Turbulent boundary layer simulations and models

The logarithmic law for the mean velocity in turbulent boundary layers has long provided a valuable and robust reference for comparison with theories, models, and large-eddy simulations of wall-bounded turbulence. More recently, analysis of high-Reynolds-number experimental boundary-layer data has shown that the variance and higher-order moments of the streamwise velocity fluctuations u₀⁺ also display logarithmic laws. Such observations motivate the question whether LES can accurately reproduce these moments, in particular their logarithmic dependence on distance from the wall. In Stevens et al., J. Fluid Mech. 757, 888-907 (2014), we performed LES of very-high-Reynolds-number turbulent boundary-layer flow and focused on profiles of the variance and higher-order moments of the streamwise velocity fluctuations. Figure 1a shows that high-resolution simulations with the scale-dependent Lagrangian subgrid model capture the velocity fluctuations and logarithmic law for the variance well, while lower-resolution simulations using the standard Smagorinsky model do not. The LES also yields approximate logarithmic laws for the higher-order moments. As highlighted in the Focus on Fluids article by Elie Bou-Zeid, the advanced tests introduced in this work provide more demanding measures of LES accuracy. After validating the simulation results against experimental data, we used the simulation database to develop and test a new analytical wavenumber-frequency model for space-time correlations in atmospheric-boundary-layer simulations [2], [3], [4].

Movie 1: Visualization of the flow in an atmospheric boundary layer.

Figure 1. (a) The profile of the second-order moment of the streamwise velocity fluctuations as a function of z/H, obtained from high-resolution LES with the scale-dependent Lagrangian model, compares well with the experimental findings. Results from a reference LES using the Smagorinsky model at a standard LES resolution are shown for comparison. Figure based on Stevens et al., J. Fluid Mech. 757, 888-907 (2014). Because the streamwise turbulence intensity u^'/u influences the expansion rate of wind-turbine wakes, it is important to capture the fluctuations accurately in wind-farm simulations. (b,c) The wavenumber-frequency spectra of streamwise velocity from LES and an analytical model compare well [2], [3]. The vertical lines indicate a representative turbine scale. (d) Normalized cuts from panels (b) and (c), comparing the model (lines) and LES results (symbols).