Role of Third-Order Structure Function in Studying Two-Dimensionalisation of Turbulence
Sagar Chakraborty
备注：
This article (to be published in EJTP 2008 Landau special Issue, http://www.ejtp.com/landau.html) is a rather comprehensive review of the works done by the author on the two-dimensionalisation effect during his PhD period
发表信息：
Lev Davidovich Landau and His Impact on Contemporary Theoretical Physics, Horizons in World Physics, Volume 264, Nova Publishers (2008)
We look at various correlation functions, which include those that involve both the velocity and the vorticity fields, in two-dimensional (2D) isotropic homogeneous unforced turbulence. We adopt the more intuitive approach due to Kolmogorov (and subsequently, Landau in his text on fluid dynamics) and show that how the 2D turbulence's results, obtainable using other methods, may be established in a simpler way. Same method is used to calculate some third-order structure functions for quasi-geostrophic (QG) turbulence for the forward cascade of pseudo-potential enstrophy and the inverse energy cascade in quasi-geostrophic turbulence. These results motivate us to study the two-point third order structure function in the context of the two-dimensionalisation effect. Consequent studies enable us to give a reason for the inverse energy cascade in the two-dimensionalised rapidly rotating three dimensional (3D) incompressible turbulence. For such a system, literature shows a possibility of the exponent of wavenumber in the energy spectrum's relation to lie between -2 and -3. We argue the existence of a stricter range of -2 to -7/3 for the exponent in the case of rapidly rotating turbulence which is in accordance with the recent experiments. Also, a derivation for the two point third order structure function has been provided helping one to argue that even with slow rotation one gets, although dominated, a spectrum with the exponent -2.87, thereby hinting at the initiation of the two-dimensionalisation effect with rotation. Moreover, using the Gledzer-Ohkitani-Yamada (GOY) shell model, modified for rotation, these signatures of two-dimensionalisation effect have been verified.
A reason has been given for the inverse energy cascade in the two-dimensionalised rapidly rotating 3D incompressible turbulence. For such system, literature shows a possibility of the exponent of wavenumber in the energy spectrum's relation to lie between -2 and -3. We argue the existence of a more strict range of -2 to -7/3 for the exponent in the case of rapidly rotating turbulence which is in accordance with the recent experiments. Also, a rigorous derivation for the two point third order structure function has been provided helping one to argue that even with slow rotation one gets, though…
A form for the two-point third order structure function has been calculated for three dimensional homogeneous incompressible slowly rotating turbulent fluid. It has been argued that it may possibly hint at the initiation of the phenomenon of two-dimensionalisation of the 3D incompressible turbulence owing to rotation.
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Turbulence and Star Formation Suppression in Elliptical Galaxies: The Role of Active Galactic Nucleus Jet Wind Interaction
Astrophysics Division, Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台天体物理分部）；ShanghaiTech University（上海科技大学）；University of Chinese Academy of Sciences（中国科学院大学）；Center for Astronomy and Astrophysics and Department of Physics, Fudan University（复旦大学天文与空间科学中心及物理系）；Key Laboratory of Nuclear Physics and Ion-Beam Application (MOE), Fudan University（复旦大学核物理与离子束应用教育部重点实验室）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）
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