Search Results (78)

The logarithmic law of the wall is a foundational element in turbulence modeling. Its classical derivation, rooted in Prandtl’s mixing-length theory, is predicated on the existence of a constant shear stress layer. This paper demonstrates that this foundational assumption is not strictly satisfied for two-dimensional, uniform open-channel flows, where the Reynolds shear stress profile exhibits a distinct peak near the bed and never forms a true constant stress zone. We present a novel mechanistic derivation that circumvents this inconsistency. By reframing the bed shear stress as the time-averaged momentum flux from discrete, wall-coherent eddy impacts, we recover the log law through a mechanistic framework. Our model starts from the physical definition of the Reynolds stress at the bed, employs kinematic scaling for the velocity fluctuations, and incorporates the geometric constraint of eddy size. This approach does not require a constant stress layer and provides a more physically defensible explanation for the emergence and robustness of the log-law, directly linking it to the underlying structure of wall turbulence. The derivation resolves the long-standing paradox between the theory’s assumption and the empirical reality in open channel flows. Full article

This study investigates the mechanical and thermodynamic effects of evaporating ocean spray on the structure and dynamics of a hurricane marine atmospheric boundary layer using Eulerian multifluid and mixture model approaches coupled with the $E-ϵ$ turbulence closure. The multifluid framework treats air and spray as interpenetrating phases, enabling a physically consistent representation of air–droplet interactions governing momentum transfer, enthalpy exchange, and turbulence modulation. The mixture approach is based on a simplified description that captures only part of the underlying physics yet offers an advantage in its ability to yield analytical insight. Mechanically, spray produces competing effects: on one hand, droplet inertia causes wind deceleration, and on the other, spray-induced turbulence attenuation, primarily resulting from the air–droplet friction, leads to strengthening the wind. Analytical and numerical results show that the latter effect prevails for typical spray droplet sizes leading to wind acceleration and drag reduction at hurricane wind speeds. Thermodynamically, evaporating droplets redistribute total heat flux in favor of its latent component, with effects strongly dependent on the droplet size. Small droplets suppress turbulence and reduce the total enthalpy flux, whereas large ones enhance it. Furthermore, spray significantly increases the total enthalpy-to-drag coefficient ratio with wind speed, which agrees with field observations. Full article

Large-eddy simulation (LES) of wind farms is often limited by the computational cost required to represent many turbine rows and to obtain statistically converged wake and power statistics. Here, we present LES of an extended wind-farm configuration using the PALM model system, where cyclic lateral boundary conditions are employed to emulate interior-farm interaction in an idealized neutral boundary layer. The setup consists of nine identical horizontal-axis wind turbines arranged in a staggered array within the computational domain. Time-averaged hub-height fields show coherent wake corridors with a mean inflow-speed reduction of $23.7$% (array-mean across turbines) relative to an undisturbed background wind speed, and peak wake deficits reaching $71.4$% in the near-wake region. Turbulence levels increase markedly in the wake shear layers, with hub-height turbulence intensity enhanced by $32.2$% in the rotor region compared to background conditions; correspondingly, the peak hub-height SGS-TKE increases by a factor of 6.74 relative to background. Vertically averaged profiles indicate a momentum deficit within the turbine layer and gradual recovery aloft; the streamwise turbulent momentum flux remains predominantly negative, demonstrating the downward transport of higher-momentum air from above as a key recovery mechanism. Turbine rotor-power statistics show an initial adjustment followed by a quasi-stationary regime, with a farm-mean rotor power of $1.93$ MW and persistent inter-turbine variability characterized by a mean coefficient of variation of $61.2$%. Overall, the results demonstrate that the proposed extended-farm LES approach enables computationally efficient quantification of wake dynamics, vertical momentum transport, and their impact on power variability under idealized neutral wind-farm conditions. Full article

Building upon our previous aerodynamic characterizations of skewed jets, this study extends the investigation to systematically evaluate their thermal performance. Turbulent air jets are produced by unilaterally supplying coolant and forcing it through a series of concave perforated blockages having varying relative inner diameters (D_in/D_j = 3.0, 4.0 and 5.0) or relative thicknesses (t/D_j = 0.5, 2.0, 4.0, 6.0 and 8.0), with the jet diameter and Reynolds number fixed at D_j = 21 mm and Re_j = 20,000, respectively. The results demonstrate that the skewed jets exhibit pronounced asymmetric velocity profiles in both the x-z and y-z planes. Unlike the Gaussian distributions characteristic of conventional axisymmetric jets, these profiles manifest as distinctly skewed or saddle-shaped topologies. This topological distortion is exacerbated by reducing either D_in/D_j or t/D_j, albeit through fundamentally different mechanisms: the former only leads to jet deflection from the geometric axis, with the deflection angle increasing non-linearly from α = 4°, 5° to 12°; whilst the latter induces asymmetric internal flow development and exit momentum redistribution. The thermal performance of these jets on an iso-flux target flat plate, characterized by Nusselt number distributions at different jet-to-target spacings (H/D_j = 0 to 8.0), is shown to significantly differ from conventional axisymmetric jets. Full article

