Turbulent channel flow: comparison of streamwise velocity data from experiments and direct numerical simulation

Abstract

<jats:p>Recently there has been remarkable progress made in the direct numerical simulation (DNS) of wall-bounded turbulence, particularly of turbulent channel flow, with numerical data now available above <jats:italic>Re</jats:italic><jats:sub>τ</jats:sub> ≈ 2000 (Hoyas &amp; Jiménez, <jats:italic>Phys. Fluids</jats:italic>, vol. 18, 2006, p. 011702; Iwamoto <jats:italic>et al</jats:italic>., <jats:italic>Proceedings of the Sixth Symposium Smart Control of Turbulence</jats:italic>, 2005). Much knowledge has been gained from these results, particularly in the areas of flow structure and dynamics. Yet, while the value of such simulations is undoubted, only very limited comparisons with experimental data have been documented. Although the physics of the flow are captured correctly in an <jats:italic>ideal</jats:italic> DNS, as with any <jats:italic>real</jats:italic> numerical or physical experiment, there are opportunities for misrepresentation of the characteristics of turbulence. As such, this article seeks to make a comparison between a well-documented high Reynolds number (<jats:italic>Re</jats:italic><jats:sub>τ</jats:sub> = 934), large box size (8π<jats:italic>h</jats:italic> × 2<jats:italic>h</jats:italic> × 3π<jats:italic>h</jats:italic>) DNS from del Álamo <jats:italic>et al</jats:italic>. (<jats:italic>J. Fluid Mech</jats:italic>., vol. 500, 2004, p. 135) and laboratory channel flow data measured by the authors. Results show that there is excellent agreement between the streamwise velocity statistics of the two data sets. The spectra are also very similar, however, throughout the logarithmic region the secondary peak in energy is clearly reduced in the DNS results. Although the source of the difference is not certain, the wavelengths concerned are close to the DNS box length, leading to the recommendation that longer box lengths should be investigated. Another large-scale spectral discrepancy near the wall results from the incorrect assumption of a constant convection velocity used to infer spatial information from the temporal. A near-wall convection velocity modification function is tentatively proposed. While the modification gives good agreement between the data sets, higher Reynolds number comparisons are required to better understand the intricate convection velocity issue.</jats:p>