We present a collection of eight data sets from state-of-the-art experiments and numerical simulations on turbulent velocity statistics along particle trajectories obtained in different flows with Reynolds numbers in the range R 2 120:740. Lagrangian structure functions from all data sets are found to collapse onto each other on a wide range of time lags, pointing towards the existence of a universal behavior, within present statistical convergence, and calling for a unified theoretical description. ParisiFrisch multifractal theory, suitably extended to the dissipative scales and to the Lagrangian domain, is found to capture the intermittency of velocity statistics over the whole three decades of temporal scales investigated here.

The effects of an anisotropic Navier slip-length boundary condition on turbulent channel flow are investigated parametrically by direct numerical simulations. The slip-length boundary condition is made direction dependent by specifying the value of the slip length independently for the streamwise and spanwise direction. The change in drag is mapped versus a wide range of streamwise and spanwise slip-length combinations at two different friction Reynolds numbers, Re τ0 = 180 and Re τ0 = 360. For moderate slip lengths both drag-reducing and drag-increasing slip-length combinations are found. The percentage drag increase saturates at approximately 60% for high spanwise slip. Once a threshold value for the streamwise slip length is exceeded, drag is reduced in all cases irrespective of the value of the spanwise slip length. The Reynolds number appears to have only little influence on the change in drag for the moderate Reynolds numbers studied here. A detailed comparison with the implicit theoretical formula of Fukagata et al. [Phys. Fluids 18, 051703 (2006)], which relates the change in drag with the streamwise and spanwise slip length, has been made. In general, this formula gives a fair representation of the change in drag; a modified version of this relation is presented, which improves the prediction for the change in drag for small slip length values and reduces the number of free parameters contained in the model. The effects of the slip-length boundary condition on the flow are further investigated using mean flow and turbulence statistics. For drag-neutral slip-length combinations the level of turbulent fluctuations is approximately unchanged. The presence of a slip-length boundary condition affects both the level of wall-shear stress fluctuations and the degree of intermittency of the wall-shear stress probability density function. The correlation statistics of the velocity field show that a high spanwise slip length causes a disruption of the near-wall streaks, while high streamwise slip favours an increasing streak regularity.

We present an ultrafast neural network (NN) model, QLKNN, which predicts core tokamak transport heat and particle fluxes. QLKNN is a surrogate model based on a database of 300 million flux calculations of the quasilinear gyrokinetic transport model QuaLiKiz. The database covers a wide range of realistic tokamak core parameters. Physical features such as the existence of a critical gradient for the onset of turbulent transport were integrated into the neural network training methodology. We have coupled QLKNN to the tokamak modelling framework JINTRAC and rapid control-oriented tokamak transport solver RAPTOR. The coupled frameworks are demonstrated and validated through application to three JET shots covering a representative spread of H-mode operating space, predicting turbulent transport of energy and particles in the plasma core. JINTRAC-QLKNN and RAPTOR-QLKNN are able to accurately reproduce JINTRAC-QuaLiKiz T i,e and n e profiles, but 3 to 5 orders of magnitude faster. Simulations which take hours are reduced down to only a few tens of seconds. The discrepancy in the final source-driven predicted profiles between QLKNN and QuaLiKiz is on the order 1%-15%. Also the dynamic behaviour was well captured by QLKNN, with differences of only 4%-10% compared to JINTRAC-QuaLiKiz observed at mid-radius, for a study of density buildup following the L-H transition. Deployment of neural network surrogate models in multi-physics integrated tokamak modelling is a promising route towards enabling accurate and fast tokamak scenario optimization, Uncertainty Quantification, and control applications.

