Turbulence Mechanics in Progress—From Classical to Postclassical

Abstract

This paper explains the basic steps form the classical turbulence mechanics (CTM) to the postclassical turbulence mechanics (PCTM). When the CTM stems from the characterization of the motion states in the infinitesimal surroundings of the flowfield points by the flow velocity at these points then the PCTM complements this characterization by the curvature of the velocity fluctuation streamlines passing these points. The complementation is formalized by the inclusion of the curvature of the velocity fluctuation streamlines to the arguments of the probability distribution of the motion states in the infinitesimal surroundings of the flow field points. The most radical physical outcome of the realized formalism is the characterization of the turbulence viscosity properties by two types of turbulence viscosity against only one shear viscosity within the CTM.

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J. Heinloo, "Turbulence Mechanics in Progress—From Classical to Postclassical," World Journal of Mechanics, Vol. 3 No. 4, 2013, pp. 224-229. doi: 10.4236/wjm.2013.34022.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] J. Boussinesq, “Théorie de l’Ecoulement Tourbillant,” Mém. prés. Acad. Sci., Vol. XXIII, 1877, p. 46.
[2] O. Reynolds, “On the Dynamical Theory of Incompressible Viscous Fluids and Determination of the Criterion,” Philosophical Transactions of the Royal Society, Vol. 186, 1884, pp. 123-161.
[3] L. Prandtl, “über die Ausgebildete Turbulentz,” ZAMM, Vol. 5, 1925, pp. 136-139.
[4] G. I. Taylor, “The Transport of Vorticity and Heat through Fluids in Turbulent Motion,” Proceedings of the Royal Society A, Vol. 135, 1932, pp. 685-705.
[5] D. C. Wilcox, “Turbulence Modeling for CFD,” 2nd Edition, DCW Industries, Anaheim, 1998.
[6] B. E. Launder and B. I. Sharma, “Application of the Energy Dissipation Model of Turbulence to the Calculation of Flow near a Spinning Disc,” Letters in Heat and Mass Transfer, Vol. 1, No. 2, 1974, pp. 131-138.
[7] L. F. Richardson, “Weather Prediction by Numerical Pro cess,” Cambridge University Press, Cambridge, 1922.
[8] A. N. Kolmogorov, “The Local Structure of Turbulence in Incompressible Viscous Fluids for Very Large Reynolds Numbers,” Doklady Akademii Nauk SSSR, Vol. 30, 1941, pp. 376-387 (in Russian).
[9] J. Heinloo, “Formulation of Turbulence Mechanics,” Physical Review E, Vol. 69, 2004, Article ID: 056317. doi:10.1103/PhysRevE.69.056317
[10] J. Heinloo, “Postclassical Turbulence Mechanics,” Journal of Modern Physics, Vol. 4, No. 4, 2013, pp. 505-516. doi:10.4236/jmp.2013.44072
[11] J. Heinloo, “Physical Doctrine of Turbulence,” International Journal of Research and Reviews in Applied Sciences, Vol. 12, No. 2, 2012, pp. 214-221.
[12] J. Heinloo, “On Description of Stochastic Systems,” Proceedings of the Estonian Academy of Sciences, Physics and Mathematics, Vol. 53, No. 3, 2004, pp. 186-200.
[13] J. Heinloo, “A Setup of Systemic Description of Fluids Motion,” Proceedings of the Estonian Academy of Sciences, Vol. 58, No. 3, 2009, pp. 184-189. doi:10.3176/proc.2009.3.05
[14] A. Ishiara, “Statistical Physics,” Academic Press, New York, London, 1971.
[15] L. I. Sedov, “A Course in Continuum Mechanics,” Kluwer, 1987.
