Viscous anti-parallel vortex reconnection is studied by means of direct numerical simulation for vortex Reynolds numbers reconnection, but also shed light on the physics of turbulence cascade and present the reconnection avalanche as a realistic physical model for turbulence cascade.

Direct numerical simulations of compressible turbulent channel flows are performed for bulk Mach numbers 0.8 and 1.5 and bulk Reynolds numbers in the range of $3000\text{–}34000$. The compressibility effects are well accounted for when using the semilocal scaling, as expected. Compared to incompressible flows at comparable semilocal Reynolds number ${\text{Re}}_{\tau c}^{*}$, the mean velocity profile perfectly collapses after the Trettel and Larsson transformation [Trettel and Larsson, Phys. Fluids 28, 026102 (2016)]. Furthermore, the Reynolds stresses, such as their peak values and locations, follow similar trends as in incompressible cases. In particular, the Reynolds shear stress peak follows the nonuniversal scaling transition predicted by Chen et al. [ J. Fluid Mech. 871, R2 (2019)]. Although the streamwise Reynolds stress peak continuously increases with Mach number, this increase becomes smaller as the Reynolds number increases. The streamwise and spanwise velocity spectra reveal that the typical eddy size does not vary with the Mach number when scaled using the local friction velocity and thermodynamic properties. Additionally, the compressibility contribution to the skin friction continuously decreases with Reynolds numbers. These results suggest that incompressible and compressible flows differ little at sufficiently high Reynolds number.

Drag control using a newly developed spanwise opposed wall-jet forcing (SOJF) method is studied via direct numerical simulation of the incompressible Navier–Stokes equations in a turbulent channel flow (at the friction Reynolds numbers $Re_{\unicode[STIX]{x1D70F}}=180$ and 550). SOJF is characterized by three control parameters: the forcing amplitude $A^{+}$ , the spanwise spacing $\unicode[STIX]{x1D706}^{+}$ and the wall-jet height $y_{c}^{+}$ ( $+$ indicates viscous scaling). At $Re_{\unicode[STIX]{x1D70F}}=180$ , notable drag reduction is achieved for wide ranges of $A^{+}$ , $\unicode[STIX]{x1D706}^{+}$ and $y_{c}^{+}$ , with an optimal drag reduction of approximately 19 % found for $A^{+}\approx 0.015$ , $\unicode[STIX]{x1D706}^{+}\approx 1200$ and $y_{c}^{+}\approx 30$ . The drag reduction results from mergers of numerous low-speed typical individual streaks together by the wall jets, so that the slope of the merged streak envelope and hence the streak strength are reduced below the critical values required for streak instability as well as for transient growth; consequently, the generation of drag inducing near-wall streamwise vortices is suppressed. Through analysis using the FIK identity (Fukagata et al. Phys. Fluids, vol. 14 (11), 2002, pp. L73–L76) in combination with the triple decomposition and the spanwise wavenumber spectrum of the Reynolds shear stress, we find that the control significantly decreases skin friction due to the small scale random turbulent structures (from 75 to 23 % for the optimal case), but injects a dominant contribution at the forcing scale (approximately 34 %). As $A^{+}$ or $y_{c}^{+}$ increases, the drag reduction degrades due to the downwash near the initiation of the forcing wall jet. The energy input required for the excitation is found to be small, yielding a 17 % net power saving for the optimal control case. To determine the $Re$ dependence of the drag reduction, the control strategy is further validated at a higher $Re_{\unicode[STIX]{x1D70F}}=550$ . If the control parameters are kept the same as at $Re_{\unicode[STIX]{x1D70F}}=180$ (i.e. $A^{+}\approx 0.015$ , $\unicode[STIX]{x1D706}^{+}\approx 1200$ , $y_{c}^{+}\approx 30$ ), the drag reduction decreases to 10 %; however, interestingly, with modestly changed parameters ( $A^{+}\approx 0.018$ , $\unicode[STIX]{x1D706}^{+}\approx 1700$ , $y_{c}^{+}\approx 50$ ), drag reduction increases to about 15 %. This additional drag reduction results from the further suppression of turbulent structures in the buffer and log regions. This result, therefore, suggests prospects for drag reduction at even higher $Re$ via a proper choice of the SOJF parameters.