The Reynolds-number dependence of turbulent channel flow over two irregular rough surfaces, based on scans of a graphite and a grit-blasted surface, is studied by direct numerical simulation. The aim is to characterise the changes in the flow in the immediate vicinity of and within the rough surfaces, an area of the flow where it is difficult to obtain experimental measurements. The average roughness heights and spatial correlation of the roughness features of the two surfaces are similar, but the two surfaces have a significant difference in the skewness of their height distributions, with the graphite sample being positively skewed (peak-dominated) and the grit-blasted surface being negatively skewed (valley-dominated). For both cases, numerical simulations were conducted at seven different Reynolds numbers, ranging from Re τ = 90 to Re τ = 720. The positively skewed surface gives rise to higher friction factors than the negatively skewed surface in all cases. For the highest Reynolds numbers, the flow has values of the roughness function U + well in excess of 7 for both surfaces and the bulk flow profile has attained a constant shape across the full height of the channel except for the immediate vicinity of the roughness, which would indicate fully rough flow. However, the mean flow profile within and directly above the rough surface still shows considerable Reynolds-number dependence and the ratio of form to viscous drag continues to increase, which indicates that at least for some types of rough surfaces the flow retains aspects of the transitionally rough regime to values of U + or k + well in excess of the values conventionally assumed for the transitionally to fully rough threshold. This is also reflected in the changes that the near-wall flow undergoes as the Reynolds number increases: the viscous sublayer, within which the surface roughness is initially buried, breaks down and regions of reverse flow intensify. At the highest Reynolds numbers, a layer of near-wall flow is observed to follow the contours of the local surface. The distribution of thickness of this 'blanketing' layer has a mixed scaling, showing that viscous effects are still significant in the near-wall flow.

a b s t r a c tTypical engineering rough surfaces show only limited resemblance to the artificially constructed rough surfaces that have been the basis of most previous fundamental research on turbulent flow over rough walls. In this article flow past an irregular rough surface is investigated, based on a scan of a rough graphite surface that serves as a typical example for an irregular rough surface found in engineering applications. The scanned map of surface height versus lateral coordinates is filtered in Fourier space to remove features on very small scales and to create a smoothly varying periodic representation of the surface. The surface is used as a no-slip boundary in direct numerical simulations of turbulent channel flow. For the resolution of the irregular boundary an iterative embedded boundary method is employed. The effects of the surface filtering on the turbulent flow are investigated by studying a series of surfaces with decreasing level of filtering. Mean flow, Reynolds stress and dispersive stress profiles show good agreement once a sufficiently large number of Fourier modes are retained. However, significant differences are observed if only the largest surface features are resolved. Strongly filtered surfaces give rise to a higher mean-flow velocity and to a higher variation of the streamwise velocity in the roughness layer compared with weakly filtered surfaces. In contrast, for the weakly filtered surfaces the mean flow is reversed over most of the lower part of the roughness sublayer and higher levels of dispersive shear stress are found.

Analytic results are derived for the apparent slip length, the change in drag and the optimum air layer thickness of laminar channel and pipe flow over an idealised superhydrophobic surface, i.e. a gas layer of constant thickness retained on a wall. For a simple Couette flow the gas layer always has a drag reducing effect, and the apparent slip length is positive, assuming that there is a favourable viscosity contrast between liquid and gas. In pressure-driven pipe and channel flow blockage limits the drag reduction caused by the lubricating effects of the gas layer; thus an optimum gas layer thickness can be derived. The values for the change in drag and the apparent slip length are strongly affected by the assumptions made for the flow in the gas phase. The standard assumptions of a constant shear rate in the gas layer or an equal pressure gradient in the gas layer and liquid layer give considerably higher values for the drag reduction and the apparent slip length than an alternative assumption of a vanishing mass flow rate in the gas layer. Similarly, a minimum viscosity contrast of four must be exceeded to achieve drag reduction under the zero mass flow rate assumption whereas the drag can be reduced for a viscosity contrast greater than unity under the conventional assumptions. Thus, traditional formulae from lubrication theory lead to an overestimation of the optimum slip length and drag reduction when applied to superhydrophobic surfaces, where the gas is trapped.

