Response of the temporal turbulent boundary layer to decaying free-stream turbulence.

*(English)*Zbl 07207858Summary: The turbulent boundary layer developing under a turbulence-laden free stream is numerically investigated using the temporal boundary layer framework. This study focuses on the interaction between the fully turbulent boundary layer and decaying free-stream turbulence. Previous experiments and simulations of this physical problem have considered a spatially evolving boundary layer beset by free-stream turbulence. The state of the boundary layer at any given downstream position in fact reflects the accumulated history of the co-evolution of boundary layer and free-stream turbulence. The central aim of the present work is to isolate the effect of local free-stream disturbances existing at the same time as the ‘downstream’ boundary layer. The temporal framework used here helps expose when and how disturbances directly above the boundary layer actively impart change upon it. The bulk of our simulations were completed by seeding the free stream above boundary layers that were ‘pre-grown’ to a desired thickness with homogeneous isotropic turbulence from a precursor simulation. Moreover, this strategy allowed us to test various combinations of the turbulence intensity and large-eddy length scale of the free-stream turbulence with respect to the corresponding scales of the boundary layer. The relative large-eddy turnover time scale between the free-stream turbulence and the boundary layer emerges as an important parameter in predicting if the free-stream turbulence and boundary layer interaction will be ‘strong’ or ‘weak’ before the free-stream turbulence eventually fades to a negligible level. If the large-eddy turnover time scale of the free-stream turbulence is much smaller than that of the boundary layer, the interaction will be ‘weak’, as the free-stream disturbances will markedly decay before the boundary layer is able be altered significantly as a result of the free-stream disturbances. For a ‘strong’ interaction, the injected free-stream turbulence causes increased spreading of the boundary layer away from the wall, permitting large incursions of free-stream fluid deep within it.

##### MSC:

76 | Fluid mechanics |

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\textit{M. Kozul} et al., J. Fluid Mech. 896, Paper No. A11, 32 p. (2020; Zbl 07207858)

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[1] | Antonia, R. A., Lee, S. K., Djenidi, L., Lavoie, P. & Danaila, L.2013Invariants for slightly heated decaying grid turbulence. J. Fluid Mech.727, 379-406. · Zbl 1291.76155 |

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

[3] | Bernardini, M., Pirozzoli, S., Quadrio, M. & Orlandi, P.2013Turbulent channel flow simulations in convecting reference frames. J. Comput. Phys.232, 1-6. |

[4] | Blair, M. F.1983aInfluence of free-stream turbulence on turbulent boundary layer heat transfer and mean profile development, Part I - Experimental data. Trans. ASME C: J. Heat Transfer105, 33-40. |

[5] | Blair, M. F.1983bInfluence of free-stream turbulence on turbulent boundary layer heat transfer and mean profile development, Part II - Analysis of results. Trans. ASME C: J. Heat Transfer105, 41-47. |

[6] | Bradshaw, P.1996Turbulence modeling with application to turbomachinery. Prog. Aerosp. Sci.32, 575-624. |

[7] | Brandt, L., Schlatter, P. & Henningson, D. S.2004Transition in boundary layers subject to free-stream turbulence. J. Fluid Mech.517, 167-198. · Zbl 1131.76326 |

[8] | Carati, D., Ghosal, S. & Moin, P.1995On the representation of backscatter in dynamic localization models. Phys. Fluids7, 606-616. · Zbl 1032.76559 |

[9] | Castro, I. P.1984Effects of free stream turbulence on low Reynolds number boundary layers. Trans. ASME I: J. Fluids Engng106, 298-306. |

[10] | Chung, D. & Matheou, G.2012Direct numerical simulation of stationary homogeneous stratified sheared turbulence. J. Fluid Mech.696, 434-467. · Zbl 1250.76098 |

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

[12] | Hack, M. J. P. & Zaki, T. A.2014Streak instabilities in boundary layers beneath free-stream turbulence. J. Fluid Mech.741, 280-315. |

