Inner-outer interactions of large-scale structures in turbulent channel flow.

*(English)*Zbl 1382.76124Summary: Direct numerical simulation data of turbulent channel flow (\(Re_{{\tau}}=930\)) are used to investigate the statistics of long motions of streamwise velocity fluctuations (\(u\)), and the interaction of these structures with the near-wall disturbances, which is facilitated by their associated large-scale circulations. In the log layer, the negative-\(u\) structures are organized into longer streamwise extent (\({>}3{\delta}\)) in comparison to the positive-\(u\) counterparts. Near the wall, the footprint of negative-\(u\) structures is relatively narrow in comparison to the footprint of positive-\(u\) structures. This difference is due to the opposite spanwise motions in the vicinity of the footprints, which are either congregative or dispersive depending on the circulation of the outer roll cells. Conditional sampling of the footprints shows that the spanwise velocity fluctuations (\(w\)) are significantly enhanced by the dispersive motions of high-speed structures. On the other hand, the near-wall congregative motions of negative-\(u\) structures generate relatively weak \(w\) but intense negative-\(u\) regions due, in part, to the spanwise collective migration of near-wall streaks. The concentrated near-wall regions of negative-\(u\) upwell during the merging of the outer long scales – an effect that is demonstrated using statistical analysis of the merging process. This leads to a reduction of the convection speed of downstream negative-\(u\) structures and thus promotes the merging with upstream ones. These top-down and bottom-up interactions enhance the spatial coherence of long negative-\(u\) structures in the log region.

##### MSC:

76F40 | Turbulent boundary layers |

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##### References:

[1] | Adrian, R. J., Hairpin vortex organization in wall turbulence, Phys. Fluids, 19, 4, (2007) · Zbl 1146.76307 |

[2] | Adrian, R. J.; Meinhart, C. D.; Tomkins, C. D., Vortex organization in the outer region of the turbulent boundary layer, J. Fluid Mech., 422, 1-54, (2000) · Zbl 0959.76503 |

[3] | Agostini, L.; Leschziner, M. A., On the influence of outer large-scale structures on near-wall turbulence in channel flow, Phys. Fluids, 26, 7, (2014) |

[4] | Ahn, J.; Lee, J. H.; Lee, J.; Kang, J.-H; Sung, H. J., Direct numerical simulation of a \(30R\) long turbulent pipe flow at \(Re_{{\textit\tau}}=3008\), Phys. Fluids, 27, 6, (2015) |

[5] | Del Álamo, J. C.; Jiménez, J., Spectra of the very large anisotropic scales in turbulent channels, Phys. Fluids, 15, 6, L41, (2003) · Zbl 1186.76136 |

[6] | Del Álamo, J. C.; Jiménez, J., Linear energy amplification in turbulent channels, J. Fluid Mech., 559, 205-213, (2006) · Zbl 1095.76021 |

[7] | Balakumar, B. J.; Adrian, R. J., Large- and very-large-scale motions in channel and boundary-layer flows, Phil. Trans. R. Soc. Lond. A, 365, 1852, 665-681, (2007) · Zbl 1152.76369 |

[8] | Baltzer, J. R.; Adrian, R. J.; Wu, X., Structural organization of large and very large scales in turbulent pipe flow simulation, J. Fluid Mech., 720, 236-279, (2013) · Zbl 1284.76218 |

[9] | Chung, D.; Mckeon, B. J., Large-eddy simulation of large-scale structures in long channel flow, J. Fluid Mech., 661, 341-364, (2010) · Zbl 1205.76146 |

[10] | Dennis, D. J. C.; Nickels, T. B., Experimental measurement of large-scale three-dimensional structures in a turbulent boundary layer. Part 2. Long structures, J. Fluid Mech., 673, 218-244, (2011) · Zbl 1225.76034 |

[11] | Ganapathisubramani, B., Statistical structure of momentum sources and sinks in the outer region of a turbulent boundary layer, J. Fluid Mech., 606, 225-237, (2008) · Zbl 1178.76017 |

[12] | Ganapathisubramani, B.; Hutchins, N.; Monty, J. P.; Chung, D.; Marusic, I., Amplitude and frequency modulation in wall turbulence, J. Fluid Mech., 712, 61-91, (2012) · Zbl 1275.76138 |

[13] | Ganapathisubramani, B.; Longmire, E. K.; Marusic, I., Characteristics of vortex packets in turbulent boundary layers, J. Fluid Mech., 478, 35-46, (2003) · Zbl 1032.76500 |

[14] | Guala, M.; Hommema, S. E.; Adrian, R. J., Large-scale and very-large-scale motions in turbulent pipe flow, J. Fluid Mech., 554, 521-542, (2006) · Zbl 1156.76316 |

[15] | Hoyas, S.; Jiménez, J., Scaling of the velocity fluctuations in turbulent channels up to \(Re_{{\textit\tau}}=2003\), Phys. Fluids, 18, 1, (2006) |

[16] | Hutchins, N.; Marusic, I., Evidence of very long meandering features in the logarithmic region of turbulent boundary layers, J. Fluid Mech., 579, 1-28, (2007) · Zbl 1113.76004 |

