Tip-vortex cavitation is among the first forms of cavitation to appear around ship propellers. In the present study, the time-resolved three-dimensional flow field around non-cavitating and cavitating tip vortices in the wake of a marine propeller is investigated with tomographic PIV. The advance ratio of the propeller and the Reynolds number of the flow are kept constant, while the cavitation number is varied by changing the pressure inside the cavitation tunnel. The importance of masking the tip-vortex cavities before performing the tomographic reconstruction is firstly demonstrated, followed by a description of the applied masking algorithm. From the three-dimensional velocity vector fields, coherent structures of vorticity are identified using the Q-criterion. Three types of coherent structures are observed to populate the wake of the propeller, i.e. tip vortex, hub vortex, and secondary vortical structures. The secondary vortical structures surrounding the tip vortex appear to be progressively smaller in size and more chaotically-organized for decreasing cavitation number. This can be attributed to the pressure fluctuations induced by the cavity, which strengthen when the cavity size grows.

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Direct numerical simulations up to Reλ = 1445 show that the scaling exponents for the enstrophy and the dissipation rate extrema are different and depend on the Reynolds number. A similar Reynolds number dependence of the scaling exponents is observed for the moments of the dissipation rate, but not for the moments of the enstrophy. Significant changes in the exponents occur at approximately Reλ ≈ 250, where Reλ is the Taylor based Reynolds number, which coincides with structural changes in the flow, in particular the development of large-scale shear layers. A model for the probability density functions (PDFs) of the enstrophy and dissipate rate is presented, which is an extension of our existing model (Proc. R. Soc. A, vol. 476, 2020, p. 20200591) and is based on the mentioned development of large-scale layer regions within the flow. This model is able to capture the observed Reynolds number dependencies of the scaling exponents, in contrast to the existing theories which yield constant exponents. Moreover, the model reconciles the scaling at finite Reynolds number with the theoretical limit, where the enstrophy and dissipation rate scale identically at infinite Reynolds number. It suggests that the large-scale shear layers are vital for understanding the scaling of the extrema. Furthermore, to reach the theoretical limit, the scaling exponents must remain Reynolds number dependent beyond the present Reλ range.@en

Following their inception, vortex cavities emanating from stationary wing tips in cavitation tunnels are often observed to grow. These effects are usually attributed to the free and dissolved non-condensable gases in the liquid. However, a detailed mechanism for the cavity's growth is not known. Consequently, the repeatability of vortex cavitation in different flow facilities is generally poor. The main aim of our work is to highlight the contribution of dissolved gases to the cavity's growth, hence addressing water-quality influence in nuclei-depleted conditions. A model is provided for a steady-state diffusion-driven mechanism that transports dissolved gases from the surrounding liquid into the vortex cavitation through a diffusion layer located outside its interface. The model results show that the cavity grows uncontrollably when the dissolved gas concentration in the liquid is saturated or oversaturated relative to its saturation level at ambient pressure conditions (c_∞/c_sat≥1). In addition, it is shown that stable cavity sizes can be achieved when the c_∞/c_sat<1. The predictions in the range 1.04≤c_∞/c_sat≤1.33 are compared with experimental data and infer either of the two geometries for the diffusion layer: (i) a 5μm thin film approximated by a hollow cylinder around the cavity, or (ii) one that evolves like a boundary layer along the axis of the cavity. For the latter modeling approach, the observed length of the cavity was much larger than that required to match with the experimental data, skewing a preference to the thin-film assumption. In the undersaturated regime (c_∞/c_sat=0.14 & 0.39), the proposed model has a qualitative agreement with the data of Briançon-Marjollet and Merle (1996).

