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The boundary-layer stability on a section of a rotating wind turbine blade with an FFA-W3 series aerofoil at a chord Reynolds number of $3 \\times 10^5$, with varying rotation and radii, is studied with direct numerical simulations and linear stability analyses. Low rotation does not significantly affect transition in the outboard blade region. The relative insensitivity to rotation is due to a laminar separation bubble near the leading edge, spanwise-deformed by a primary self-excited instability, promoting the secondary absolute instability of the Kelvin–Helmholtz (KH) vortices and rapid transition. Moderate increases in rotation, or moving inboard, stabilise the flow by accelerating the attached boundary layer and possibly inducing competition between cross-flow and KH modes. This delays separation and transition. Initially, for high rotation rates or radial locations close to the hub, transition is delayed. Nevertheless, strong stationary and travelling cross-flow modes are eventually triggered, spanwise modulating the KH rolls and shifting the transition line close to the leading edge. Cross-flow velocities as high as $56\\,\\%$ of the free stream velocity directed towards the blade tip are reached at the transition location. For radial locations farther from the hub, the effective angle of attack is decreased, and cross-flow transition occurs at lower rotation rates. The advance or delay of the transition line compared with a non-rotating configuration depends on the competing rotation effects of stabilising the attached boundary layer and triggering cross-flow modes in the separation flow region.

Direct numerical simulation (DNS) of rotating pipe flows up to $Re_\\tau \\approx 3000$ is carried out to investigate drag reduction effects associated with axial rotation, extending previous studies carried out at a modest Reynolds number (Orlandi & Fatica, J. Fluid Mech., vol. 343, 1997, pp. 43–72; Orlandi & Ebstein, Intl J. Heat Fluid Flow, vol. 21, 2000, pp. 499–505). The results show that the drag reduction, which we theoretically show to be equivalent to net power saving assuming no mechanical losses, monotonically increases as either the Reynolds number or the rotation number increases, proportionally to the inner-scaled rotational speed. Net drag reduction up to approximately $70\\,\\%$ is observed, while being far from flow relaminarisation. Scaling laws for the mean axial and azimuthal velocity are proposed, from which a predictive formula for the friction factor is derived. The formula can correctly represent the dependency of the friction factor on the Reynolds and rotation numbers, maintaining good accuracy for low-to-moderate rotation numbers. Examination of the turbulent structures highlights the role of rotation in widening and elongating the small-scale streaks, with subsequent suppression of sweeps and ejections. In the core part of the flow, clear weakening of large-scale turbulent motions is observed at high Reynolds numbers, with subsequent suppression of the outer-layer peak in the pre-multiplied spectra. The Fukagata–Iwamoto–Kasagi decomposition indicates that, consistent with a theoretically derived formula, the outer layer yields the largest contribution to drag reduction at increasingly high Reynolds numbers. In contrast, both the inner and the outer layers contribute to drag reduction as the rotation number increases.

Three-dimensional direct numerical simulations of rotating Rayleigh–Bénard convection in the planar geometry with no-slip top and bottom and periodic lateral boundary conditions are performed for a broad parameter range with the Rayleigh number spanning in $5\\times 10^{6}\\leq Ra \\leq 5\\times 10^{13}$, Ekman number within $5\\times 10^{-9}\\leq Ek \\leq 5\\times 10^{-5}$ and Prandtl number $Pr=1$. The thermal and Ekman boundary layer (BL) statistics, temperature drop within the thermal BL, interior temperature gradient and scaling behaviours of the heat and momentum transports (reflected in the Nusselt $Nu$ and Reynolds numbers $Re$) as well as the convective length scale are investigated across various flow regimes. The global and local momentum transports are examined via the $Re$ scaling derived from the classical theoretical balances of viscous–Archimedean–Coriolis (VAC) and Coriolis–inertial–Archimedean (CIA) forces. The VAC-based $Re$ scaling is shown to agree well with the data in the cellular and columnar regimes, where the characteristic convective length scales as the onset length scale ${\\sim } Ek^{1/3}$, while the CIA-based $Re$ scaling and the inertia length scale $\\sim (ReEk)^{1/2}$ work well in the geostrophic turbulence regime for $Ek\\leq 1.5\\times 10^{-8}$. The examinations of $Nu$, global and local $Re$, and convective length scale as well as the temperature drop within the thermal BL and its thickness scaling behaviours, indicate that for extreme parameters of $Ek\\leq 1.5\\times 10^{-8}$ and $80\\lesssim RaEk^{4/3}\\lesssim 200$, we have reached the diffusion-free geostrophic turbulence regime.

A turbulent two-vortex system (T-2VS) is obtained by inserting analytical model wake vortices into very weak homogeneous isotropic turbulence (HIT) and by evolving them in time using large-eddy simulation until a turbulent state at statistical equilibrium is reached. The T-2VS is characterised as follows: circulation distribution of the vortices; energy of the mean and fluctuating fields; energy dissipation rate. It is also verified that essentially the same T-2VS is obtained when varying the initial model or initial HIT perturbation. A wall-resolved simulation of the T-2VS further interacting with a smooth ground is then performed at $Re_\\varGamma = 2 \\times 10^5$; this is $10 \\times$ higher than in previous works, which allows us to better capture the high Reynolds number behaviour. The high release height of the T-2VS also ensures a physically correct approach to the ground. The results are compared with the literature and also to what is obtained for the case of non-turbulent vortices interacting with the same ground at the same Reynolds number. The flow topologies are discussed, and significant differences are highlighted regarding the separation of the boundary layer generated at the ground, and the way this secondary vorticity interacts with the primary vortices and makes them decay. The vortex trajectories are also measured, together with their circulation distribution and global circulation evolution, and the differences are discussed.

