Numerical Investigation of Very-Large-Scale Motions in a Turbulent Boundary Layer for Different Roughness

Wall-model large eddy simulations (WMLES) are conducted to investigate the spatial features of large-scale and very-large-scale motions (LSMs and VLSMs) in turbulent boundary flow in different surface roughnesses at a very high Reynolds number, O (10 6 –10 7 ). The results of the simulation of nearly smooth cases display good agreement with field observations and experimental data, both dimensioned using inner and outer variables. Using pre-multiplied spectral analysis, the size of VLSMs can be reduced or even disappear with increasing roughness, which indirectly supports the concept that the bottom-up mechanism is one of the origins of VLSMs. With increases in height, the power of pre-multiplied spectra at both high and low wavenumber regions decreases, which is consistent with most observational and experimental results. Furthermore, we find that the change in the spectrum scaling law from −1 to −5/3 is a gradual process. Due to the limitations of the computational domain and coarse grid that were adopted, some VLSMs and small-scale turbulence are truncated. However, the size of LSMs is fully accounted for. From the perspective of the spatial correlation of the flow field, the structural characteristics of VLSMs under various surface roughnesses, including three-dimensional length scales and inclination angles, are obtained intuitively, and the conclusions are found to be in good agreement with the velocity spectra. Finally, the generation, development and extinction of three-dimensional VLSMs are analyzed by instantaneous flow and vorticity field, and it shows that the instantaneous flow field gives evidence of low-speed streamwise-elongated flow structures with negative streamwise velocity fluctuation component, and which are flanked on each side by similarly high-speed streamwise-elongated flow structures. Moreover, each of the low-speed streamwise-elongated flow structure lies beneath many vortices.