B • TURBULENT FLOW 



Statistical theories of shear and inhomogeneous turbulence. In statisti- 

 cal theories of turbulence, it is important to study the structure of corre- 

 lations and spectral functions on the basis of hydrodynamical equations 

 of motion. The spectral tensor in anisotropic turbulence has a much 

 more complicated form than in isotropic turbulence. Exact mathemati- 

 cal theories are not yet possible. Dimensional arguments and simplifying 

 reasoning are necessary. If a reasonably simple equation of motion of 

 one-dimension is used, such as in Burgers' model, the solution can be 

 obtained exactly, and many characteristics of turbulence can be studied 

 without introducing simplifying assumptions at an early stage. 



Burgers, J. M. Some considerations on turbulent flow with shear. Proc. Acad. Sci. 



Amsterdam B56, 125-136, 137-147 (1953). 

 Burgers, J. M., and Mitchner, M. On homogeneous non-isotropic turbulence con- 

 nected with a mean motion having a constant velocity gradient. Proc. Acad. Sci. 



Amsterdam B56, 228-235, 343-354 (1953). 

 Kamp6 de Feriet, J. Le tenseur spectral de la turbulence homogene non isotrope 



dans un fluide incompressible. Proc. Seventh Intern. Congress Appl. Mech., 



London, 6-26 (1948). 

 von Kdrmdn, Th. The fundamentals of the statistical theory of turbulence. J. 



Aeronaut. Sci. 4, 131 (1937). 

 Monin, A. S. Characteristics of anisotropic turbulence. Doklady Akad. Nauk. 



S.S.S.R. 75, 621-624 (1950). 

 Parker, E. N. The concept of physical subsets and application to hydrodynamic 



theory. Naval Ord. Test Station Tech. Mem. 988, China Lake, Calif., 1953. 

 Rotta, J. Statische Theorie nichthomogener Turbulenz I, II. Z. Physik 129, 547 



(1951); 131, 51 (1951). 

 Tchen, C. M. On the spectrum of energy in turbulent shear flow. J. Research Natl. 



Bur. Standards 60, 51 (1953). 

 Tchen, C. M. Transport processes as foundations of the Heisenberg and Obukhoff 



theories of turbulence. Phys. Rev. 93, 4 (1954). 



Structure of turbulence in wall-bounded flow {boundary layer, channel 

 and pipe) . Turbulent measurements are made on energy, shear stresses, 

 correlation, spectral functions of energy, and shear stress. In the case of 

 the boundary layer, the flow is complicated by the fact that there exist 

 a laminar sublayer near the wall and an irregular outer limit producing 

 a region of intermittent turbulence near the free edge of the boundary 

 layer. The intermittencies and the probability of their occurrence are 

 important for the understanding of the boundary layer, and for the formu- 

 lation of a realistic theory of the boundary layer structure. Phenomeno- 

 logical theories are based on transport concepts (such as mixing length) 

 to express nonlinear turbulent terms. Other theories assume some definite 

 relation between the fourth and second orders of correlations, and a third 

 group of theories make some assumption involving physical and dimen- 

 sional reasoning on the role of the turbulent pressure. 



Chou, P. Y. On velocity correlation and the solutions of the equations of turbulent 



fluctuation. Quart. Appl. Math. 3, 38-54 (1945). 

 Chou P. Y. Pressure flow of a turbulent fluid between two infinite parallel plates. 



Quart. Appl. Math. 3, 198-209 (1945). 



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