Philosophical transactions. Series A, Mathematical, physical, and engineering sciences最新文献_第9页

100 years of mathematical cosmology: Models, theories, and problems, Part A 数学宇宙学的100年:模型、理论和问题，A部分

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences Pub Date : 2022-03-14 DOI: 10.1098/rsta.2021.0191

S. Cotsakis, A. Yefremov

{"title":"100 years of mathematical cosmology: Models, theories, and problems, Part A","authors":"S. Cotsakis, A. Yefremov","doi":"10.1098/rsta.2021.0191","DOIUrl":"https://doi.org/10.1098/rsta.2021.0191","url":null,"abstract":"An elementary survey of mathematical cosmology is presented. We cover certain key ideas and developments in a qualitative way, from the time of the Einstein static universe in 1917 until today. We divide our presentation into four main periods, the first one containing important cosmologies discovered until 1960. The second period (1960–80) contains discussions of geometric extensions of the standard cosmology, singularities, chaotic behaviour and the initial input of particle physics ideas into cosmology. Our survey for the third period (1980–2000) continues with brief descriptions of the main ideas of inflation, the multiverse, quantum, Kaluza-Klein and string cosmologies, wormholes and baby universes, cosmological stability and modified gravity. The last period that ends today includes various more advanced topics such as M-theoretic cosmology, braneworlds, the landscape, topological issues, the measure problem, genericity, dynamical singularities and dark energy. We emphasize certain threads that run throughout the whole period of development of theoretical cosmology and underline their importance in the overall structure of the field. This is Part A of our survey covering the first two periods of development of the subject. The second part will include the third and fourth periods. We end this outline with an inclusion of the abstracts of all papers contributed to the Philosophical Transactions of the Royal Society A theme issue, ‘The Future of Mathematical Cosmology’. This article is part of the theme issue ‘The future of mathematical cosmology, Volume 1’.","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124962402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

Weak stability and closure in turbulence. 弱稳定性和湍流闭合。

IF 5

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences Pub Date : 2022-03-07 Epub Date: 2022-01-17 DOI: 10.1098/rsta.2021.0091

C De Lellis, L Székelyhidi

引用次数: 8

A correspondence between the multifractal model of turbulence and the Navier-Stokes equations. 湍流多重分形模型与Navier-Stokes方程的对应关系。

IF 5

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences Pub Date : 2022-03-07 Epub Date: 2022-01-17 DOI: 10.1098/rsta.2021.0092

B Dubrulle, J D Gibbon

引用次数: 8

Correction to 'The added value of satellite observations of methane for understanding the contemporary methane budget'. 对“甲烷卫星观测对理解当代甲烷收支的附加价值”的修正。

IF 5

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences Pub Date : 2022-03-07 Epub Date: 2022-01-17 DOI: 10.1098/rsta.2021.0421

Paul I Palmer, Liang Feng, Mark F Lunt, Robert J Parker, Hartmut Bösch, Xin Lan, Alba Lorente, Tobias Borsdorff

引用次数: 1

Remarks on the principles of statistical fluid mechanics. 统计流体力学原理评述。

IF 5

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences Pub Date : 2022-03-07 Epub Date: 2022-01-17 DOI: 10.1098/rsta.2021.0077

Koji Ohkitani

引用次数: 2

Laws of turbulence decay from direct numerical simulations. 湍流规律从直接数值模拟中衰减。

IF 5

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences Pub Date : 2022-03-07 Epub Date: 2022-01-17 DOI: 10.1098/rsta.2021.0089

John Panickacheril John, Diego A Donzis, Katepalli R Sreenivasan

{"title":"Laws of turbulence decay from direct numerical simulations.","authors":"John Panickacheril John, Diego A Donzis, Katepalli R Sreenivasan","doi":"10.1098/rsta.2021.0089","DOIUrl":"https://doi.org/10.1098/rsta.2021.0089","url":null,"abstract":"Inspection of available data on the decay exponent for the kinetic energy of homogeneous and isotropic turbulence (HIT) shows that it varies by as much as 100%. Measurements and simulations often show no correspondence with theoretical arguments, which are themselves varied. This situation is unsatisfactory given that HIT is a building block of turbulence theory and modelling. We take recourse to a large base of direct numerical simulations and study decaying HIT for a variety of initial conditions. We show that the Kolmogorov decay exponent and the Birkhoff-Saffman decay are both observed, albeit approximately, for long periods of time if the initial conditions are appropriately arranged. We also present, for both cases, other turbulent statistics such as the velocity derivative skewness, energy spectra and dissipation, and show that the decay and growth laws are approximately as expected theoretically, though the wavenumber spectrum near the origin begins to change relatively quickly, suggesting that the invariants do not strictly exist. We comment briefly on why the decay exponent has varied so widely in past experiments and simulations. This article is part of the theme issue 'Scaling the turbulence edifice (part 1)'.","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210089"},"PeriodicalIF":5.0,"publicationDate":"2022-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39824204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

C^0,α boundary regularity for the pressure in weak solutions of the 2d Euler equations. 二维欧拉方程弱解压力的边界正则性。

IF 5

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences Pub Date : 2022-03-07 Epub Date: 2022-01-17 DOI: 10.1098/rsta.2021.0073

Claude W Bardos, Edriss S Titi

引用次数: 10

The Onsager theory of wall-bounded turbulence and Taylor's momentum anomaly. Onsager的壁面湍流理论和Taylor的动量异常。

IF 5

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences Pub Date : 2022-03-07 Epub Date: 2022-01-17 DOI: 10.1098/rsta.2021.0079

