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Original Articles

Analysis of structure function equations up to the seventh order

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Pages 1001-1032 | Received 06 Mar 2017, Accepted 13 Jun 2017, Published online: 06 Jul 2017

References

  • Kolmogorov AN. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. In: Doklady akademii nauk SSSR. Vol. 30, 1941. p. 299–303.
  • Kolmogorov AN. Dissipation of energy in locally isotropic turbulence. In: Doklady akademii nauk SSSR. Vol. 32, 1941. p. 16–18.
  • Monin AS, Yaglom AM. Statistical fluid mechanics II. Cambridge (MA): MIT Press; 1975.
  • Rotta JC. Turbulente Strömungen: eine Einführung in die Theorie und ihre Anwendung. Vol. 8. Göttingen: Universitätsverlag Göttingen; 2010.
  • Yakhot V. Mean-field approximation and a small parameter in turbulence theory. Phys Rev E. 2001;63:026307.
  • Hill RJ. Equations relating structure functions of all orders. J Fluid Mech. 2001;434:379–388.
  • Hill R. Exact second-order structure-function relationships. J Fluid Mech. 2002;468:317–326.
  • Hill RJ, Boratav ON. Next-order structure-function equations. Phys Fluids. 2001;13:276.
  • Kurien S, Sreenivasan KR. Dynamical equations for high-order structure functions, and a comparison of a mean-field theory with experiments in three-dimensional turbulence. Phys Rev E. 2001;64:056302.
  • Nakano T, Gotoh T, Fukayama D. Roles of convection, pressure, and dissipation in three-dimensional turbulence. Phys Rev E. 2003;67:026316.
  • Gotoh T, Nakano T. Role of pressure in turbulence. J Stat Phys. 2003;113:855–874.
  • Grauer R, Homann H, Pinton JF. Longitudinal and transverse structure functions in high-Reynolds-number turbulence. New J Phys. 2012;14:063016.
  • Yakhot V. Pressure-velocity correlations and scaling exponents in turbulence. J Fluid Mech. 2003;495:135–143.
  • Peters N, Boschung J, Gauding M, et al. Higher-order dissipation in the theory of homogeneous isotropic turbulence. J Fluid Mech 2016;803:250–274.
  • Frisch U. Turbulence: the legacy of AN Kolmogorov. Cambridge: Cambridge University Press.
  • Hill RJ. Opportunities for use of exact statistical equations. J Turbul. 2006; 7. Available from: http://dx.doi.org/10.1080/14685240600595636
  • Hill RJ. Applicability of Kolmogorov's and Monin's equations of turbulence. J Fluid Mech. 1997;353:67–81.
  • Lesieur M. Turbulence in fluids. Dordrecht: Kluwer Academic Publishers; 1997.
  • Oberlack M, Peters N. Closure of the two-point correlation equation as a basis for Reynolds stress models. Appl Sci Res. 1993;51:533–538.
  • Thiesset F, Antonia R, Danaila L, et al. Kármán-Howarth closure equation on the basis of a universal eddy viscosity. Phys Rev E. 2013;88:011003.
  • Schaefer P, Gampert M, Goebbert J, et al. Asymptotic analysis of homogeneous isotropic decaying turbulence with unknown initial conditions. J Turbul. 2011; 12. Available from: http://dx.doi.org/10.1080/14685248.2011.601313
  • Boschung J, Gauding M., Hennig F, et al. Finite Reynolds number corrections of the 4/5 law for decaying turbulence. Phys Rev Fluids. 2016;1:064403.
  • Siggia ED. Invariants for the one-point vorticity and strain rate correlation functions. Phys Fluids (1958–1988). 1981;24:1934–1936.
  • Boschung J. Exact relations between the moments of dissipation and longitudinal velocity derivatives in turbulent flows. Phys Rev E. 2015;92:043013.
  • Boschung J, Hennig F, Gauding M, et al. Generalised higher-order Kolmogorov scales. J Fluid Mech. 2016;794:233–251.
  • Hou TY, Li R. Computing nearly singular solutions using pseudo-spectral methods. J Comput Phys. 2007;226:379–397.
  • Eswaran V, Pope S. Direct numerical simulations of the turbulent mixing of a passive scalar. Phys Fluids. 1988;31:506–520.
  • Li N, Laizet S. 2DECOMP & FFT-A highly scalable 2D decomposition library and FFT interface. In: Cray user group 2010 conference, Edinburgh. 2010. p. 1–13. Available from: http://www.2decomp.org/
  • Ishihara T, Gotoh T, Kaneda Y. Study of high-Reynolds number isotropic turbulence by direct numerical simulation. Annu Rev Fluid Mech. 2009;41:165–180.
  • Gotoh T, Watanabe T, Suzuki Y. Universality and anisotropy in passive scalar fluctuations in turbulence with uniform mean gradient. J Turbul. 2011; 12. Available from: http://dx.doi.org/10.1080/14685248.2011.631926