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A combination of time-resolved tomographic particle image velocimetry, refractive index matching technique and machine vision algorithms was used to measure the translational and rotational motion of freely moving, nearly neutrally buoyant spheres in a fully developed turbulent boundary layer (TBL). Located in the buffer and logarithmic layers, the hydrogel spheres (70 inner wall units in diameter) were refractive index matched with the water and tagged by 'spokes'. Besides translational motion, the spheres exhibited significant rotation. The spheres were surrounded by typical coherent structures observed in TBLs, among them hairpin packets and transverse and longitudinal vortices that induced ejections and sweeps. While the majority of instantaneous sphere Reynolds numbers did not exceed 100, and vortex shedding was not observed, the results showed that the spheres may affect the evolution of hairpin packets in TBLs due to their finite size. The instantaneous rotation-, wall- and shear-induced lift forces, as well as the drag forces, acting on the spheres were estimated using available correlations for the lift and drag coefficients. Results hinted at negative shear-induced lift due to flow separation at a smaller critical Reynolds number than incorporated in the correlations that do not include the effect of ambient turbulence. The results indicated further that the drag force aided by the rotation-induced lift force was instrumental in keeping one of the spheres aloft. For the wall-ward moving spheres, lift forces opposed sphere motion. As a result, the spheres approached the wall with velocities lower than their quiescent settling velocity.

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The small scales of turbulence in a high-Reynolds-number jet (R e λ≈ 350) are investigated with a µPIV setup to overcome the optical limitations of conventional tomographic PIV setups. With the aim of validating the performances of tomographic long-distance µPIV, analyses are carried out involving statistical aspects of the small scales of turbulence. The technique is assessed and the data are bench-marked to be applied to the analysis of any three-dimensional small-scale phenomena in large-scale flow domains. Graphical abstract: [Figure not available: see fulltext.].@en

Direct numerical simulations (DNS) of forced (statistically stationary) isotropic turbulence are used to assess the characteristics of the intense vorticity structures (IVS) or "worms"at higher Reynolds numbers than previously available. The simulations cover a range of Taylor-based Reynolds numbers in the range 90≤Reλ≤399, for a resolution of kmaxη≈2.0, where kmax is the maximum resolved wave number and η is the Kolmogorov microscale. Most of the IVS characteristics are confirmed at the higher Reynolds numbers analyzed in this work; e.g., the results confirm that the mean radius of the IVS (Rivs) is approximately equal to (Rivs)/η≈4-5 and that the mean radius is equal to the radius of the stationary Burgers vortex (Rivs/RB)≈1.0, with RB=2(ν/α)1/2, where ν is the kinematic viscosity and α is the (locally) imposed rate of strain. Moreover, the tangential velocity of the IVS scales with the root-mean-square velocity of the flow Uivs∼u′. These IVS characteristics seem to be robust and relatively independent of the Reynolds number; however, there are other quantities for which the classical results do not hold. A notable example is the mean length of the IVS (Livs), which previous works, carried out at smaller Reynolds numbers, claimed to scale with either the Taylor microscale λ or the integral scale of turbulence L. It turns out that the correct scaling for this quantity can be observed only at Reλ200, and the results consistently show that Livs scales with the Kolmogorov microscale Livs∼η, with a mean value equal to (Livs)≈60η. The present findings provide further evidence that Reλ200 is required for the small scales to be fully developed.

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The Richardson-scaling law states that the mean square separation of a fluid particle pair grows according to twithin the inertial range and at intermediate times. The theories predicting this scaling regime assume that the pair separation is within the inertial range and that the dispersion is local, which means that only eddies at the scale of the separation contribute. These assumptions ignore the structural organization of the turbulent flow into large-scale shear layers, where the intense small-scale motions are bounded by the large-scale energetic motions. Therefore, the large scales contribute to the velocity difference across the small-scale structures. It is shown that, indeed, the pair dispersion inside these layers is highly non-local and approaches Taylor dispersion in a way that is fundamentally different from the Richardson-scaling law. Also, the layer's contribution to the overall mean square separation remains significant as the Reynolds number increases. This calls into question the validity of the theoretical assumptions. Moreover, a literature survey reveals that, so far, tscaling is not observed for initial separations within the inertial range. We propose that the intermediate pair dispersion regime is a transition region that connects the initial Batchelor- with the final Taylor-dispersion regime. Such a simple interpretation is shown to be consistent with observations and is able to explain why tscaling is found only for one specific initial separation outside the inertial range. Moreover, the model incorporates the observed non-local contribution to the dispersion, because it requires only small-time-scale properties and large-scale properties.