We explore ${\\rm CO}_2$ injection into a layered permeable rock consisting of high permeability reservoir layers, separated by low permeability mudstone, and taking the shape of an anticline within a laterally extensive aquifer. We first show how the storage capacity of the formation depends on the capillary entry pressure of the inter-layer mudstone, so that ${\\rm CO}_2$ cannot flow from one layer into the next. We then consider a formation composed of two layers, overlain by a cap rock. For injection into the lowest layer, we show that the injection rate, capillary entry pressure and buoyancy driven flux through the mudstone determine whether the lower or upper layer fills to the spill point first. We also show that at the end of the injection phase, ${\\rm CO}_2$ may continue to flow from the lower to the upper layer. This implies that injection should be stopped once the injected volume matches the static capacity of the formation in order to prevent spilling after injection. We present a series of analogue experiments of a two layered system that illustrate some of the principles described by the model, and assess the implications of the results for field scale systems.

An equation for the evolution of mean kinetic energy, $E$, in a two-dimensional (2-D) or 3-D Rayleigh–Bénard system with domain height $L$ is derived. Assuming classical Nusselt-number scaling, $Nu \\sim Ra^{1/3}$, and that mean enstrophy, in the absence of a downscale energy cascade, scales as $\\sim E/L^2$, we find that the Reynolds number scales as $Re \\sim Pr^{-1}Ra^{2/3}$ in the 2-D system, where $Ra$ is the Rayleigh number and $Pr$ the Prandtl number. Using the evolution equation and the Reynolds-number scaling, it is shown that $\\tilde {\\tau } \\gtrsim Pr^{-1/2}Ra^{1/2}$, where $\\tilde {\\tau }$ is the non-dimensional convergence time scale. For the 3-D system, we make the estimate $\\tilde {\\tau } \\gtrsim Ra^{1/6}$ for $Pr = 1$. It is estimated that the total computational cost of reaching the high $Ra$ limit in a simulation is comparable between two and three dimensions. The predictions are compared with data from direct numerical simulations.

We perform two-way coupled direct numerical simulation of particle-laden flow in an open channel at a friction Reynolds number ($Re_{\\tau }$) of 5186, which exhibits many characteristics of high-Reynolds-number wall-bounded turbulence, such as the distinct separation of scales in the inner and outer layers. Three representative cases, an unladen case and low- and high-Stokes-number particle-laden cases, are performed to investigate the turbulent modification by particles. To this end, we compare several statistical quantities to understand the particle effect on momentum exchange and interphasial energy transfer. The modulation of large-scale motions (LSMs) and very-large-scale motions (VLSMs) are analysed using spectral information, and we find that the LSMs and VLSMs are generally weakened in the inner and outer layers, which is qualitatively different from similar simulations at lower Reynolds numbers ($Re_{\\tau } \\approx 500$). The spatial structures are investigated with correlation analysis, and inclined VLSMs are observed in the near-wall region, with decreased inclination angles by particles. The particles tend to widen and shorten the spanwise and streamwise extent of coherent structures, respectively. Furthermore, we find that the vorticity vector displays a preferential alignment with the eigenvector corresponding to the intermediate eigenvalue of the strain-rate tensor, independent of the particle Stokes number.

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.

Tandem cylinder flow comprises several different flow regimes. Within the reattachment regime, the development of the gap shear layers is of utmost importance to the flow, but has received little attention so far. Through direct numerical simulations at $Re = 10^{4}$, for a gap ratio of 3.0, we have discovered that the shear layers are significantly altered with respect to a single cylinder. These differences include early onset of separation, crossflow stabilising, delayed transition to turbulence and little meandering of the transition region. Vortex pairing in the gap shear layers is reported for the first time. The interaction between the recirculating gap flow and the shear layers was investigated. Asymmetrical, large-scale gap vortices influence the position of transition to turbulence through direct contact and through secondary flows. The occurrence of transition in the gap shear layers has consequences for both the reattachment mechanism and the development of the downstream cylinder wake. The reattachment points are unsteady with large amplitude fluctuations on a fine time scale. Reattachment is seen to be a combination of impingement and modification of the upstream shear layers, which causes a double shear layer in the downstream cylinder near-wake. Buffeting by and interaction with the gap shear layers likely cause transition to turbulence in the downstream cylinder boundary layer. This leads to significant changes in the wake topology, compared with a single-cylinder wake.

The outer layer dynamics of a high-Reynolds-number boundary layer recovering from non-equilibrium is studied utilising the multi-resolution approach of zonal detached eddy simulation mode 3. The non-equilibrium conditions are obtained from a boundary layer separation over a rounded step enhancing the turbulent production, and recovery happens during redevelopment after reattachment at high Reynolds numbers ($Re_{\\theta,max}\\approx 24{,}000$). Most of the outer layer turbulence is resolved by the simulation, which reproduces accurately the experimental boundary layer relaxation. The spectral analysis of streamwise velocity fluctuations and turbulent kinetic energy (TKE) production evidences the different turbulent content distribution at separation and within the redevelopment region, at which very large-scale motions are identified with streamwise wavelengths up to $\\lambda _x = 9\\delta$, where $\\delta$ is the boundary layer thickness. The redevelopment of the boundary layer is analysed in terms of the persistence of a secondary peak in the TKE production and the evolution of the wall-shear stress statistics. The skewness and probability density function of the skin friction show a slower relaxation than the downstream flow fraction. This confirms the long-lasting impact of perturbations of the outer layer in high-Reynolds-number wall-bounded flows. This persistent non-equilibrium state is suggested to be the reason for the reported lack of accuracy of the considered Reynolds-averaged Navier–Stokes models in the relaxation region.