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Camassa-Holm equations as a closure model for turbulent channel and pipe flow. (English) Zbl 1042.76525

Summary: We propose the viscous Camassa-Holm equations as a closure approximation for the Reynolds-averaged equations of the incompressible Navier-Stokes fluid. This approximation is tested on turbulent channel and pipe flows with steady mean. Analytical solutions for the mean velocity and the Reynolds shear stress are consistent with experiments in most of the flow region.

MSC:

76F02 Fundamentals of turbulence
76D05 Navier-Stokes equations for incompressible viscous fluids
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[1] H. Reichhardt, Naturwissenschaften 24/25 pp 404– (1938)
[2] H. Eckelmann, J. Fluid Mech. 65 pp 439– (1974)
[3] T. Wei, J. Fluid Mech. 204 pp 57– (1989)
[4] R. A. Antonia, J. Fluid Mech. 236 pp 579– (1992)
[5] J. Kim, J. Fluid Mech. 177 pp 133– (1987) · Zbl 0616.76071
[6] J. O. Hinze, in: Turbulence (1975)
[7] R. L. Panton, J. Fluids Eng. 119 pp 325– (1997)
[8] G. I. Barenblatt, Appl. Mech. Rev. 50 pp 413– (1997)
[9] G. I. Barenblatt, SIAM Rev. 40 pp 265– (1998) · Zbl 0947.76035
[10] A. A. Townsend, in: The Structure of Turbulent Flow (1967)
[11] D. D. Holm, Phys. Rev. Lett. 80 pp 4173– (1998)
[12] R. Camassa, Phys. Rev. Lett. 71 pp 1661– (1993) · Zbl 0972.35521
[13] J. E. Dunn, Arch. Ration. Mech. Anal. 56 pp 191– (1974) · Zbl 0324.76001
[14] J. E. Dunn, Int. J. Eng. Sci. 33 pp 689– (1995) · Zbl 0899.76062
[15] R. S. Rivlin, Q. Appl. Math. 15 pp 212– (1957) · Zbl 0079.17905
[16] A. J. Chorin, Phys. Rev. Lett. 60 pp 1947– (1988)
[17] T. H. Shih, Comput. Methods Appl. Mech. Eng. 125 pp 287– (1995)
[18] A. Yoshizawa, Phys. Fluids 27 pp 1377– (1984) · Zbl 0572.76048
[19] R. Rubinstein, Phys. Fluids A 2 pp 1472– (1990) · Zbl 0709.76068
[20] M. Abramowitz, in: Handbook of Mathematical Functions (1972) · Zbl 0543.33001
[21] L. D. Landau, in: Fluid Mechanics (1987)
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