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Viscous vortex layers subject to a more general uniform strain are considered. They include Townsend's steady solution for plane strain (corresponding to a parameter a = 1), in which all the strain in the plane of the layer goes toward vorticity stretching, as well as Migdal's recent steady asymmetric solution for axisymmetric strain (a = 1/2), in which half of the strain goes into vorticity stretching. In addition to considering asymmetric, symmetric, and antisymmetric steady solutions Λ a ≥ 0, it is shown that for a < 1, i.e., anything less than the Townsend case, the vorticity inherently decays in time: only boundary conditions that maintain a supply of vorticity at one or both ends lead to a non-zero steady state. For the super-Townsend case a > 1, steady states have a sheath of opposite sign vorticity. Comparison is made with homogeneous-isotropic turbulence, in which case the average vorticity in the strain eigenframe is layer-like, has wings of opposite vorticity, and the strain configuration is found to be super-Townsend. Only zero-integral perturbations of the a > 1 steady solutions are stable; otherwise, the solution grows. Finally, the appendix shows that the average flow in the strain eigenframe is (apart from an extra term) the Reynolds-averaged Navier-Stokes equation.

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The effect of drag reducing riblets on the flow structure was examined experimentally for a turbulent boundary layer at Re_θ = 9890 and riblet spacing s⁺ = 13.4. Trapezoidal riblets were used, which were attached to the water tunnel wall as a coating. Force measurements were performed to quantify the amount of drag reduction. Then, the mechanism underlying this reduction was investigated by stereo-PIV measurements in the cross-stream plane. To determine the effect of the drag reducing riblets, the results were compared with the smooth flat plate. Time-averaged turbulent statistics such as turbulent kinetic energy and Reynolds shear stress were found to be lower over the riblets compared to the flat surface. Two-point correlations of the fluctuating velocity components were calculated to elucidate the average flow structure size and strength, where riblets significantly suppressed the turbulent structures. Quadrant analysis of the Reynolds shear stress was performed to assess the change in ejection and sweep events and the results were found to be in correspondence with previous works.

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We report on the experimental investigation of the large-scale instantaneous flow structures in turbulent Taylor–Couette flow using tomographic particle image velocimetry. The results indicate three distinct regimes for counter-rotating flow within a shear Reynolds number range of 11000<ReS<47000 . Close to only inner cylinder rotation, large-scale structures are aligned in the azimuthal direction, similar to Taylor vortices. Near the point of only outer cylinder rotation, we observe columnar vortical structures in the axial direction, which are associated with small Rossby numbers. This is the first time such columnar structures are reported in a fully turbulent Taylor–Couette flow. A transition between these two regimes is observed around the point of exact counter-rotation, where the instantaneous azimuthal structures are inclined with respect to the walls. Furthermore, it is shown that the reported transitions in the turbulent flow structure modify the angular momentum transport, thereby affecting the torque scaling.@en

