×

zbMATH — the first resource for mathematics

Dynamical eigenfunction decomposition of turbulent pipe flow. (English) Zbl 1273.76192
Summary: The results of an analysis of turbulent pipe flow based on a Karhunen-Loève decomposition are presented. The turbulent flow is generated by a direct numerical simulation of the Navier-Stokes equations using a spectral element algorithm at a Reynolds number \(Re = 150\). This simulation yields a set of basis functions that captures 90% of the energy after 2763 modes. The eigenfunctions are categorized into two classes and six subclasses based on their wavenumber and coherent vorticity structure. Of the total energy, 81% is in the propagating class, characterized by constant phase speeds; the remaining energy is found in the non-propagating subclasses, the shear and roll modes. The four subclasses of the propagating modes are the wall, lift, asymmetric and ring modes. The wall modes display coherent vorticity structures near the wall, the lift modes display coherent vorticity structures that lift away from the wall, the asymmetric modes break the symmetry about the axis, and the ring modes display rings of coherent vorticity. Together, the propagating modes form a wave packet, as found from a circular normal speed locus. The energy transfer mechanism in the flow is a four-step process. The process begins with energy being transferred from mean flow to the shear modes, then to the roll modes. Energy is then transferred from the roll modes to the wall modes, and then eventually to the lift modes. The ring and asymmetric modes act as catalysts that aid in this four-step energy transfer. Physically, this mechanism shows how the energy in the flow starts at the wall and then propagates into the outer layer.

MSC:
76F65 Direct numerical and large eddy simulation of turbulence
PDF BibTeX Cite
Full Text: DOI
References:
[1] DOI: 10.1016/S0376-0421(01)00009-4
[2] DOI: 10.1017/S0022112069000115
[3] DOI: 10.1017/S0022112095001984
[4] DOI: 10.1017/S0022112083000518 · Zbl 0556.76039
[5] DOI: 10.1063/1.868421 · Zbl 0848.76022
[6] DOI: 10.1017/S0022112099004681 · Zbl 0979.76039
[7] Loulou P., NASA Technical Memorandum-110436 (1997)
[8] DOI: 10.1017/S002211209400131X
[9] DOI: 10.1006/jcph.1996.0033 · Zbl 0849.76055
[10] DOI: 10.1006/jcph.2002.7138 · Zbl 1178.76260
[11] Lumley J. L., Atmospheric Turbulence and Radio Wave Propagation pp 166– (1967)
[12] Lumley J. L., Stochastic Tools in Turbulence (1970) · Zbl 0273.76035
[13] DOI: 10.1002/fld.1650120606 · Zbl 0721.76042
[14] DOI: 10.1063/1.857808
[15] DOI: 10.1007/BF00271470 · Zbl 0732.76046
[16] DOI: 10.1017/S0022112088001818 · Zbl 0643.76066
[17] DOI: 10.1063/1.858340 · Zbl 0762.76045
[18] DOI: 10.1103/PhysRevLett.72.340
[19] DOI: 10.1017/S0022112005005288 · Zbl 1108.76031
[20] DOI: 10.1063/1.869323 · Zbl 1185.76787
[21] DOI: 10.1002/fld.414 · Zbl 1025.76038
[22] Boyd J. P., Chebyshev and Fourier Spectral Methods (2000)
[23] DOI: 10.1016/0045-7949(88)90228-3 · Zbl 0668.76039
[24] DOI: 10.1145/331532.331599
[25] DOI: 10.1007/s10915-004-4787-3 · Zbl 1078.65570
[26] DOI: 10.1103/PhysRevLett.93.064503
[27] Gullbrand J., Center for Turbulence Research (2000)
[28] Jiménez J., Center for Turbulence Research (1998)
[29] DOI: 10.1090/qam/910462 · Zbl 0676.76047
[30] DOI: 10.1090/qam/910463
[31] DOI: 10.1090/qam/910464
[32] DOI: 10.1016/0167-2789(89)90123-1
[33] DOI: 10.1063/1.857730
[34] DOI: 10.1088/0951-7715/18/6/R01 · Zbl 1084.76033
[35] Theodorsen T., Proceedings of the Second Midwestern Conference on Fluid Mechanics pp 1– (1952)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.