[17] | Hutchins, N.; Marusic, I., Large-scale influences in near-wall turbulence, Phil. Trans. R. Soc. Lond. A, 365, 1852, 647-664, (2007) · Zbl 1152.76421 |

[18] | Hwang, Y.; Cossu, C., Self-sustained process at large scales in turbulent channel flow, Phys. Rev. Lett., 105, 4, (2010) |

[19] | Kim, K.; Baek, S. J.; Sung, H. J., An implicit velocity decoupling procedure for the incompressible Navier-Stokes equations, Intl J. Numer. Meth. Fluids, 38, 2, 125-138, (2002) · Zbl 1059.76046 |

[20] | Kim, K. C.; Adrian, R. J., Very large-scale motion in the outer layer, Phys. Fluids, 11, 2, 417-422, (1999) · Zbl 1147.76430 |

[21] | Lee, J.; Ahn, J.; Sung, H. J., Comparison of large- and very-large-scale motions in turbulent pipe and channel flows, Phys. Fluids, 27, 2, (2015) |

[22] | Lee, J.; Lee, J. H.; Choi, J.-I.; Sung, H. J., Spatial organization of large-and very-large-scale motions in a turbulent channel flow, J. Fluid Mech., 749, 818-840, (2014) |

[23] | Lee, J. H.; Sung, H. J., Very-large-scale motions in a turbulent boundary layer, J. Fluid Mech., 673, 80-120, (2011) · Zbl 1225.76162 |

[24] | Lee, J. H.; Sung, H. J., Comparison of very-large-scale motions of turbulent pipe and boundary layer simulations, Phys. Fluids, 25, 4, (2013) |

[25] | Liu, Z.; Adrian, R. J.; Hanratty, T. J., Large-scale modes of turbulent channel flow: transport and structure, J. Fluid Mech., 448, 53-80, (2001) · Zbl 1102.76314 |

[26] | Mathis, R.; Hutchins, N.; Marusic, I., Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers, J. Fluid Mech., 628, 311-337, (2009) · Zbl 1181.76008 |

[27] | Mckeon, B. J.; Sharma, A. S., A critical-layer framework for turbulent pipe flow, J. Fluid Mech., 658, 336-382, (2010) · Zbl 1205.76138 |

[28] | Mito, Y.; Hanratty, T. J.; Zandonade, P.; Moser, R. D., Flow visualization of superbursts and of the log-layer in a DNS at \(Re_{{\textit\tau}}=950\), Flow Turbul. Combust., 79, 2, 175-189, (2007) · Zbl 1201.76092 |

[29] | Monty, J. P.; Hutchins, N.; Ng, H. C. H.; Marusic, I.; Chong, M. S., A comparison of turbulent pipe, channel and boundary layer flows, J. Fluid Mech., 632, 431-442, (2009) · Zbl 1183.76036 |

[30] | Monty, J. P.; Stewart, J. A.; Williams, R. C.; Chong, M. S., Large-scale features in turbulent pipe and channel flows, J. Fluid Mech., 589, 147-156, (2007) · Zbl 1141.76316 |

[31] | Nolan, K. P.; Zaki, T. A., Conditional sampling of transitional boundary layers in pressure gradients, J. Fluid Mech., 728, 306-339, (2013) · Zbl 1291.76106 |

[32] | Sillero, J. A.; Jiménez, J.; Moser, R. D., Two-point statistics for turbulent boundary layers and channels at Reynolds numbers up to \({\textit\delta}^{+}=2000\), Phys. Fluids, 26, 10, (2014) |

[33] | Talluru, K. M.; Baidya, R.; Hutchins, N.; Marusic, I., Amplitude modulation of all three velocity components in turbulent boundary layers, J. Fluid Mech., 746, R1, (2014) · Zbl 1416.76065 |

[34] | Toh, S.; Itano, T., Interaction between a large-scale structure and near-wall structures in channel flow, J. Fluid Mech., 524, 249-262, (2005) · Zbl 1065.76553 |

[35] | Tomkins, C. D.; Adrian, R. J., Spanwise structure and scale growth in turbulent boundary layers, J. Fluid Mech., 490, 37-74, (2003) · Zbl 1063.76514 |

[36] | Wallace, J. M.; Eckelmann, H.; Brodkey, R. S., The wall region in turbulent shear flow, J. Fluid Mech., 54, 1, 39-48, (1972) |

[37] | Wu, X.; Baltzer, J. R.; Adrian, R. J., Direct numerical simulation of a \(30R\) long turbulent pipe flow at \(R^{+}=685\): large- and very large-scale motions, J. Fluid Mech., 698, 235-281, (2012) · Zbl 1250.76116 |

[38] | Zaki, T. A., From streaks to spots and on to turbulence: exploring the dynamics of boundary layer transition, Flow Turbul. Combust., 91, 3, 451-473, (2013) |

[39] | Zhou, J.; Adrian, R. J.; Balachandar, S.; Kendall, T. M., Mechanisms for generating coherent packets of hairpin vortices in channel flow, J. Fluid Mech., 387, 353-396, (1999) · Zbl 0946.76030 |

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