This paper provides an experimental investigation on the internal shear layers and the edges of the uniform momentum zones (UMZs) in a turbulent pipe flow. The time-resolved stereoscopic particle image velocimetry data are acquired in the cross-section of the pipe, and span the range of Reynolds number Reτ=340--1259. In the first part of the study, internal shear layers are detected using a three-dimensional detection method, and both their geometry as well as their fingerprint in the flow statistics are examined. Three-dimensional conditional mean flow analysis revealed a strong low-speed region beneath the average shear layers. This low-speed region is associated with positive wall-normal fluctuations, and it is accompanied by two swirling motions having opposite signs on either side in the azimuthal direction. Moreover, the shear layers are stretched by the two opposite azimuthal motions. In the second part of the study, the shear layers are treated as the continuous edges of the UMZs, which are detected using the histogram method following Adrian et al. (J. Fluid Mech., vol. 422, 2000, pp. 1–54) and de Silva et al. (J. Fluid Mech., vol. 786, 2016, pp. 309–331). For this part, two different orientation of the planes are used, i.e. the wall-normal–streamwise plane and the wall-normal–spanwise plane (cross-section of the pipe). Comparison of the detected structures shows that the shear layers mostly overlap with a UMZ edge (in either plane).
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Extreme dissipation events in turbulent flows are rare, but they can be orders of magnitude stronger than the mean dissipation rate. Despite its importance in many small-scale physical processes, there is presently no accurate theory or model for predicting the extrema as a function of the Reynolds number. Here, we introduce a new model for the dissipation probability density function (PDF) based on the concept of significant shear layers, which are thin regions of elevated local mean dissipation. At very high Reynolds numbers, these significant shear layers develop layered substructures. The flow domain is divided into the different layer regions and a background region, each with their own PDF of dissipation. The volume-weighted regional PDFs are combined to obtain the overall PDF, which is subsequently used to determine the dissipation variance and maximum. The model yields Reynolds number scalings for the dissipation maximum and variance, which are in agreement with the available data. Moreover, the power law scaling exponent is found to increase gradually with the Reynolds numbers, which is also consistent with the data. The increasing exponent is shown to have profound implications for turbulence at atmospheric and astrophysical Reynolds numbers. The present results strongly suggest that intermittent significant shear layer structures are key to understanding and quantifying the dissipation extremes, and, more generally, extreme velocity gradients.

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The reduction of turbulent skin-friction drag and the response of vortical structures in a zero-pressure gradient, turbulent boundary layer subjected to spanwise wall oscillation is investigated using planar and tomographic particle image velocimetry (PIV). The experiments are conducted at a momentum based Reynolds number of 1000, while the range of spanwise oscillation amplitude and frequency is chosen around the optimum reported in previous studies. A high-resolution planar PIV measurement is employed to determine the drag reduction directly from wall shear measurements and to analyze the accompanying modifications in the turbulent vortical structures. Drag reduction of up to 15% is quantified, with variations following the trends reported in the literature. The analysis of the turbulence structure of the flow is made in terms of Reynolds shear stresses, turbulence production, and vortex visualization. A pronounced drop of turbulence production is observed up to a height of 100 wall units from the wall. The vorticity analysis, both in the streamwise wall-normal plane and in the volumetric results, indicates a reduction of vorticity fluctuations in the near-wall domain. A distortion of the hairpin-packet arrangement is hypothesized, suggesting that the drag-reduction mechanism lies in the inhibition of the hairpin auto-generation by the spanwise wall oscillations.

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The average patterns of the velocity and scalar fields near turbulent/non-turbulent interfaces (TNTI), obtained from direct numerical simulations (DNS) of planar turbulent jets and shear free turbulence, are assessed in the strain eigenframe. These flow patterns help to clarify many aspects of the flow dynamics, including a passive scalar, near a TNTI layer, that are otherwise not easily and clearly assessed. The averaged flow field near the TNTI layer exhibits a saddle-node flow topology associated with a vortex in one half of the interface, while the other half of the interface consists of a shear layer. This observed flow pattern is thus very different from the shear-layer structure consisting of two aligned vortical motions bounded by two large-scale regions of uniform flow, that typically characterizes the average strain field in the fully developed turbulent regions. Moreover, strain dominates over vorticity near the TNTI layer, in contrast to internal turbulence. Consequently, the most compressive principal straining direction is perpendicular to the TNTI layer, and the characteristic 45-degree angle displayed in internal shear layers is not observed at the TNTI layer. The particular flow pattern observed near the TNTI layer has important consequences for the dynamics of a passive scalar field, and explains why regions of particularly high scalar gradient (magnitude) are typically found at TNTIs separating fluid with different levels of scalar concentration. Finally, it is demonstrated that, within the fully developed internal turbulent region, the scalar gradient exhibits an angle with the most compressive straining direction with a peak probability at around 20. The scalar gradient and the most compressive strain are not preferentially aligned, as has been considered for many years. The misconception originated from an ambiguous definition of the positive directions of the strain eigenvectors.