Rough surfaces are usually characterised by a single equivalent sandgrain roughness height scale that typically needs to be determined from laboratory experiments. Recently, this method has been complemented by a direct numerical simulation approach, whereby representative surfaces can be scanned and the roughness effects computed over a range of Reynolds number. This development raises the prospect over the coming years of having enough data for different types of rough surfaces to be able to relate surface characteristics to roughness effects, such as the roughness function that quantifies the downward displacement of the logarithmic law of the wall. In the present contribution, we use simulation data for 17 irregular surfaces at the same friction Reynolds number, for which they are in the transitionally rough regime. All surfaces are scaled to the same physical roughness height. Mean streamwise velocity profiles show a wide range of roughness function values, while the velocity defect profiles show a good collapse. Profile peaks of the turbulent kinetic energy also vary depending on the surface. We then consider which surface properties are important and how new properties can be incorporated into an empirical model, the accuracy of which can then be tested. Optimised models with several roughness parameters are systematically developed for the roughness function and profile peak turbulent kinetic energy. In determining the roughness function, besides the known parameters of solidity (or frontal area ratio) and skewness, it is shown that the streamwise correlation length and the root-mean-square roughness height are also significant. The peak turbulent kinetic energy is determined by the skewness and rootmean-square roughness height, along with the mean forward-facing surface angle and spanwise effective slope. The results suggest feasibility of relating rough-wall flow properties (throughout the range from hydrodynamically smooth to fully rough) to surface parameters.

The nonlinear dynamics of magnetic helicity H M , which is responsible for large-scale magnetic structure formation in electrically conducting turbulent media, is investigated in forced and decaying three-dimensional magnetohydrodynamic turbulence. This is done with the help of high-resolution direct numerical simulations and statistical closure theory. The numerically observed spectral scaling of H M is at variance with earlier work using a statistical closure model [Pouquet et al., J. Fluid Mech. 77, 321 (1976)]. By revisiting this theory, a universal dynamical balance relation is found that includes the effects of kinetic helicity as well as kinetic and magnetic energies on the inverse cascade of H M and explains the above-mentioned discrepancy. Consideration of the result in the context of mean-field dynamo theory suggests a nonlinear modification of the α-dynamo effect, which is important in the context of magnetic-field excitation in turbulent plasmas. The emergence of large-scale magnetic structures in turbulent plasmas is dynamically important in many astrophysical settings such as with regard to the interstellar medium or the magnetic-field generation in planets and stars by the turbulent dynamo effect [1][2][3]. The structure formation can be studied via the magnetic helicitywhere b is the magnetic field and a denotes the magnetic vector potential. This topological characteristic of magnetic fields yields a measure of the linkage and the twist of the field lines [4,5]. In the magnetohydrodynamic (MHD) single-fluid approximation [6], which neglects microscopic scales and the associated kinetic dynamics H M , is ideally conserved in a three-dimensional volume with periodic or closed boundary conditions [7]. It is thus prone to a nonlinear and conservative inverse spectral cascade process in the inertial range of MHD plasma turbulence. If driven at small scales , the cascade results in spectral transfer of magnetic helicity toward small spatial wave numbers k ∼ −1 [8], i.e., to the formation of large-scale magnetic structures. This process is thus of fundamental importance with regard to, e.g., the dynamics of magnetic fields in the above-mentioned turbulent astrophysical settings. In spite of its importance, little is known about the nonlinear dynamics that underlies the inverse cascade. It is the purpose of this Rapid Communication to shed some light on the rather mysterious nonlinear phenomenon creating largescale order out of quasirandom turbulent magnetic fluctuations. Please note that although the constraining effect of magnetic helicity conservation on certain α-dynamo configurations is important, it is beyond the scope of this work (for further details see Ref. [9] deals theoretically with the spectral self-similarity of magnetic helicity. The associated self-similar spectral signature in the turbulent inertial range ∼k −2 is in agreement with dimensional analysis based on a constant nonlinear spectral flux. Several studies applying direct numerical simulations find an inverse transfer of magnetic...