A Lagrangian dynamic subgrid-scale model of turbulence. (English) Zbl 0882.76029

Meneveau, Charles; Lund, Thomas S.; Cabot, William H.

J. Fluid Mech. 319, 353-385 (1996).

We introduce a new dynamic model formulation that combines advantages of the statistical and local approaches. We propose to accumulate the averages over flow pathlines rather than over directions of statistical homogeneity. This procedure allows the application of the dynamic model with averaging to inhomogeneous flows in complex geometries. We analyse direct numerical simulation data to document the effects of such averaging on the Smagorinsky coefficient. The characteristic Lagrangian time scale over which the averaging is performed is chosen based on measurements of the relevant Lagrangian autocorrelation functions, and on the requirement that the model is purely dissipative, guaranteeing numerical stability when coupled with the Smagorinsky model. The formulation is tested in forced and decaying isotropic turbulence and in fully developed and transitional channel flow.

MSC:

76F05	Isotropic turbulence; homogeneous turbulence
76F10	Shear flows and turbulence

Keywords:

averages over flow pathlines; inhomogeneous flows in complex geometries; Lagrangian autocorrelation functions; Smagorinsky model; transitional channel flow

References:

[1]	DOI: 10.1007/BF00849115 · doi:10.1007/BF00849115
[2]	DOI: 10.1063/1.857955 · Zbl 0825.76334 · doi:10.1063/1.857955
[3]	DOI: 10.1017/S0022112071001599 · doi:10.1017/S0022112071001599
[4]	DOI: 10.1017/S002211207900001X · Zbl 0394.76052 · doi:10.1017/S002211207900001X
[5]	DOI: 10.1063/1.868911 · Zbl 1086.76032 · doi:10.1063/1.868911
[6]	DOI: 10.1175/1520-0469(1981)038 2.0.CO;2 · doi:10.1175/1520-0469(1981)038 · doi:2.0.CO;2
[7]	DOI: 10.1017/S0022112091001957 · Zbl 0721.76036 · doi:10.1017/S0022112091001957
[8]	DOI: 10.1063/1.857878 · Zbl 0718.76050 · doi:10.1063/1.857878
[9]	DOI: 10.1063/1.858537 · Zbl 0781.76044 · doi:10.1063/1.858537
[10]	DOI: 10.1063/1.868585 · Zbl 1032.76559 · doi:10.1063/1.868585
[11]	Schumann, Proc. R. Soc. Lond. 451 pp 293– (1995)
[12]	DOI: 10.1017/S0022112094000753 · Zbl 0804.76040 · doi:10.1017/S0022112094000753
[13]	Rogallo, NASA Tech. Memo 65 pp 224– (1981)
[14]	Bardina, AIAA Paper none pp none– (1980)
[15]	DOI: 10.1016/0010-4655(91)90175-K · Zbl 0900.76079 · doi:10.1016/0010-4655(91)90175-K
[16]	DOI: 10.1063/1.868607 · Zbl 1039.76514 · doi:10.1063/1.868607
[17]	DOI: 10.1063/1.858586 · doi:10.1063/1.858586
[18]	DOI: 10.1017/S0022112094002296 · doi:10.1017/S0022112094002296
[19]	DOI: 10.1063/1.858280 · doi:10.1063/1.858280
[20]	Lilly, Proc. IBM Sci. Comput. Symp. on Environmental Sciences 91 pp 195– (1967)
[21]	DOI: 10.1017/S0022112079000045 · Zbl 0411.76045 · doi:10.1017/S0022112079000045
[22]	DOI: 10.1063/1.857779 · doi:10.1063/1.857779
[23]	DOI: 10.1175/1520-0469(1976)033 2.0.CO;2 · doi:10.1175/1520-0469(1976)033 · doi:2.0.CO;2
[24]	DOI: 10.1017/S0022112087000892 · Zbl 0616.76071 · doi:10.1017/S0022112087000892
[25]	DOI: 10.1017/S0022112093002393 · Zbl 0800.76156 · doi:10.1017/S0022112093002393
[26]	Hussain, Stanford Univ. Dept. of Mech. Eng. Rep. 286 pp 229– (1970)
[27]	DOI: 10.1017/S0022112095000711 · Zbl 0837.76032 · doi:10.1017/S0022112095000711
[28]	DOI: 10.1063/1.858675 · Zbl 0925.76242 · doi:10.1063/1.858675
[29]	Morris, Bull. Am. Phys. Soc. 39 pp 1896– (1994)
[30]	Meneveau, Proc. Summer Program 1992 Stanford University 6 pp 61– (1992)
[31]	DOI: 10.1063/1.868170 · Zbl 0828.76038 · doi:10.1063/1.868170
[32]	DOI: 10.1063/1.868320 · Zbl 0825.76279 · doi:10.1063/1.868320
[33]	McMillan, AIAA J. 17 pp 1340– (1979)
[34]	DOI: 10.1017/S0022112092002271 · Zbl 0765.76039 · doi:10.1017/S0022112092002271