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Abstract: The feasibility of particle image velocimetry (PIV) in a thermally convective supercritical fluid was investigated. Hereto a Rayleigh–Bénard convection flow was studied at pressure and temperature above their critical values. The working fluid chosen was trifluoromethane because of its experimentally accessible critical point. The experiments were characterized by strong differences in the fluid density from the bottom to the top of the cell, where the maximum relative density difference was between 17 and 42%. These strong density changes required a careful selection of tracer particles and introduced optical distortions associated with strong refractive index changes. A preliminary background oriented schlieren (BOS) study confirmed that the tracer particles remained visible despite significant local blurring. BOS also allowed estimating the velocity error associated with optical distortions in the PIV measurements. Then, the instantaneous velocity and time-averaged velocity distributions were measured in the mid plane of the cubical cell. Main difficulties were due to blurring and optical distortions in the boundary layer and thermal plumes regions. An a posteriori estimation of the PIV measurement uncertainty was done with the statistical correlation method proposed by Wieneke (Measure Sci Technol 26:074002, 2015). It allowed to conclude that the velocity values were reliably measured in about 75% of the domain. Graphic abstract: [Figure not available: see fulltext.].

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The motion of tracer particles is kinematically simulated around three elementary flow patterns; a Burgers vortex, a shear-layer structure with coincident vortices and a node-saddle topology. These patterns are representative for their broader class of coherent structures in turbulence. Therefore, examining the dispersion in these elementary structures can improve the general understanding of turbulent dispersion at short time scales. The shear-layer structure and the node-saddle topology exhibit similar pair dispersion statistics compared to the actual turbulent flow for times up to (Formula presented.), where, (Formula presented.) is the Kolmogorov time scale. However, oscillations are observed for the pair dispersion in the Burgers vortex. Furthermore, all three structures exhibit Batchelor’s scaling. Richardson’s scaling was observed for initial particle pair separations (Formula presented.) for the shear-layer topology and the node-saddle topology and was related to the formation of the particle sheets. Moreover, the material line orientation statistics for the shear-layer and node-saddle topology are similar to the actual turbulent flow statistics, up to at least (Formula presented.). However, only the shear-layer structure can explain the non-perpendicular preferential alignment between the material lines and the direction of the most compressive strain, as observed in actual turbulence. This behaviour is due to shear-layer vorticity, which rotates the particle sheet generated by straining motions and causes the particles to spread in the direction of compressive strain also. The material line statistics in the Burgers vortex clearly differ, due to the presence of two compressive principal straining directions as opposed to two stretching directions in the shear-layer structure and the node-saddle topology. The tetrad dispersion statistics for the shear-layer structure qualitatively capture the behaviour of the shape parameters as observed in actual turbulence. In particular, it shows the initial development towards planar shapes followed by a return to more volumetric tetrads at approximately (Formula presented.), which is associated with the particles approaching the vortices inside the shear layer. However, a large deviation is observed in such behaviour in the node-saddle topology and the Burgers vortex. It is concluded that the results for the Burgers vortex deviated the most from actual turbulence and the node-saddle topology dispersion exhibits some similarities, but does not capture the geometrical features associated with material lines and tetrad dispersion. Finally, the dispersion around the shear-layer structure shows many quantitative (until 2–(Formula presented.)) and qualitative (until (Formula presented.)) similarities to the actual turbulence.

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While laboratory experiments, numerical simulations as well as field tests have underlined the influence of noise barriers in dispersing vehicular emissions and reducing downwind peak concentrations, these pollutants still remain in the atmosphere. Artificial pollutant sinks (for example, particle capturing or toxic gas treating devices) installed on top of noise barriers can further alleviate this problem by eliminating the pollutants passing through it. However, it is not known how the installation of a semi-permeable pollutant sink affects the aerodynamics of the pollutants’ flow. By finding an optimal position and orientation for these sinks, the mass of the pollutants reaching the sink inlet can be maximized. Scaled down water tunnel experiments have been used to investigate the effectiveness of installing such a pollutant sink, of fixed dimensions, on top of a noise barrier adjacent to a highway. It is found that installing a sink is more beneficial on top of shorter barriers and that vertically elevating the sink, only slightly, can enhance its pollutant capturing performance. Using a sink in a ‘highway canyon’ (two noise barriers placed symmetrically with respect to the highway) must be done cautiously as there are several flow regimes observed, which are sensitive not only to the canyon aspect ratio (ratio between canyon width and height), but also to the presence/absence of the sink. The results here not only demonstrate the effectiveness of installing pollutant sinks on noise barriers, but also provide ballpark estimates on the optimal placement, orientation and performance of these devices, prior to field tests or even large-scale installation.