Hydrogen-enriched fuel injection in staged gas-turbine combustors is commonly achieved through jet-in-crossflow (JICF) configurations, where flame stabilization is governed by a local balance between flow-induced strain/mixing and chemical reaction rates. This work investigates turbulent reacting JICF relevant to staged combustion conditions using high-fidelity simulations with adaptive mesh refinement (AMR) and differential-diffusion effects together with Lagrangian particle statistics. Chemistry model uncertainties are incorporated by using a projection method that maps uncertainty estimates from detailed mechanisms into the model used in this work. Results show that the macroscopic flame topology remains in a stable two-branch regime (lee-stabilized and lifted) and is primarily controlled by the jet momentum–flux ratio J. Visualization of the normalized scalar dissipation rate reveals that the flame front resides on the low-dissipation side of intense mixing layers, occupying an intermediate region between over-strained and under-mixed regions. While hydrogen content does not significantly change the global stabilization mode for the cases studied, uncertainty analysis reveals composition-dependent differences that are not apparent in the mean behavior alone. In particular, visualization in Eulerian (χ, T) state-space analysis and particle statistics conditioned on the stoichiometric surface demonstrate that higher-hydrogen cases observe a lower scalar dissipation rate and exhibit substantially reduced variability in OH production under kinetic-parameter perturbations, whereas lower-hydrogen blends experience higher dissipation and amplified chemical sensitivity. These findings highlight that, even in globally similar JICF regimes, the hydrogen content can modify the local response of the flame to kinetic-parameter uncertainty, motivating uncertainty-aware interpretation and design for hydrogen-fueled staging systems. Full article

Wind-driven shear and vertical mixing in the upper meter of the ocean strongly regulate near-surface circulation and buoyant tracer transport, yet direct field observations immediately beneath the air–sea interface remain scarce. We present Lagrangian observations, equipped with an upward-looking Acoustic Doppler Current Profiler (ADCP), collected during 5–7 April 2022 in the Jeju Strait under wind stresses of 0.0006–0.19 Pa. Near-surface shear and turbulence metrics were resolved within the top surface layer (TSL), and a response-time analysis showed that upper-layer shear responded most promptly to wind variability, whereas deeper-layer shear and sea-state metrics adjusted more slowly. Wave-period variability exhibited the weakest coupling, indicating additional nonlocal influences. Reynolds-stress estimates showed that the along-wind momentum flux was predominantly negative, indicating net downward transfer of downwind momentum, while cross-direction fluxes were smaller on average and frequently reversed sign, consistent with intermittent lateral transfers associated with evolving wave–current interactions. Using an eddy-viscosity framework, we derived stress-based exponential-saturation parameterizations for depth-averaged shear and vertical diffusivity, with the diffusivity magnitude treated as sensitive to the assumed turbulent Prandtl number. The relationships are intended for event-scale conditions within the observed forcing range and provide field-constrained, implementation-ready formulations for near-surface transport and mixing models. Full article

The momentum transport and scale-dependent motion characteristics within vegetation canopies play a crucial role in shaping near-surface turbulent structures and exchange processes, yet the interactions among different turbulent scales and their statistical representations remain insufficiently understood. Based on a series of controlled wind tunnel experiments, this study identifies coherent turbulent structures using a phase-space algorithm constructed from streamwise velocity fluctuation u′, acceleration a, and jerk j, and compares transport efficiency (exuberance η). This study uses scale-wise (cut-off frequency) momentum flux contribution analysis, natural visibility graph (NVG), and large–small-scale amplitude modulation to examine transport and multiscale behaviors across different canopy densities, array layouts, and inflow conditions. Results show that canopy density (different C_d drag coefficient) is a primary factor governing transport efficiency. Under low-wind staggered configurations, increasing canopy density strengthens the contribution of low-frequency large-scale motions to total momentum flux. In contrast, high-wind aligned configurations intensify canopy-top shear, enhancing small-scale motions and thereby reducing the relative contribution of large-scale motions. NVG analysis further reveals that in high-density canopies, large-scale acceleration and deceleration events tend toward equilibrium, whereas deceleration events dominate consistently in low- and medium-density cases. Amplitude modulation results indicate that high-density cases exhibit highly consistent modulation behavior, followed by low-density cases, while medium-density cases display a pronounced height-dependent variation, characterized by a distinct modulation critical point. This study proposes a unified analytical framework integrating coherent structure detection, graph-theoretic analysis, multiscale transport characterization, and large–small-scale modulation, providing a comprehensive description of momentum transport and scale motions within canopy flows, and it offers new insight into the mechanisms governing complex vegetation canopy turbulence. Full article

