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Phys Rev Fluids 2018 Oct;3(10):100505

Center for Turbulence Research, Stanford University, Stanford, California 94305-3024, USA.

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http://dx.doi.org/10.1103/PhysRevFluids.3.100505 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6800704 | PMC |

October 2018

J Fluid Mech 2019 Jun;868:698-725

Center for Turbulence Research, Stanford University, CA 94305, USA.

Townsend , 1976, Cambridge University Press) proposed a structural model for the logarithmic layer (log layer) of wall turbulence at high Reynolds numbers, where the dominant momentum-carrying motions are organised into a multiscale population of eddies attached to the wall. In the attached-eddy framework, the relevant length and velocity scales of the wall-attached eddies are the friction velocity and the distance to the wall. In the present work, we hypothesise that the momentum-carrying eddies are controlled by the mean momentum flux and mean shear with no explicit reference to the distance to the wall and propose new characteristic velocity, length and time scales consistent with this argument. Our hypothesis is supported by direct numerical simulation of turbulent channel flows driven by non-uniform body forces and modified mean velocity profiles, where the resulting outer-layer flow structures are substantially altered to accommodate the new mean momentum transfer. The proposed scaling is further corroborated by simulations where the no-slip wall is replaced by a Robin boundary condition for the three velocity components, allowing for substantial wall-normal transpiration at all length scales. We show that the outer-layer one-point statistics and spectra of this channel with transpiration agree quantitatively with those of its wall-bounded counterpart. The results reveal that the wall-parallel no-slip condition is not required to recover classic wall-bounded turbulence far from the wall and, more importantly, neither is the impermeability condition at the wall.

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http://dx.doi.org/10.1017/jfm.2019.209 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6800708 | PMC |

June 2019

J Fluid Mech 2019 Jan;859:400-432

Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA.

Wall modelling in large-eddy simulation (LES) is necessary to overcome the prohibitive near-wall resolution requirements in high-Reynolds-number turbulent flows. Most existing wall models rely on assumptions about the state of the boundary layer and require prescription of tunable coefficients. They also impose the predicted wall stress by replacing the no-slip boundary condition at the wall with a Neumann boundary condition in the wall-parallel directions while maintaining the no-transpiration condition in the wall-normal direction. In the present study, we first motivate and analyse the Robin (slip) boundary condition with transpiration (non-zero wall-normal velocity) in the context of wall-modelled LES. The effect of the slip boundary condition on the one-point statistics of the flow is investigated in LES of turbulent channel flow and a flat-plate turbulent boundary layer. It is shown that the slip condition provides a framework to compensate for the deficit or excess of mean momentum at the wall. Moreover, the resulting non-zero stress at the wall alleviates the well-known problem of the wall-stress under-estimation by current subgrid-scale (SGS) models (Jiménez & Moser, ., vol. 38 (4), 2000, pp. 605-612). Second, we discuss the requirements for the slip condition to be used in conjunction with wall models and derive the equation that connects the slip boundary condition with the stress at the wall. Finally, a dynamic procedure for the slip coefficients is formulated, providing a dynamic slip wall model free of specified coefficients. The performance of the proposed dynamic wall model is tested in a series of LES of turbulent channel flow at varying Reynolds numbers, non-equilibrium three-dimensional transient channel flow and a zero-pressure-gradient flat-plate turbulent boundary layer. The results show that the dynamic wall model is able to accurately predict one-point turbulence statistics for various flow configurations, Reynolds numbers and grid resolutions.

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http://dx.doi.org/10.1017/jfm.2018.838 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6800713 | PMC |

January 2019

J Comput Phys 2019 Sep;392:532-555

Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA, 91125, USA.

We study the error scaling properties of large-eddy simulation (LES) in the outer region of wall-bounded turbulence at moderately high Reynolds numbers. In order to avoid the additional complexity of wall-modeling, we perform LES of turbulent channel flows in which the no-slip condition at the wall is replaced by a Neumann condition supplying the exact mean wall-stress. The statistics investigated are the mean velocity profile, turbulence intensities, and kinetic energy spectra. The errors follow , where Δ is the characteristic grid resolution, is the friction Reynolds number, and is the meaningful length-scale to normalize Δ in order to collapse the errors across the wall-normal distance. We show that Δ can be expressed as the -norm of the grid vector and that is well represented by the ratio of the friction velocity and mean shear. The exponent is estimated from theoretical arguments for each statistical quantity of interest and shown to roughly match the values computed by numerical simulations. For the mean profile and kinetic energy spectra, ≈ 1, whereas the turbulence intensities converge at a slower rate < 1. The exponent is approximately 0, i.e. the LES solution is independent of the Reynolds number. The expected behavior of the turbulence intensities at high Reynolds numbers is also derived and shown to agree with the classic log-layer profiles for grid resolutions lying within the inertial range. Further examination of the LES turbulence intensities and spectra reveals that both quantities resemble their filtered counterparts from direct numerical simulation (DNS) data, but that the mechanism responsible for this similarity is related to the balance between the input power and dissipation rather than to filtering.

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http://dx.doi.org/10.1016/j.jcp.2019.04.063 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6800710 | PMC |

September 2019

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