Direct numerical simulation of turbulent channel flow up to Reτ≈5200Re_\tau \approx 5200

A direct numerical simulation of incompressible channel flow at $Re_\tau$ = 5186 has been performed, and the flow exhibits a number of the characteristics of high Reynolds number wall-bounded turbulent flows. For example, a region where the mean velocity has a logarithmic variation is observed, with von Karman constant $\kappa = 0.384 \pm 0.004$. There is also a logarithmic dependence of the variance of the spanwise velocity component, though not the streamwise component. A distinct separation of scales exists between the large outer-layer structures and small inner-layer structures. At intermediate distances from the wall, the one-dimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits $k^{-1}$ dependence over a short range in $k$. Further, consistent with previous experimental observations, when these spectra are multiplied by $k$ (premultiplied spectra), they have a bi-modal structure with local peaks located at wavenumbers on either side of the $k^{-1}$ range.Comment: Under consideration for publication in J. Fluid Mec

A data-driven quasi-linear approximation for turbulent channel flow

A data-driven implementation of a quasi-linear approximation is presented, extending a minimal quasi-linear approximation (MQLA) (Hwang & Ekchardt, J. Fluid Mech., 2020, 894:A23) to incorporate non-zero streamwise Fourier modes. A data-based approach is proposed, matching the two-dimensional wavenumber spectra for a fixed spanwise wavenumber between a direct numerical simulation (DNS) (Lee & Moser, J. Fluid Mech., 2015, 774:395-415) and that generated by the eddy viscosity-enhanced linearised Navier-Stokes equations at $Re{\tau} \simeq 5200$. Leveraging the self-similar nature of the energy-containing part in the DNS velocity spectra, a universal self-similar streamwise wavenumber weight is determined for the linearised fluctuation equations at $Re_{\tau} \simeq 5200$. This data-driven quasi-linear approximation (DQLA) offers qualitatively similar findings to the MQLA, with quantitative improvements in the turbulence intensities and additional insights from the streamwise wavenumber spectra. By comparing the one-dimensional streamwise wavenumber spectra and two-dimensional spectra to DNS results, the limitations of the presented framework are discussed, mainly pertaining to the lack of the streak instability (or transient growth) mechanism and energy cascade from the linearised model. The DQLA is subsequently employed over a range of Reynolds numbers up to $Re_{\tau} = 10^5$. Overall, the turbulence statistics and spectra produced by the DQLA scale consistently with the available DNS and experimental data, with the Townsend-Perry constants displaying a mild Reynolds dependence (Hwang, Hutchins & Marusic, J. Fluid Mech., 2022, 933:A8). The scaling behaviour of the turbulence intensity profiles deviates away from the classic $\ln(Re_{\tau})$ scaling, following the inverse centreline velocity scaling for the higher Reynolds numbers

Wall-pressure--velocity coupling in high-Reynolds number wall-bounded turbulence

Wall-pressure fluctuations are a practically robust input for real-time control systems aimed at modifying wall-bounded turbulence. The scaling behaviour of the wall-pressure--velocity coupling requires investigation to properly design a controller with such input data, so that the controller can actuate upon the desired turbulent structures. A comprehensive database from direct numerical simulations of turbulent channel flow is used for this purpose, spanning a Reynolds-number range $Re_\tau \sim 550 - 5200$. A spectral analysis reveals that the streamwise velocity is most strongly coupled to the linear term of the wall-pressure, at a wall-scaling of $\lambda_x/y \approx 14$ (and $\lambda_x/y \approx 8.5$ for the wall-normal velocity). When extending the analysis to both homogeneous directions in $x$ and $y$, the peak-coherence is centred at $\lambda_x/\lambda_z \approx 2$ and $\lambda_x/\lambda_z \approx 1$ for $p_w$ and $u$, and $p_w$ and $v$, respectively. A stronger coherence is retrieved when the quadratic term of the wall-pressure is concerned, but there is only weak evidence for a wall-attached-eddy type of scaling. Experimental data are explored in the second part of this work: wall-pressure data are denoised and subsequently used for predicting the binary-state of the streamwise velocity fluctuations in the logarithmic region. A binary estimation accuracy of up to 72% can be achieved by including both the linear and quadratic terms of the wall-pressure. This study demonstrates that a controller for wall-bounded turbulence (solely relying on wall-pressure data) has merit in terms of a sufficient state estimation capability, even in the presence of significant facility noise

Direct numerical simulation (DNS) for incompressible turbulent channel flow at Reτ = 5200

Nearly all moving objects on Earth pass through fluids and many of them move at high speed. This makes high Re wall-bounded turbulent flows of great technological impor- tance. To study high Re wall-bounded turbulence, high spatial and temporal resolution is required due to the multi-scale nature of turbulence. Direct numerical simulation (DNS) is a technique for the study of turbulence in which the Navier-Stoke equations, the governing equations of fluid flow, are solved with sufficient resolution to represent all the scales of tur- bulence. Hence, DNS is very expensive and always limited by computational capability. To perform DNS on the most advanced high performance computing systems, extensive code optimization is required. A new turbulence DNS code, PoongBack, was developed for the studies reported here. It shows excellent performance and scalability (∼97%) on upto 786k cores on Mira at Argonne Leadership Computing Facility. We have performed DNS of turbulent channel flow using a Fourier-Galerkin method in the streamwise(x) and spanwise (z) directions and a B-Splines collocation method in the wall-normal (y) direction. The highest Reynolds number based on shear velocity (uτ = √(τw/ρ)), Reτ is approximately 5200. The simulation results exhibit a number of the char- acteristics of high Re wall-bounded turbulent flows. For example, a region where the mean velocity has a logarithmic variation is observed, with von Kármán constant κ = 0.384±0.004. There is also a logarithmic dependence of the variance of the spanwise velocity component, though not the streamwise component. A distinct separation of scales exists between the large outer-layer structures and small inner-layer structures. At intermediate distances from the wall, the one-dimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits 1/k dependence over a short range in wavenum- ber (k). Further, consistent with previous experimental observations, when these spectra are multiplied by k (premultiplied spectra), they have a bimodal structure with local peaks located at wavenumbers on either side of the 1/k range. To study the scale dependence of the dynamics of the Reynolds stress components, we applied a spectral analysis to the terms in the Reynolds stress transport equation (RSTE). It is shown that only the turbulent transport terms show significant Re dependencies. Further- more, the turbulent transport terms can be decomposed into two parts, one that contributes to transport in the wall-normal direction and one that is responsible for transfer between length scales. The results show that the large scale motion in the outer region has direct effects on the flow in the near-wall region through transport of turbulent kinetic energy. Also, a reverse energy cascade from intermediate scales to large scales is observed in the spanwise velocity fluctuations.Mechanical Engineerin