[13] | Hancock, P. E.1980 The effect of free-stream turbulence on turbulent boundary layers. PhD thesis, Imperial College, University of London. |

[14] | Hancock, P. E. & Bradshaw, P.1983The effect of free-stream turbulence on turbulent boundary layers. Trans. ASME I: J. Fluids Engng105, 284-289. |

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

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

[17] | Hearst, R. J. & Lavoie, P.2016Effects of multi-scale and regular grid geometries on decaying turbulence. J. Fluid Mech.803, 528-555. |

[18] | Hoyas, S. & Jiménez, J.2008Reynolds number effects on the Reynolds-stress budgets in turbulent channels. Phys. Fluids20, 101511. · Zbl 1182.76330 |

[19] | Huang, M.-J. & Leonard, A.1994Power-law decay of homogeneous turbulence at low Reynolds numbers. Phys. Fluids6, 3765-3775. · Zbl 0832.76031 |

[20] | Ishida, T., Davidson, P. A. & Kaneda, Y.2006On the decay of isotropic turbulence. J. Fluid Mech.564, 455-475. · Zbl 1100.76028 |

[21] | Kaminski, A. K. & Smyth, W. D.2019Stratified shear instability in a field of pre-existing turbulence. J. Fluid Mech.862, 639-658. · Zbl 1415.76274 |

[22] | Kaneda, Y., Ishihara, T., Yokokawa, M., Itakura, K. & Uno, A.2003Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box. Phys. Fluids15, L21-L24. · Zbl 1185.76191 |

[23] | Kozul, M., Chung, D. & Monty, J. P.2016Direct numerical simulation of the incompressible temporally developing turbulent boundary layer. J. Fluid Mech.796, 437-472. |

[24] | Kreilos, T., Khapko, T., Schlatter, P., Duguet, Y., Henningson, D. S. & Eckhardt, B.2016Bypass transition and spot nucleation in boundary layers. Phys. Rev. Fluids1, 043602. · Zbl 1284.76106 |

[25] | Krogstad, P.-Å. & Davidson, P. A.2010Is grid turbulence Saffman turbulence?J. Fluid Mech.642, 373-394. · Zbl 1183.76749 |

[26] | Lavoie, P., Djenidi, L. & Antonia, R. A.2007Effects of initial conditions in decaying turbulence generated by passive grids. J. Fluid Mech.585, 395-420. · Zbl 1118.76008 |

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

[28] | Mansour, N. N. & Wray, A. A.1994Decay of isotropic turbulence at low Reynolds number. Phys. Fluids6, 808-814. · Zbl 0825.76278 |

[29] | Mydlarski, L. & Warhaft, Z.1996On the onset of high-Reynolds-number grid-generated wind tunnel turbulence. J. Fluid Mech.320, 331-368. |

[30] | Nagata, K., Sakai, Y. & Komori, S.2011Effects of small-scale freestream turbulence on turbulent boundary layers with and without thermal convection. Phys. Fluids23, 065111. |

[31] | Pal, A. & Sarkar, S.2015Effect of external turbulence on the evolution of a wake in stratified and unstratified environments. J. Fluid Mech.772, 361-385. |

[32] | Péneau, F., Boisson, H. C. & Djilali, N.2000Large eddy simulation of the influence of high free-stream turbulence on a spatially evolving boundary layer. Intl J. Heat Fluid Flow21, 640-647. |

[33] | Perot, J. B.1993An analysis of the fractional step method. J. Comput. Phys.108, 51-58. · Zbl 0778.76064 |

[34] | Pirozzoli, S., Bernardini, M. & Orlandi, P.2016Passive scalars in turbulent channel flow at high Reynolds number. J. Fluid Mech.788, 614-639. · Zbl 1381.76109 |

