Second-order closure models for rotating turbulent flows

Author:
Charles G. Speziale

Journal:
Quart. Appl. Math. **45** (1987), 721-733

MSC:
Primary 76U05; Secondary 76F99

DOI:
https://doi.org/10.1090/qam/917022

MathSciNet review:
917022

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Abstract: The physical properties of the commonly used second-order closure models are examined theoretically for rotating turbulent flows. Comparisons are made with results which are a rigorous consequence of the Navier--Stokes equations for the problem of fully-developed turbulent channel flow in a rapidly rotating framework. It is demonstrated that all existing second-order closures yield spurious physical results for this test problem of rotating channel flow. In fact, the results obtained are shown to be substantially more unphysical than those obtained from the simpler and models. Modifications in the basic structure of these second-order closure models are proposed which can alleviate this problem.

**[1]**C. Speziale,*Some interesting properties of two-dimensional turbulence*, Phys. Fluids**24**, 1425 (1981)**[2]**Charles G. Speziale,*Closure models for rotating two-dimensional turbulence*, Geophys. Astrophys. Fluid Dynamics**23**(1983), no. 1, 69–84. MR**693815****[3]**C. Speziale,*Modeling the pressure gradient-velocity correlation of turbulence*, Phys. Fluids**28**, 69 (1985)**[4]**A. K. Majumdar, V. S. Pratap, and D. B. Spalding,*Numerical computation of flow in rotating ducts*, ASME J. Fluids Eng.**99**, 148 (1977)**[5]**J. H. Howard, S. V. Patankar, R. M. Bordynuik,*Flow prediction in rotating ducts using Coriolis-modified turbulence models*, ASME J. Fluids Eng.**102**, 456 (1980)**[6]**J. M. Galmes and B. Lakshminarayana,*A turbulence model for three-dimensional turbulent shear flows over curved rotating bodies*, AIAA Paper 83-0559 (1983)**[7]**R. M. C. So,*A turbulent velocity scale for curved shear flows*, J. Fluid Mech.**70**, 37 (1975)**[8]**R. M. C. So and R. L. Peskin.*Comments on extended pressure-strain correlation models*, ZAMP**31**, 56 (1980)**[9]**G. L. Mellor and T. Yamada,*A hierarchy of turbulence closure models for planetary boundary layers*, J. Atmos. Sci.**31**, 1791 (1974)**[10]**Harvey Philip Greenspan,*The theory of rotating fluids*, Cambridge University Press, Cambridge-New York, 1980. Reprint of the 1968 original; Cambridge Monographs on Mechanics and Applied Mathematics. MR**639897****[11]**D. C. Haworth and S. B. Pope,*A generalized Langevin model for turbulent flows*, Phys. Fluids**29**(1986), no. 2, 387–405. MR**828171**, https://doi.org/10.1063/1.865723**[12]**J. O. Hinze,*Turbulence*, McGraw-Hill, New York, 1975**[13]**G. L. Mellor and H. J. Herring,*A survey of the mean turbulent field closure models*, AIAA J.**11**, 590 (1973)**[14]**B. E. Launder, G. Reece, and W. Rodi,*Progress in the development of a Reynolds-stress turbulence closure*, J. Fluid Mech.**68**, 537 (1975)**[15]**John L. Lumley,*Computational modeling of turbulent flows*, Advances in applied mechanics, Vol. 18, Academic Press, New York-London, 1978, pp. 123–176. MR**564894****[16]**J. P. Johnston, R. M. Halleen, and D. K. Lezius,*Effects of spanwise rotation on the structure of two-dimensional fully developed turbulent channel flow*, J. Fluid Mech.**56**, 533 [16].**[17]**C. Speziale,*Material frame-indifference in turbulence modeling*, ASME J. Appl. Mech.**51**, 942 (1984)

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DOI:
https://doi.org/10.1090/qam/917022

Article copyright:
© Copyright 1987
American Mathematical Society