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This paper describes the hysteresis in the torque for Taylor–Couette flow in the turbulent flow regime for different shear Reynolds numbers, aspect ratios and boundary conditions. The hysteresis increases with decreasing shear Reynolds number and becomes more pronounced as the aspect ratio is increased from 22 to 88. Measurements conducted in two different Taylor–Couette set-ups depict the effect of the flow conditions at the ends of the cylinders on the flow hysteresis by showing reversed hysteresis behaviour. In addition, the flow structure in the different branches of the hysteresis loop was investigated by means of stereoscopic particle image velocimetry. The results show that the dominant flow structures differ in shape and magnitude depending on the branch of the hysteresis loop. Hence, it can be concluded that the geometry could have an effect on the hysteresis behaviour of turbulent Taylor–Couette flow, but its occurrence is related to a genuine change in the flow dynamics.

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Simultaneous particle-image velocimetry and laser-induced fluorescence combined with large-eddy simulations are used to investigate the flow and pollutant dispersion behaviour in a rural-to-urban roughness transition. The urban roughness is characterized by an array of cubical obstacles in an aligned arrangement. A plane fence is added one obstacle height h upstream of the urban roughness elements, with three different fence heights considered. A smooth-wall turbulent boundary layer with a depth of 10h is used as the approaching flow, and a passive tracer is released from a uniform line source 1h upstream of the fence. A shear layer is formed at the top of the fence, which increases in strength for the higher fence cases, resulting in a deeper internal boundary layer (IBL). It is found that the mean flow for the rural-to-urban transition can be described by means of a mixing-length model provided that the transitional effects are accounted for. The mixing-length formulation for sparse urban canopies, as found in the literature, is extended to take into account the blockage effect in dense canopies. Additionally, the average mean concentration field is found to scale with the IBL depth and the bulk velocity in the IBL.

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Time-resolved tomographic particle image velocimetry (PIV) measurements (acquisition rate 250 Hz) were performed in a turbulent boundary layer on the side wall of an open channel, water flow facility (cross section 60 × 60 cm2, W × H), 3.5m downstream of the inlet at a bulk flow velocity of Ub = 0.17m/s (Reb = UbH/ν = 97, 679, δ0.99 = 45.0 mm, Reθ = 752). The measurement volume was a horizontal slab (60 × 15 × 60mm3, l × w × h) extending from the wall, 30 cm above the bottom. The setup comprised four high-speed ImagerPro HS cameras (2016×2016 pixels), a high-speed laser (Nd:YLF, Darwin Duo 80M, Quantronix), optics/prisms, and data acquisition/processing software (LaVision, DaVis 8.2). Data were acquired with and without a stationary held sphere that had a diameter, D = 6mm (D+ = 51, “+” denotes inner wall scaling), and was positioned at x3 = 5.4 and 37.6mm ( = 43 and 306) from the wall (measured from the sphere’s center). Sphere Reynolds numbers based on D and the average streamwise velocity at the sphere’s center were 692 and 959, respectively. The mean streamwise velocity profiles of the undisturbed boundary layer clearly exhibit a canonical shape. Introducing the sphere strongly affected log layer and buffer layer mean velocity and Reynolds stress profiles. Recovery to the undisturbed boundary layer characteristics is faster with the sphere positioned closest to the wall. When positioned at h+ = 306, near-wall, uplifted, coherent vortical structures extend from the wall up to the sphere’s wake with which they interact.@en