Gregory L Eyink, Samvit Kumar, Hao Quan

{"title":"The Onsager theory of wall-bounded turbulence and Taylor's momentum anomaly.","authors":"Gregory L Eyink, Samvit Kumar, Hao Quan","doi":"10.1098/rsta.2021.0079","DOIUrl":"https://doi.org/10.1098/rsta.2021.0079","url":null,"abstract":"We discuss the Onsager theory of wall-bounded turbulence, analysing the momentum dissipation anomaly hypothesized by Taylor. Turbulent drag laws observed with both smooth and rough walls imply ultraviolet divergences of velocity gradients. These are eliminated by a coarse-graining operation, filtering out small-scale eddies and windowing out near-wall eddies, thus introducing two arbitrary regularization length-scales. The regularized equations for resolved eddies correspond to the weak formulation of the Navier-Stokes equation and contain, in addition to the usual turbulent stress, also an inertial drag force modelling momentum exchange with unresolved near-wall eddies. Using an Onsager-type argument based on the principle of renormalization group invariance, we derive an upper bound on wall friction by a function of Reynolds number determined by the modulus of continuity of the velocity at the wall. Our main result is a deterministic version of Prandtl's relation between the Blasius [Formula: see text] drag law and the 1/7 power-law profile of the mean streamwise velocity. At higher Reynolds, the von Kármán-Prandtl drag law requires instead a slow logarithmic approach of velocity to zero at the wall. We discuss briefly also the large-eddy simulation of wall-bounded flows and use of iterative renormalization group methods to establish universal statistics in the inertial sublayer. This article is part of the theme issue 'Scaling the turbulence edifice (part 1)'.","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210079"},"PeriodicalIF":5.0,"publicationDate":"2022-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8762344/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39824206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Generation of intense dissipation in high Reynolds number turbulence. 高雷诺数湍流中强耗散的产生。

IF 5

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences Pub Date : 2022-03-07 Epub Date: 2022-01-17 DOI: 10.1098/rsta.2021.0088

Dhawal Buaria, Alain Pumir, Eberhard Bodenschatz

{"title":"Generation of intense dissipation in high Reynolds number turbulence.","authors":"Dhawal Buaria, Alain Pumir, Eberhard Bodenschatz","doi":"10.1098/rsta.2021.0088","DOIUrl":"https://doi.org/10.1098/rsta.2021.0088","url":null,"abstract":"Intense fluctuations of energy dissipation rate in turbulent flows result from the self-amplification of strain rate via a quadratic nonlinearity, with contributions from vorticity (via the vortex stretching mechanism) and pressure-Hessian-which are analysed here using direct numerical simulations of isotropic turbulence on up to [Formula: see text] grid points, and Taylor-scale Reynolds numbers in the range 140-1300. We extract the statistics involved in amplification of strain and condition them on the magnitude of strain. We find that strain is self-amplified by the quadratic nonlinearity, and depleted via vortex stretching, whereas pressure-Hessian acts to redistribute strain fluctuations towards the mean-field and hence depletes intense strain. Analysing the intense fluctuations of strain in terms of its eigenvalues reveals that the net amplification is solely produced by the third eigenvalue, resulting in strong compressive action. By contrast, the self-amplification acts to deplete the other two eigenvalues, whereas vortex stretching acts to amplify them, with both effects cancelling each other almost perfectly. The effect of the pressure-Hessian for each eigenvalue is qualitatively similar to that of vortex stretching, but significantly weaker in magnitude. Our results conform with the familiar notion that intense strain is organized in sheet-like structures, which are in the vicinity of, but never overlap with tube-like regions of intense vorticity due to fundamental differences in their amplifying mechanisms. This article is part of the theme issue 'Scaling the turbulence edifice (part 1)'.","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210088"},"PeriodicalIF":5.0,"publicationDate":"2022-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9289790/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39938043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 13

Transition of fluctuations from Gaussian state to turbulent state. 波动从高斯态到湍流态的跃迁。

IF 5

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences Pub Date : 2022-03-07 Epub Date: 2022-01-17 DOI: 10.1098/rsta.2021.0097

Toshiyuki Gotoh, Jingyuan Yang

{"title":"Transition of fluctuations from Gaussian state to turbulent state.","authors":"Toshiyuki Gotoh, Jingyuan Yang","doi":"10.1098/rsta.2021.0097","DOIUrl":"https://doi.org/10.1098/rsta.2021.0097","url":null,"abstract":"Variation of the statistical properties of an incompressible velocity, passive vector and passive scalar in isotropic turbulence was studied using direct numerical simulation. The structure functions of the gradients, and the moments of the dissipation rates, began to increase at about [Formula: see text] from the Gaussian state and grew rapidly at [Formula: see text] in the turbulent state. A contour map of the probability density functions (PDFs) indicated that PDF expansion of the gradients of the passive vector and passive scalar begins at around [Formula: see text], whereas that of the longitudinal velocity gradient PDF is more gradual. The left tails of the dissipation rate PDF were found to follow a power law with an exponent of 3/2 for the incompressible velocity and passive vector dissipation rates, and 1/2 for the scalar dissipation rate and the enstrophy; they remained constant for all Reynolds numbers, indicating the universality of the left tail. The analytical PDFs of the dissipation rates and enstrophy of the Gaussian state were obtained and found to be the Gamma distribution. It was shown that the number of terms contributing to the dissipation rates and the enstrophy determines the decay rates of the two PDFs for low to moderate amplitudes. This article is part of the theme issue 'Scaling the turbulence edifice (part 1)'.","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210097"},"PeriodicalIF":5.0,"publicationDate":"2022-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8762345/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39938040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5