Well-resolved direct numerical simulations (DNS) have been performed of the flow in a smooth circular pipe of radius $R$ and axial length $10{\rm \pi} R$ at friction Reynolds numbers up to $Re_\tau =5200$ using the pseudo-spectral code OPENPIPEFLOW. Various turbulence statistics are documented and compared with other DNS and experimental data in pipes as well as channels. Small but distinct differences between various datasets are identified. The friction factor $\lambda$ overshoots by $2\,\%$ and undershoots by $0.6\,\%$ the Prandtl friction law at low and high $Re$ ranges, respectively. In addition, $\lambda$ in our results is slightly higher than in Pirozzoli et al. (J. Fluid Mech., vol. 926, 2021, A28), but matches well the experiments in Furuichi et al. (Phys. Fluids, vol. 27, issue 9, 2015, 095108). The log-law indicator function, which is nearly indistinguishable between pipe and channel up to $y^+=250$ , has not yet developed a plateau farther away from the wall in the pipes even for the $Re_\tau =5200$ cases. The wall shear stress fluctuations and the inner peak of the axial turbulence intensity – which grow monotonically with $Re_\tau$ – are lower in the pipe than in the channel, but the difference decreases with increasing $Re_\tau$ . While the wall value is slightly lower in the channel than in the pipe at the same $Re_\tau$ , the inner peak of the pressure fluctuation shows negligible differences between them. The Reynolds number scaling of all these quantities agrees with both the logarithmic and defect-power laws if the coefficients are properly chosen. The one-dimensional spectrum of the axial velocity fluctuation exhibits a $k^{-1}$ dependence at an intermediate distance from the wall – also seen in the channel. In summary, these high-fidelity data enable us to provide better insights into the flow physics in the pipes as well as the similarity/difference among different types of wall turbulence.

The effect of Reynolds number (Re_τ) on drag reduction using spanwise wall oscillation is studied through direct numerical simulation of incompressible turbulent channel flows with Re_τ ranging from 200 to 2000. For the nondimensional oscillation period T⁺ = 100 with maximum velocity amplitude A⁺ = 12, the drag reduction ($\mathcal{D}\mathcal{R}$ ) decreases from 35.3% ± 0.5% at Re_τ = 200 to 22.3% ± 0.7% at Re_τ = 2000. The oscillation frequency ω⁺ for maximum $\mathcal{D}\mathcal{R}$ slightly increases with Re_τ, i.e., from ω⁺ ≈ 0.06 at Re_τ = 200 to 0.08 at Re_τ = 2000, with ${\mathcal{D}\mathcal{R}}_{max}=23.2\%\pm 0.6\%$ . These results show that $\mathcal{D}\mathcal{R}$ progressively decreases with increasing Re_τ. Turbulent statistics and coherent structures are examined to explain the degradation of drag control effectiveness at high Re_τ. Fukagata, Iwamoto, and Kasagi analysis in combination with the spanwise wavenumber spectrum of Reynolds stresses reveals that the decreased drag reduction at higher Re_τ is due to the weakened effectiveness in suppressing the near-wall large-scale turbulence, whose contribution continuously increases due to the enhanced modulation and penetration effect of the large-scale and very large-scale motions in the log and outer regions. Both the power-law model ($DR\propto R{e}_{\tau }^{-\gamma }$ ) and the log-law model [DR = f(Re_τ, ΔB), where ΔB is the vertical shift of the log-law intercept under control] are examined here by comparing them with our simulation data, from these two models we predict more than 10% drag reduction at very high Reynolds numbers, say, Re_τ = 10⁵.

Well-resolved direct numerical simulations of turbulent open channel flows (OCFs) are performed for friction Reynolds numbers up to $Re_\tau =2000$ . Various turbulent statistics are documented and compared with the closed channel flows (CCFs). As expected, the mean velocity profiles of the OCFs match well with the CCFs in the near-wall region but diverge notably in the outer region. Interestingly, a logarithmic layer with Kárman constant $\kappa =0.363$ occurs for OCF at $Re_\tau =2000$ , distinctly different from CCF. Except for a very thin layer near the free surface, most of the velocity and vorticity variances match between OCFs and CCFs. The one-dimensional energy spectra reveal that the very-large-scale motions (VLSMs) with streamwise wavelength $\lambda _x>3 h$ or spanwise wavelength $\lambda _z>0.5 h$ contribute the most to turbulence intensity and Reynolds shear stress in the overlap and outer layers (where h is the water depth). Furthermore, the VLSMs in OCFs are stronger than those in CCFs, resulting in a slightly higher streamwise velocity variance in the former. Due to the footprint effect, these structures also have significant contributions to the mean wall shear stress, and the difference between OCF and CCF enlarges with increasing $Re_\tau$ . In summary, the free surface in OCFs plays an essential role in various flow phenomena, including the formation of stronger VLSMs and turbulent kinetic energy redistribution.