Turbulence in intermittent transitional boundary layers and in turbulence spots.

*(English)*Zbl 1415.76279Summary: Direct numerical simulation data of bypass transition in flat-plate boundary layers are analysed to examine the characteristics of turbulence in the transitional regime. When intermittency is 50% or less, the flow features a juxtaposition of turbulence spots surrounded by streaky laminar regions. Conditionally averaged turbulence statistics are evaluated within the spots, and are compared to standard time averaging in both the transition region and in fully turbulent boundary layers. The turbulent-conditioned root-mean-square levels of the streamwise velocity perturbations are notably elevated in the early transitional boundary layer, while the wall-normal and spanwise components are closer to the levels typical for fully turbulent flow. The analysis is also extended to include ensemble averaging of the spots. When the patches of turbulence are sufficiently large, they develop a core region with similar statistics to fully turbulent boundary layers. Within the tip and the wings of the spots, however, the Reynolds stresses and terms in the turbulence kinetic energy budget are elevated. The enhanced turbulence production in the transition zone, which exceeds the levels from fully turbulent boundary layers, contributes to the higher skin-friction coefficient in that region. Qualitatively, the same observations hold for different spot sizes and levels of free-stream turbulence, except for young spots which do not yet have a core region of developed turbulence.

##### MSC:

76F06 | Transition to turbulence |

76F40 | Turbulent boundary layers |

76F65 | Direct numerical and large eddy simulation of turbulence |

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\textit{O. Marxen} and \textit{T. A. Zaki}, J. Fluid Mech. 860, 350--383 (2019; Zbl 1415.76279)

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##### References:

[1] | Andersson, P.; Brandt, L.; Bottaro, L.; Henningson, D. S., On the breakdown of boundary layer streaks, J. Fluid Mech., 428, 29-60, (2001) · Zbl 0983.76025 |

[2] | Anthony, R. J.; Jones, T. V.; Lagraff, J. E., High frequency surface heat flux imaging of bypass transition, J. Turbomach., 127, 241-250, (2005) |

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

[4] | Brandt, L., The lift-up effect: the linear mechanism behind transition and turbulence in shear flows, Eur. J. Mech. (B/Fluids), 47, 80-96, (2014) · Zbl 1297.76073 |

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

[6] | Cantwell, B.; Coles, D.; Dimotakis, P., Structure and entrainment in the plane of symmetry of a turbulent spot, J. Fluid Mech., 87, 4, 641-672, (1978) |

[7] | Dhawan, S.; Narasimha, R., Some properties of boundary layer flow during the transition from laminar to turbulent motion, J. Fluid Mech., 3, 4, 418-436, (1958) · Zbl 0079.40703 |

[8] | Durbin, P.; Wu, X., Transition beneath vortical disturbances, Annu. Rev. Fluid Mech., 39, 1, 107-128, (2007) · Zbl 1296.76061 |

[9] | Ge, X.; Arolla, S.; Durbin, P. A., A bypass transition model based on the intermittency function, Flow Turbul. Combust., 93, 1, 37-61, (2014) |

[10] | Hack, M. J. P.; Zaki, T. A., The influence of harmonic wall motion on transitional boundary layers, J. Fluid Mech., 760, 63-94, (2014) |

[11] | Hack, M. J. P.; Zaki, T. A., Data-enabled prediction of streak breakdown in pressure-gradient boundary layers, J. Fluid Mech., 801, 43-64, (2016) |

[12] | Herbert, T., Secondary instability of boundary layers, Annu. Rev. Fluid Mech., 20, 487-526, (1988) |

[13] | Hunt, J. C. R.; Carruthers, D. J., Rapid distortion theory and the ‘problems’ of turbulence, J. Fluid Mech., 212, 497-532, (1990) · Zbl 0692.76054 |

[14] | Itsweire, E. C.; Atta, C. W. V., An experimental investigation of coherent substructures associated with turbulent spots in a laminar boundary layer, J. Fluid Mech., 148, 319-348, (1984) |

[15] | Jacobs, R. G.; Durbin, P. A., Simulations of bypass transition, J. Fluid Mech., 428, 185-212, (2001) · Zbl 0983.76027 |

[16] | Kachanov, Y. S., Physical mechanisms of laminar-boundary-layer transition, Annu. Rev. Fluid Mech., 26, 1, 411-482, (1994) |

[17] | Kendall, J.; Reda, X., Studies on laminar boundary layer receptivity to free stream turbulence near a leading edge, Boundary Layer Stability and Transition to Turbulence, 114, 23-30, (1991), ASME-FED |

