when dealing with unsteady or inhomogeneous flows. However, embracing Kolmogorov’s inertial range spectrum for isotropic turbulence as a dynamic equilibrium provides a conceptual starting point for perturbation theory. [...] Read more.
Extracting statistics for turbulent flows directly from the Navier–Stokes equations poses a formidable challenge, particularly when dealing with unsteady or inhomogeneous flows. However, embracing Kolmogorov’s inertial range spectrum for isotropic turbulence as a dynamic equilibrium provides a conceptual starting point for perturbation theory. We review theoretical results, combining perturbation approaches, and phenomenological turbulence closures, which allow us to gain valuable insights into the statistics of unsteady and inhomogeneous turbulence. Additionally, we extend the ideas to the case of the mixing of a passive scalar. Full article
(This article belongs to the Special Issue Isotropic Turbulence: Recent Advances and Current Challenges)
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18 pages, 889 KiB  
Review
Finite Reynolds Number Effect on Small-Scale Statistics of Homogeneous Isotropic Turbulence
by S. L. Tang, L. Danaila and R. A. Antonia
Atmosphere 2024, 15(5), 540; https://doi.org/10.3390/atmos15050540 - 28 Apr 2024
Viewed by 347
Abstract
Since about 1997, the realisation that the finite Reynolds number (FRN) effect needs to be carefully taken into account when assessing the behaviour of small-scale statistics came to the fore. The FRN effect can be analysed either in the real domain or in [...] Read more.
Since about 1997, the realisation that the finite Reynolds number (FRN) effect needs to be carefully taken into account when assessing the behaviour of small-scale statistics came to the fore. The FRN effect can be analysed either in the real domain or in the spectral domain via the scale-by-scale energy budget equation or the transport equation for the energy spectrum. This analysis indicates that the inertial range (IR) is established only when the Taylor microscale Reynolds number Reλ is infinitely large, thus raising doubts about published power-law exponents at finite values of Reλ, for either the second-order velocity structure function (δu)2¯ or the energy spectrum. Here, we focus on the transport equation of (δu)2¯ in decaying grid turbulence, which represents a close approximation to homogeneous isotropic turbulence. Regarding small-scale effects, the large-scale forcing term associated with streamwise advection decreases as Reλ increases and finally disappears when Reλ is sufficiently large. An approach based on the dual scaling of (δu)2¯, i.e., a scaling based on the Kolmogorov scales (when the separation r is small) and another based on the integral scales (when r is large), yields (δu)2¯∼r2/3 when Reλ is infinitely large. This approach also yields (δu)n¯∼rn/3 when Reλ is infinitely large. These results seem to be supported by the trend as Reλ increases according to the available experimental data. Overall, the results for decaying turbulence strongly suggest that a tendency towards the predictions of K41 cannot be dismissed at least at Reynolds numbers that are currently beyond the reach of experiments and direct numerical simulations. Full article
(This article belongs to the Special Issue Isotropic Turbulence: Recent Advances and Current Challenges)
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33 pages, 6490 KiB  
Review
Some Early Studies of Isotropic Turbulence: A Review
by John Z. Shi
Atmosphere 2024, 15(4), 494; https://doi.org/10.3390/atmos15040494 - 17 Apr 2024
Viewed by 467
Abstract
A re-examination of some early classic turbulence literature, mainly of isotropic turbulence, is given in this selective review. Some early studies, including original concepts and points, are reviewed or highlighted. Two earliest studies and six major original concepts are found: (i) Lord Kelvin’s [...] Read more.
A re-examination of some early classic turbulence literature, mainly of isotropic turbulence, is given in this selective review. Some early studies, including original concepts and points, are reviewed or highlighted. Two earliest studies and six major original concepts are found: (i) Lord Kelvin’s pioneering elementary studies of homogeneous, isotropic turbulence; (ii) Kelvin’s early introduction of Fourier Principles into turbulence studies; (iii) the Kelvin elementary concept of the direct energy cascade; (iv) the Kelvin early concept of the symmetry of turbulence; (v) the Taylor concept of the coefficient of eddy viscosity; (vi) the Taylor concept of the ‘age’ of the eddy; (vii) the Taylor–Fage–Townend concept of small eddies or microturbulence or small scale turbulence; and (viii) the Obukhov concept of a function of the inner Reynolds number (i.e., Re dependent coefficient) in both the balance equation and the energy distribution equation (the two-thirds law). Both Kelvin and Taylor should be regarded as the co-founders of the statistical theory of homogeneous, isotropic turbulence. The notion, ‘the Maxwell–Reynolds decomposition of turbulent flow velocity’, should be used. The Kolmogorov–Obukhov scaling laws are reviewed in detail. Heisenberg’s inverse seventh power spectrum is briefly reviewed. The implications or significances of these early studies, original concepts and points are briefly discussed, with special reference to their possible links with modern approaches and theories. Full article
(This article belongs to the Special Issue Isotropic Turbulence: Recent Advances and Current Challenges)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Statistical Dynamics and Subgrid Modelling of Turbulence: From Isotropic to Inhomogeneous
Authors: Jorgen Frederiksen, Vassili Kitsios, and Terence O'Kane

Title: Chaotic measures an alternative to spectral measures for analysing turbulent flow
Authors: Arjun Berera, Richard Ho, and Daniel Clark

Title: Isotropized turbulence: theory and modeling
Author: Claude Cambon

Title: The zeroth law of turbulence
Author: K.R. Sreenivasan

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