Conditional statistics and flow structures in turbulent boundary layers buffeted by free-stream disturbances.

*(English)*Zbl 1415.76413Summary: Direct numerical simulations are performed to study zero-pressure-gradient turbulent boundary layers beneath quiescent and vortical free streams. The inflow boundary layer is computed in a precursor simulation of laminar-to-turbulence transition, and the free-stream vortical forcing is obtained from direct numerical simulations of homogeneous isotropic turbulence. A level-set approach is employed in order to objectively distinguish the boundary-layer and free-stream fluids, and to accurately evaluate their respective contributions to flow statistics. When free-stream turbulence is present, the skin friction coefficient is elevated relative to its value in the canonical boundary-layer configuration. An explanation is provided in terms of an increase in the power input into production of boundary-layer turbulence kinetic energy. This increase takes place deeper than the extent of penetration of the external perturbations towards the wall, and also despite the free-stream perturbations being void of any Reynolds shear stress. Conditional statistics demonstrate that the free-stream turbulence has two effects on the boundary layer: one direct and the other indirect. The low-frequency components of the free-stream turbulence penetrate the logarithmic layer. The associated wall-normal Reynolds stress acts against the mean shear to enhance the shear stress, which in turn enhances turbulence production. This effect directly enlarges the scale and enhances the energy of outer large-scale motions in the boundary layer. The second, indirect effect is the influence of these newly formed large-scale structures. They modulate the near-wall shear stress and, as a result, increase the turbulence kinetic energy production in the buffer layer, which is deeper than the extent of penetration of free-stream turbulence towards the wall.

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\textit{J. You} and \textit{T. A. Zaki}, J. Fluid Mech. 866, 526--566 (2019; Zbl 1415.76413)

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##### References:

[1] | Ames, F. E.; Moffat, R. J. |

[2] | Batchelor, G. K., The Theory of Homogeneous Turbulence, (1953), Cambridge University Press · Zbl 0053.14404 |

[3] | Bernardini, M.; Pirozzoli, S., Inner/outer layer interactions in turbulent boundary layers: a refined measure for the large-scale amplitude modulation mechanism, Phys. Fluids, 23, (2011) |

[4] | Bisset, D. K.; Hunt, J. C. R.; Rogers, M. M., The turbulent/non-turbulent interface bounding a far wake, J. Fluid Mech., 451, 383-410, (2002) · Zbl 1156.76397 |

[5] | Blair, M. F., Influence of free-stream turbulence on turbulent boundary layer heat transfer and mean profile development. Part I. Experimental data, Trans. ASME: J. Heat Transfer, 105, 33-40, (1983) |

[6] | Borrell, G.; Jiménez, J., Properties of the turbulent/non-turbulent interface in boundary layers, J. Fluid Mech., 801, 554-596, (2016) |

[7] | Brzek, B.; Torres-Nieves, S.; Lebrón, J.; Cal, R.; Meneveau, C.; Castillo, L., Effects of free-stream turbulence on rough surface turbulent boundary layers, J. Fluid Mech., 635, 207-243, (2009) · Zbl 1183.76012 |

[8] | Castro, I. P., Effects of free-stream turbulence on low Reynolds number boundary layers, Trans. ASME: J. Fluids Engng, 106, 298-306, (1984) |

[9] | Cheung, L. C.; Zaki, T. A., Linear and nonlinear instability waves in spatially developing two-phase mixing layers, Phys. Fluids, 22, (2010) · Zbl 1190.76024 |

[10] | Cheung, L. C.; Zaki, T. A., A nonlinear PSE method for two-fluid shear flows with complex interfacial topology, J. Comput. Phys., 230, 17, 6756-6777, (2011) · Zbl 1408.76248 |

[11] | Desjardins, O.; Moureau, V.; Pitsch, H., An accurate conservative level set/ghost fluid method for simulating turbulent atomization, J. Comput. Phys., 227, 8395-8416, (2008) · Zbl 1256.76051 |