[16] M. Lesieur, O. Métais and P Comte, “Large-Eddy Simulations of Turbulence,” Cambridge University Press, Cam bridge, 2005. doi:10.1017/CBO9780511755507
[17] P. Sagaut, “Large Eddy Simulation for Incompressible Flows,” Springer, Berlin, Heidelberg, 2006.
[18] G. D. Mattioli, “Teoria Dinamica dei Regimi Fluidi Turbolenti,” Padova, 1937.
[19] A. C. Eringen, “Micromorphic Description of Turbulent Channel Flow,” Journal of Mathematical Analysis and Applications, Vol. 39, No. 1, 1972, pp. 253-266. doi:10.1016/0022-247X(72)90239-9
[20] A. C. Eringen and T. S. Chang, “Micropolar Description of Hydrodynamic Turbulence,” Advances in Materials Science and Engineering, Vol. 5, No. 1, 1970, pp.1-8.
[21] J. Peddieson, “An Application of the Micropolar Fluid Model to Calculation of Turbulent Shear Flow,” International Journal of Engineering Science, Vol. 10, No. 1, 1972, pp. 23-32. doi:10.1016/0020-7225(72)90072-9
[22] W. C. Reynolds, C. A. Langer and S. C. Kassinos, “Struc ture and Scales in Turbulence Modeling,” Physics of Flu ids, Vol. 14, No. 7, 2002, pp. 2485-2492. doi.10.1063/1.1473784
[23] S. C. Kassinos and W. C. Reynolds, “Developments in Structure-Based Turbulence Modeling,” In: M. D. Salas, J. N. Hefner and L. Sakell, Eds., Modeling Complex Turbulent Flows, Kluwer, 1999, pp. 69-87.
[24] J. Heinloo, “The Structure of Average Turbulent Flow Field,” Central European Journal of Physics, Vol. 8, No. 1, 2010, pp. 17-24. doi:10.2478/s11534-009-0015-y
[25] J. Heinloo, “Setup of Turbulence Mechanics Accounting for a Preferred Orientation of Eddy Rotation,” Concepts of Physics, Vol. 5, No. 2, 2008, pp. 205-219. doi:10.2478/v10005-007-0033-8
[26] J. Heinloo, “A Generalized Setup of the Turbulence De scription,” Advanced Studies in Theoretical Physics, Vol. 5, No. 10, 2011, pp. 477-483.
[27] T. Ariman, M. A. Turk and D. O. Silvester, “Microcontinuum Fluid Mechanics A Review,” International Journal of Engineering Science, Vol. 11, No. 8, 1973, pp. 905-930. doi:10.1016/0020-7225(73)90038-4
[28] D. W. Condiff and J. S. Dahler, “Fluid Mechanical Aspects of Antisymmetric Stress,” Physics of Fluids, Vol. 7, 1964, pp. 842-854. doi.org/10.1063/1.1711295
[29] J. S. Dahler, “Transport Phenomena in a Fluid Composed of Diatomic Molecules,” Journal of Chemical Physics, Vol. 30, 1959, pp. 1447-1475. doi.org/10.1063/1.1730220
[30] J. S. Dahler and L. F. Scriven, “Angular Momentum of Continua,” Nature, Vol. 192, No. 4797, 1961, pp. 36-37. doi:10.1038/192036a0
[31] J. S. Dahler and L. F. Scriven, “Theory of Structured Continua: General Consideration of Angular Momentum and Polarization,” Proceedings of the Royal Society, Vol. A275, 1963, pp. 504-527.
[32] A. C. Eringen, “Theory of Micropolar Fluids,” Mathematics and Mechanics, Vol. 16, No. 1, 1966, pp. 1-18.
[33] A. C. Eringen, “Mechanics of Micropolar Continua,” In: E. Kroner, Ed., Mechanics of Generalized Continua, Springer-Verlag, Berlin, 1968, pp. 18-35.
[34] P. Starr, “Physics of Negative Viscosity Phenomena,” McGrav-Hill, New York, 1968.
[35] J. Heinloo and A. Toompuu, “Gyration Effect of the Large-Scale Turbulence in the Upper Ocean,” Environ mental Fluid Mechanics, Vol. 12, No. 5, 2012, pp. 429-438. doi:10.1007/s10652-012-9247-2

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