Abstract
The mean-velocity (U) equation (2.100) and the mean-scalar (Θ) equation (2.102) do not constitute closed systems of equations owing to the presence of the Reynolds stress R ij (= 〈u′ i u′ j 〉) and the turbulent scalar flux H θ (= 〈u′θ′〉). In turbulence modeling, we relate these quantities to U and Θ explicitly or implicitly. Here we have two primary approaches. One is the algebraic modeling represented by the turbulent-viscosity approximation to R ij , and the other is the second-order modeling, in which the transport equations for R ij and H θ , (2.105) and (2.120), are treated directly. In the former, R ij and H θ are expressed in terms of U, Θ, and some one-point quantities characterizing turbulence, such as the turbulent energy K and its dissipation rate ε. In the latter, the third-order quantities such as the pressure-strain correlation function Π ij [Eq. (2.107)] need to be modeled.
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References
Abe, K., Kondoh, T., and Nagano, Y. (1995), Intern. J. Heat Mass Transfer 38, 1467.
Abe, K., Kondoh, T., and Nagano, Y. (1997), Intern. J. Heat and Fluid Flow 18, 266.
Bardina, J., Ferziger, J. H., and Rogallo, R. S. (1985), J. Fluid Mech. 154, 321.
Comte-Bellot, G. and Corrsin, S. (1966), J. Fluid Mech. 25, 657.
Durbin, P. A. (1993), J. Fluid Mech. 249, 465.
Gatski, T. B. and Speziale, C. G. (1993), J. Fluid Mech. 254, 59.
Hallbäck, M., Johansson, A. V., and Burden, A. D. (1996), in Turbulence and Transition Modeling, edited by M. Hallbäck, D. S. Henningson, A. V. Johansson, and P. H. Alfredson ( Kluwer, Dordrecht ), p. 81.
Herring, J. R., Schertzer, D., Lesieur, M., Newman, G. R., Chollet, J. P., and Larcheveque, H. (1982), J. Fluid Mech. 124, 411.
Hunt, J. C. R. and Carruthers, D. J. (1990), J. Fluid Mech. 212, 497.
Hussain, A. K. M. F. and Reynolds, W. C. (1975), J. Fluids Engn. 97, 568.
Jacquin, L., Leuchter, O., Cambon, C., and Mathiew, J. (1990), J. Fluid Mech. 220, 1.
Kajishima, T. and Miyake, Y. (1992), Computer and Fluids. 21, 151.
Kasagi, N. and Shikazono, N. (1995), Proc. Roy. Soc. London A 451, 257.
Kasagi, N., Tornita, Y., and Kuroda, A. (1992), J. Heat Transfer 114, 598.
Kawamura, H. and Kawashima, N. (1995), in Turbulence, Heat and Mass Transfer 1, edited by K. Hanjalic and J. C. F. Pereira ( Begell House, New York ), p. 197.
Kim, J., Moin, P., and Moser, R. (1987), J. Fluid Mech. 177, 133.
Kitoh, O. (1991), J. Fluid Mech. 225, 445.
Kobayashi, T. and Togashi, S. (1996), JSME Intern. J. B 39, 453.
Launder, B. E. (1996), in Turbulence and Transition Modeling, edited by M. Hallbäck, D. S. Henningson, A. V. Johansson, and P. H. Alfredson ( Kluwer, Dordrecht ), p. 193.
Launder, B. E., Reece, G., and Rodi, W. (1975), J. Fluid Mech. 68, 537.
Launder, B. E. and Shima, N. (1989), AIAA J. 27, 1319.
Lumley, J. L. (1978), Adv. in Appl. Mech. 18, 123.
Mansour, N. N., Kim, J., and Moin, P. (1989), AIAA J. 27, 1068.
Mansour, N. N., Cambon, C., and Speziale, C. G. (1992), in Studies in Turbulence, edited by G. Gatski, S. Sarkar, and C. G. Speziale ( Springer, New York ), p. 59.
Melling, A. and Whitelaw, J. H. (1976), J. Fluid Mech. 78, 289.
Mellow, G. L. and Yamada, T. (1982), Rev. Geophys. Space Phys. 20, 851.
Murakami, S., Mochida, A., and Ooka, R. (1993), in Ninth Symposium on Turbulent Shear Flows,13–5.
Myong, H. K. and Kasagi, N. (1990), JSME Intern. J. 33, 63.
Nagano, Y. and Kim, C. (1987), Trans. JSME B 53, 1773.
Nisizima, S. (1990), Theor. Comput. Fluid Dyn. 2, 61.
Pope, S. B. (1975), J. Fluid Mech. 72, 331.
Pope, S. B. (1983), Phys. Fluids 26, 404.
Rodi, W. (1976), Z. angew. Math. Mech. 56, 219.
Rotta, J. C. (1951), Z. Phys. 129, 547.
Shih, T. -H. (1996), in Turbulence and Transition Modeling, edited by M. Hallbäck, D. S. Henningson, A. V. Johansson, and P. H. Alfredson ( Kluwer, Dordrecht ), p. 155.
Shih, T. -H., Chen, J. -Y., and Lumley, J. L. (1992), AIAA J. 30, 1553.
Shih, T. -H., Zhu, J., and Lumley, J. L. (1994), NASA TM 106644.
Shih, T. -H., Zhu, J., Liou, W., Chen, K. -H., Liu, N. -S., and Lumley, J. L. (1997), NASA TM 113112.
Shima, N (1993), J. Fluid Engn. 115, 56.
Shimomura, Y. (1997), in Eleventh Symposium on Turbulent Shear Flows,34–1.
So, R. M. C., Lai, Y. G., Zang, H. S., and Hwang, B. C. (1991), AIAA J. 29, 1819.
Speziale, C. G. (1987), J. Fluid Mech. 178, 459.
Speziale, C. G. (1991), Annu. Rev. Fluid Mech. 23, 107.
Speziale, C. G. (1997), Intern. J. Nonlinear Mech. 33, 579.
Speziale, C. G., Sarkar, S., and Gatski, T. (1991), J. Fluid Mech. 227, 245.
Stratford, B. S. (1959), J. Fluid Mech. 5, 1.
Takemitsu, N. (1987), Trans. JSME B 53, 2928.
Takemitsu, N. (1989), Trans. JSME B 55, 2684.
Takemitsu, N. (1990), J. Fluids Engn. 112, 192.
Taulbee, D. (1992), Phys. Fluids A 4, 2555.
Tavouralis, S. and Corrsin, S. (1981), J. Fluid Mech. 104, 311.
Tavouralis, S. and Corrsin, S. (1985), Intern. J. Heat Mass Transfer 28, 265.
Tennekes, H. and Lumley, J. L. (1972), A First Course in Turbulence ( The MIT, Cambridge).
Wakao, Y. and Kawamura, H. (1996), Trans. JSME B 62, 3934.
Yang, Z. and Shih, T. -H. (1993), NASA TM 106263.
Yoshizawa, A. (1984), Phys. Fluids 27, 1377.
Yoshizawa, A. (1994), Phys. Rev. E 49, 4065.
Yoshizawa, A. and Nisizima, S. (1993), Phys. Fluids A 5, 3302.
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Yoshizawa, A. (1998). Conventional Turbulence Modeling. In: Hydrodynamic and Magnetohydrodynamic Turbulent Flows. Fluid Mechanics and Its Applications, vol 48. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1810-3_4
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DOI: https://doi.org/10.1007/978-94-017-1810-3_4
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