[12] | Dogan, E.; Hanson, R. E.; Ganapathisubramani, B., Interactions of large-scale free-stream turbulence with turbulent boundary layers, J. Fluid Mech., 802, 79-107, (2016) |

[13] | Dogan, E.; Hearst, R. J.; Ganapathisubramani, B., Modelling high Reynolds number wall-turbulence interactions in laboratory experiments using large-scale free-stream turbulence, Phil. Trans. R. Soc. Lond. A, 375, 2089, (2017) |

[14] | Esteban, L.; Dogan, E.; Rodríguez-López, E.; Ganapathisubramani, B., Skin-friction measurements in a turbulent boundary layer under the influence of free-stream turbulence, Exp. Fluids, 58, (2017) |

[15] | Ganapathisubramani, B.; Hutchins, N.; Hambleton, W. T.; Longmire, E. K., Investigation of large-scale coherence in a turbulent boundary layer using two-point correlations, J. Fluid Mech., 524, 57-80, (2005) · Zbl 1060.76503 |

[16] | Hancock, P. E.; Bradshaw, P., The effect of free-stream turbulence on turbulent boundary layers, Trans. ASME: J. Fluids Engng, 105, 284-289, (1983) |

[17] | Hancock, P. E.; Bradshaw, P., Turbulence structure of a boundary layer beneath a turbulent free stream, J. Fluid Mech., 205, 45-76, (1989) |

[18] | Hearst, R. J.; Dogan, E.; Ganapathisubramani, B., Robust features of a turbulent boundary layer subjected to high-intensity free-stream turbulence, J. Fluid Mech., 851, 416-435, (2018) · Zbl 1415.76336 |

[19] | Hunt, J. C. R.; Durbin, P. A., Perturbed vortical layers and shear sheltering, Fluid Dyn. Res., 24, 6, 375-404, (1999) · Zbl 1006.01511 |

[20] | 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 |

[21] | Hwang, J.; Lee, J.; Sung, H. J.; Zaki, T. A., Inner-outer interactions of large-scale structures in turbulent channel flow, J. Fluid Mech., 790, 128-157, (2016) · Zbl 1382.76124 |

[22] | Jelly, T. O.; Jung, S. Y.; Zaki, T. A., Turbulence and skin friction modification in channel flow with streamwise-aligned superhydrophobic surface texture, Phys. Fluids, 26, (2014) |

[23] | Jiménez, J.; Hoyas, S.; Simens, M. P.; Mizuno, Y., Turbulent boundary layers and channels at moderate Reynolds numbers, J. Fluid Mech., 657, 335-360, (2010) · Zbl 1197.76063 |

[24] | Jung, S. Y.; Zaki, T. A., The effect of a low-viscosity near-wall film on bypass transition in boundary layers, J. Fluid Mech., 772, 330-360, (2015) |

[25] | Lee, J.; Jung, S. Y.; Sung, H. J.; Zaki, T. A., Effect of wall heating on turbulent boundary layers with temperature-dependent viscosity, J. Fluid Mech., 726, 196-225, (2013) · Zbl 1287.76136 |

[26] | Lee, J.; Sung, H. J.; Zaki, T. A., Signature of large-scale motions on turbulent/non-turbulent interface in boundary layers, J. Fluid Mech., 819, 165-187, (2017) · Zbl 1383.76238 |

[27] | Li, Q.; Schlatter, P.; Henningson, D. S., Simulations of heat transfer in a boundary layer subject to free-stream turbulence, J. Turbul., 11, 45, 1-33, (2010) |

[28] | 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 |

[29] | Nagata, K.; Sakai, Y.; Komori, S., Effects of small-scale freestream turbulence on turbulent boundary layers with and without thermal convection, Phys. Fluids, 23, (2011) |

