Statistical Theory of Turbulence by the Late Lamented Dr. Shunichi Tsugé Case Study on Flow through a Grid in Wind Tunnel

Takeo Nakagawa, Hiroyuki Iida

School of Information Science Japan Advanced Institute of Science and Technology Nomi, Japan.
Takeo Nakagawa, Hiroyuki Iida School of Information Science Japan Advanced Institute of Science and Technology Nomi, Japan.

DOI: 10.4236/ojapps.2012.24B005                

Abstract

This paper is concerned with statistical theory of turbulence by the late lamented Dr. Shunichi Tsugé.  The theory has been applied to the primary flow through a grid fixed vertically with respect to the horizontal axis of the wind tunnel. The first analytical solution has been obtained and explained the well-known “the inverse-linear decay law” of the turbulent intensity.  It is believed that the present result is the first exact solution in the theory of turbulence.

Keywords

grid-produced turbulence;exact solution;turbulent intensity;statistical theory of turbulence;applied mathematics

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	S. Chapman, “On the kinetic theory of a gas Ⅱ,”Phil. Trans. Roy. Soc. London, vol. A217, pp.115-197, 1917.
[2]	D. Enskog, “Kinetische Theorie der Vorg?nge in m?ssig verdünten Gasen,” Dissertation, Uppsala, Sweden 1917.
[3]	H. Grad, “On the kinetic theory of rarefied gases,” Comm. Pure appl. Math. vol. 2, pp.331-407, 1949.
[4]	V. N. Zhigulev, “Equations for turbulent motion of a gas,” Soviet Physics Doklady, vol. 10, pp.1003-1005, 1966.
[5]	S. Tsugé, “On the divergent growth of molecular fluctuations in classical shear flow,” Phys. Letters, vol. 33A, pp.145-146, 1970.
[6]	L. D. Landau, and E. M. Lifshitz, Fluid Mechanics, Addison-Wesley, Mass. USA, 1959
[7]	S. Tsugé, “ Approach to origin of turbulence on the basis of two-point kinetic theory,” Phys. Fluids, vol.17, pp.22-33,1974
[8]	H. Grad, “Singular limits of solutions of Boltzmann’s equation,” in Rarefied Gas Dynamics (ed. K. Karamcheti), New York, Academic Press, pp.37-53, 1974.
[9]	T. Nakagawa, “A theory of decay of grid-produced turbulence,” ZAMM, vol.59, pp.648-651, 1979.
[10]	H. Grad, “Principles of the kinetic theory of gases,” Handbuch Der Physik, 12. Auflage, pp.205-294, 1958.
[11]	G. K. Batchelor, and A. A. Townsend, “Decay of isotropic turbulence in the initial period of turbulence,” Proc. Roy. Soc. vol. London A193, pp.539-558, 1948.