[35] | Pope, S. B.2000Turbulent Flows. Cambridge University Press. |

[36] | Rind, E. & Castro, I. P.2012Direct numerical simulation of axisymmetric wakes embedded in turbulence. J. Fluid Mech.710, 482-504. · Zbl 1275.76128 |

[37] | Rogallo, R. S.1981 Numerical experiments in homogeneous turbulence. NASA TM 81315. |

[38] | Saffman, P. G.1967The large-scale structure of homogeneous turbulence. J. Fluid Mech.27, 581-593. · Zbl 0148.22403 |

[39] | Sanderse, B., Verstappen, R. W. C. P. & Koren, B.2014Boundary treatment for fourth-order staggered mesh discretizations of the incompressible Navier-Stokes equations. J. Comput. Phys.257, 1472-1505. · Zbl 1351.76182 |

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

[41] | Sharp, N. S., Neuscamman, S. & Warhaft, Z.2009Effects of large-scale free stream turbulence on a turbulent boundary layer. Phys. Fluids21, 095105. · Zbl 1183.76470 |

[42] | Simens, M. P., Jiménez, J., Hoyas, S. & Mizuno, Y.2009A high-resolution code for turbulent boundary layers. J. Comput. Phys.228, 4218-4231. · Zbl 1273.76009 |

[43] | Spalart, P. R., Moser, R. D. & Rogers, M. M.1991Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions. J. Comput. Phys.96 (2), 297-324. · Zbl 0726.76074 |

[44] | Thole, K. A. & Bogard, D. G.1996High freestream turbulence effects on turbulent boundary layers. Trans. ASME I: J. Fluids Engng118, 276-284. |

[45] | Thornber, B.2016Impact of domain size and statistical errors in simulations of homogeneous decaying turbulence and the Richtmyer-Meshkov instability. Phys. Fluids28, 045106. |

[46] | Townsend, A. A.1961Equilibrium layers and wall turbulence. J. Fluid Mech.11, 97-120. · Zbl 0127.42602 |

[47] | Verstappen, R. W. C. P. & Veldman, A. E. P.2003Symmetry-preserving discretization of turbulent flow. J. Comput. Phys.187, 343-368. · Zbl 1062.76542 |

[48] | Watanabe, T. & Nagata, K.2018Integral invariants and decay of temporally developing grid turbulence. Phys. Fluids30, 105111. |

[49] | Watanabe, T., Zhang, X. & Nagata, K.2018Turbulent/non-turbulent interfaces detected in DNS of incompressible turbulent boundary layers. Phys. Fluids30, 035102. |

[50] | Westerweel, J., Fukushima, C., Pedersen, J. M. & Hunt, J. C. R.2009Momentum and scalar transport at the turbulent/non-turbulent interface of a jet. J. Fluid Mech.631, 199-230. · Zbl 1181.76015 |

[51] | White, F. M.2006Viscous Fluid Flow, 3rd edn. McGraw-Hill. |

[52] | Wu, X., Moin, P., Wallace, J. M., Skarda, J., Lozano-Durán, A. & Hickey, J.-P.2017Transitional-turbulent spots and turbulent-turbulent spots in boundary layers. Proc. Natl Acad. Sci. USA114, E5292-E5299. |

[53] | Wu, X., Wallace, J. M. & Hickey, J.-P.2019Boundary layer turbulence and freestream turbulence interface, turbulent spot and freestream turbulence interface, laminar boundary layer and freestream turbulence interface. Phys. Fluids31, 045104. |

[54] | Xia, S., Ito, Y., Nagata, K., Sakai, Y., Suzuki, H., Terashima, O. & Hayase, T.2014DNS study on the development of boundary layer with heat transfer under the effects of external and internal disturbances. J. Fluid Sci. Technol., JSME9, 1-13. |

[55] | You, J. & Zaki, T. A.2019Conditional statistics and flow structures in turbulent boundary layers buffeted by free-stream disturbances. J. Fluid Mech.866, 526-566. · Zbl 1415.76413 |

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