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 also the variance and higher-order moments of the streamwise velocity fluctuations u₀⁺ display logarithmic laws. Such experimental observations motivate the question whether LES can accurately reproduce the variance and the higher-order moments, in particular their logarithmic dependency on distance to 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 focus on profiles of variance and higher-order moments of the streamwise velocity fluctuations. In figure 1a we see that the high resolution simulations with the scale dependent Lagrangian subgrid model capture the velocity fluctuations and logarithmic law for the variance very well, while this is not the case for lower resolution simulations using the standard Smagorinsky model. The LES also yields approximate logarithmic laws for the higher-order moments of the streamwise velocity. As is also highlighted in the Focus on Fluids article by Elie Bou-Zeid, the advanced tests that we introduced in this work provide more challenging tests to judge the accuracy of LES, which is a simulation technique that is used more and more these days. After validating the simulation results against the experimental data we used the simulation database to develop and test a new analytical wavenumber-frequency model to describe the 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 for the streamwise velocity fluctuations as a function of z/H obtained from high resolution LES with the Lagrangian scale dependent model compares well with the experimental findings. The result from a reference LES using the Smagorinsky model with a standard LES resolution is shown for comparison. Figure based on the results presented in Stevens et al.,J. Fluid Mech. 757, 888-907 (2014). As 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) The space-time correlations in a turbulent boundary layer presented using a wavenumber-frequency spectrum for the streamwise velocity measured from LES compares well with (c) an analytic model parametrization [2], [3]. The vertical lines in panels (b) and (c) indicate a representative turbine scale. (d) Normalized cuts from panel (b) and (c) comparing the model (lines) and LES results (symbols).