[18] | Klebanoff, P. S., Effect of freestream turbulence on the laminar boundary layer, Bull. Am. Phys. Soc., 16, 1323, (1971) |

[19] | Landahl, M. T., A note on an algebraic instability of inviscid parallel shear flows, J. Fluid Mech., 98, 243-251, (1980) · Zbl 0428.76049 |

[20] | 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 |

[21] | Lee, S. J.; Zaki, T. A., Simulations of natural transition in viscoelastic channel flow, J. Fluid Mech., 820, 232-262, (2017) · Zbl 1383.76288 |

[22] | Liu, Y.; Zaki, T. A.; Durbin, P. A., Boundary-layer transition by interaction of discrete and continuous modes, J. Fluid Mech., 604, 199-233, (2008) · Zbl 1151.76497 |

[23] | Mandal, A. C.; Venkatakrishnan, L.; Dey, J., A study on boundary-layer transition induced by free-stream turbulence, J. Fluid Mech., 660, 114-146, (2010) · Zbl 1205.76019 |

[24] | Narasimha, R., On the distribution of intermittency in the transition region of a boundary layer, J. Aerosp. Sci., 24, 711-712, (1957) |

[25] | Narasimha, R., The laminar-turbulent transition zone in the boundary layer, Prog. Aerosp. Sci., 22, 1, 29-80, (1985) |

[26] | 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 |

[27] | Otsu, N., A threshold selection method from grey-level histograms, IEEE Trans. Syst. Man Cybern., 9, 1, 62-66, (1979) |

[28] | Ovchinnikov, V.; Choudhari, M. M.; Piomelli, U., Numerical simulations of boundary-layer bypass transition due to high-amplitude free-stream turbulence, J. Fluid Mech., 613, 135-169, (2008) · Zbl 1151.76498 |

[29] | Park, G. I.; Wallace, J. M.; Wu, X.; Moin, P., Boundary layer turbulence in transitional and developed states, Phys. Fluids, 24, 3, (2012) |

[30] | Perry, A. E.; Lim, T. T.; Teh, E. W., A visual study of turbulent spots, J. Fluid Mech., 104, 387-405, (1981) |

[31] | Phillips, O. M., Shear-flow turbulence, Annu. Rev. Fluid Mech., 1, 245-264, (1969) |

[32] | 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 |

[33] | 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, 1, 102-137, (1991) · Zbl 0718.76079 |

[34] | Sandham, N. D.; Kleiser, L., The late stages of transition to turbulence in channel flow, J. Fluid Mech., 245, 319, (2006) · Zbl 0825.76312 |

[35] | Sayadi, T.; Moin, P., Large eddy simulation of controlled transition to turbulence, Phys. Fluids, 24, (2012) |

[36] | Schmid, P. J.; Henningson, D. S., Stability and Transition in Shear Flows, (2000), Springer |

[37] | Simon, F.; Ashpis, D. |

[38] | Spalart, P. R., Direct simulation of a turbulent boundary layer up to R_𝜃 = 1410, J. Fluid Mech., 187, 61-98, (1988) · Zbl 0641.76050 |

[39] | Steelant, J.; Dick, E., Modeling of laminar-turbulent transition for high freestream turbulence, J. Fluids Engng, 123, 1, 22, (2001) |

[40] | Trefethen, L. N.; Trefethen, A. E.; Reddy, S. C.; Driscoll, T. A., Hydrodynamic stability without eigenvalues, Science, 261, 578-584, (1993) · Zbl 1226.76013 |

[41] | Vaughan, N. J.; Zaki, T. A., Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks, J. Fluid Mech., 681, 116-153, (2011) · Zbl 1241.76183 |

[42] | Wu, X.; Moin, P., Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer, J. Fluid Mech., 630, 5-41, (2009) · Zbl 1181.76084 |

[43] | Wu, X.; Moin, P.; Wallace, J. M.; Skarda, J.; Lozano-Durán, A.; Hickey, J.-P., Transitional-turbulent spots and turbulent-turbulent spots in boundary layers, Proc. Natl Acad. Sci. USA, 114, 27, E5292-E5299, (2017) |

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

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

[46] | Zaki, T. A.; Durbin, P. A., Continuous mode transition and the effects of pressure gradients, J. Fluid Mech., 563, 357-358, (2006) · Zbl 1177.76136 |

[47] | 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 |

[48] | Zaki, T. A.; Wissink, J. G.; Rodi, W.; Durbin, P. A., Direct numerical simulations of transition in a compressor cascade: the influence of free-stream turbulence, J. Fluid Mech., 665, 57-98, (2010) · Zbl 1225.76147 |

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