[30] | Nagib, H. M.; Chauhan, K. A.; Monkewitz, P. A., Approach to an asymptotic state for zero pressure gradient turbulent boundary layers, Phil. Trans. R. Soc. Lond. A, 365, 755-770, (2007) · Zbl 1152.76412 |

[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] | Osher, S.; Sethian, J. A., Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79, 12-49, (1988) · Zbl 0659.65132 |

[33] | Péneau, F.; Boisson, H. C.; Djilali, N., Large eddy simulation of the influence of high free-stream turbulence on a spatially evolving boundary layer, Intl J. Heat Fluid Flow, 21, 640-647, (2000) |

[34] | Peng, D.; Merriman, B.; Osher, S.; Zhao, H.; Kang, M., A PDE-based fast local level set method, J. Comput. Phys., 155, 2, 410-438, (1999) · Zbl 0964.76069 |

[35] | Pope, S. B., Turbulent Flows, (2000), Cambridge University Press · Zbl 0966.76002 |

[36] | Renard, N.; Deck, S., A theoretical decomposition of mean skin friction generation into physical phenomena across the boundary layer, J. Fluid Mech., 790, 339-367, (2016) · Zbl 1382.76056 |

[37] | Rosenfeld, M.; Kwak, D.; Vinokur, M., A fractional step solution method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems, J. Comput. Phys., 94, 102-137, (1991) · Zbl 0718.76079 |

[38] | Schlatter, P.; Li, Q.; Brethouwer, G.; Johansson, A. V.; Henningson, D. S., Simulations of spatially evolving turbulent boundary layers up to Re_𝜃 = 4300, Intl J. Heat Fluid Flow, 31, 251-261, (2010) |

[39] | Schlatter, P.; Örlü, R., Assessment of direct numerical simulation data of turbulent boundary layers, J. Fluid Mech., 659, 116-126, (2010) · Zbl 1205.76139 |

[40] | Schlatter, P.; Örlü, R., Turbulent boundary layers at moderate Reynolds numbers: inflow length and tripping effects, J. Fluid Mech., 710, 5-34, (2012) · Zbl 1275.76144 |

[41] | Sharp, N. S.; Neuscamman, S.; Warhaft, Z., Effects of large-scale free stream turbulence on a turbulent boundary layer, Phys. Fluids, 21, (2009) · Zbl 1183.76470 |

[42] | Da Silva, C. B.; Hunt, J. C. R.; Eames, I.; Westerweel, J., Interfacial layers between regions of different turbulence intensity, Annu. Rev. Fluid Mech., 46, 567-590, (2014) · Zbl 1297.76074 |

[43] | Simonich, J. C.; Bradshaw, P., Effect of free-stream turbulence on heat transfer through a turbulent boundary layer, Trans. ASME: J. Heat Transfer, 100, 671-677, (1978) |

[44] | Thole, K. A.; Bogard, D. G., Enhanced heat transfer and shear stress due to high free-stream turbulence, Trans. ASME: J. Turbomach., 117, 418-424, (1995) |

[45] | Thole, K. A.; Bogard, D. G., High freestream turbulence effects on turbulent boundary layers, Trans. ASME: J. Fluids Engng, 118, 276-284, (1996) |

[46] | Wallace, J. M., Quadrant analysis in turbulence research: history and evolution, Annu. Rev. Fluid Mech., 48, 131-158, (2016) · Zbl 1356.76107 |

[47] | Zaki, T. A.; Durbin, P. A., Mode interaction and the bypass route to transition, J. Fluid Mech., 531, 85-111, (2005) · Zbl 1070.76024 |

[48] | Zaki, T. A.; Saha, S., On shear sheltering and the structure of vortical modes in single- and two-fluid boundary layers, J. Fluid Mech., 626, 111-147, (2009) · Zbl 1171.76365 |

[49] | Zalesak, S. T., Fully multi-dimensional flux-corrected transport algorithms for fluids, J. Comput. Phys., 31, 335-362, (1979) · Zbl 0416.76002 |

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.