High-speed jet-in-crossflow (JICF) configurations are central to several aerospace applications, including turbine-blade film cooling, thrust vectoring, and fuel or hydrogen injection in combusting or reacting flows. This study employs high-fidelity direct numerical simulations (DNS) to investigate the dynamics of a supersonic jet (Mach 3.73) interacting with a subsonic crossflow (Mach 0.8) at low Reynolds numbers. Three momentum-flux ratios (J = 2.8, 5.6, and 10.2) are considered, capturing a broad range of jet–crossflow interaction regimes. Turbulent inflow conditions are generated using the Dynamic Multiscale Approach (DMA), ensuring physically consistent boundary-layer turbulence and accurate representation of jet–crossflow interactions. Modal decomposition via proper orthogonal decomposition (POD) and spectral POD (SPOD) is used to identify the dominant spatial and spectral features of the flow. Across the three configurations, near-wall mean shear enhances small-scale turbulence, while increasing J intensifies jet penetration and vortex dynamics, producing broadband spectral gains. Downstream of the jet injection, the spectra broadly preserve the expected standard pressure and velocity scaling across the frequency range, except at high frequencies. POD reveals coherent vortical structures associated with shear-layer roll-up, jet flapping, and counter-rotating vortex pair (CVP) formation, with increasing spatial organization at higher momentum ratios. Further, POD reveals a shift in dominant structures: shear-layer roll-up governs the leading mode at high J, whereas CVP and jet–wall interactions dominate at lower J. Spectral POD identifies global plume oscillations whose Strouhal number rises with J, reflecting a transition from slow, wall-controlled flapping to faster, jet-dominated dynamics. Overall, the results demonstrate that the momentum-flux ratio (J) regulates not only jet penetration and mixing but also the hierarchy and characteristic frequencies of coherent vortical, thermal, and pressure and acoustic structures. The predominance of shear-layer roll-up over counter-rotating vortex pair (CVP) dynamics at high J, the systematic upward shift of plume-oscillation frequencies, and the strong analogy with low-frequency shock–boundary-layer interaction (SBLI) dynamics collectively provide new mechanistic insight into the unsteady behavior of supersonic jet-in-crossflow flows. Full article

During tropical cyclones (TCs), intense exchanges of momentum, heat, and moisture occur across the air–sea interface. The present study was conducted to investigate the role of surface roughness parameterizations under such conditions. To this end, a series of sensitivity experiments was conducted with a focus on Tropical Cyclone Biparjoy, which originated from the Indian Ocean in 2023. The experiments evaluate the impact of different schemes for momentum, thermal, and moisture roughness length on TC track, intensity, significant wave height, and air–sea heat fluxes. The results indicate that the momentum roughness length scheme is critical for accurately forecasting TC track and intensity and for simulating significant wave height; furthermore, Drennan’s parameterization yielded slightly better results in this case, with the smallest track error (72.0 km MAE) among the momentum schemes. Under the premise that Drennan’s parameterization scheme has high accuracy in momentum roughness, sensitivity experiments on thermal and moisture roughness parameterization were conducted. The Drennan–Fairall2014 combination achieved the lowest errors in TC central pressure (4.25 hPa RMSE) and the maximum sustained wind speed (5.31 m/s RMSE). Thermal and moisture roughness mainly affects the efficiency of turbulent heat transfer between the ocean and the atmosphere and thus has a limited impact on the cooling of sea surface temperature, with SST RMSE differences among schemes within 0.3 °C. This effect is mainly confined to the uppermost ocean layer and does not significantly change the thermal structure of the upper layers. Full article

We investigate the structure of correlation singularities for the Laguerre–Gauss beam of order $n=0$ and $m=2$ in the transverse plane during the propagation of the beam in the beam-wander model. We explicitly derive analytical expressions for the cross-spectral density of the corresponding beam order and the analytic expressions representing the singular behavior. We also verify that the singular points disappear at certain z values and reappear at other z values as shown in the previous numerical study. We investigate the dependence of the absolute value of the complex degree of coherence $\mu$ on the parameter $\delta$ of the beam-wander model during the propagation of the Laguerre–Gauss beam in the corresponding order. The complex degree of coherence depends not only on $\delta$ but also on the relative positions of two transverse observation points ${\mathit{\rho }}_1$ and ${\mathit{\rho }}_2$, as well as on the propagation variable z for the fixed values of the beam waist and the wavelength of the Laguerre–Gauss beam. Experiments on $\mu$ can demonstrate the range of the applicability of the beam-wander model in the turbulent atmosphere. Finally, we examine the orbital angular momentum flux density of the beam and confirm that the general behaviors of the previous studies also hold for $m=2$. Full article

The traditional way to model the statistics of turbulent flow and dispersion is through averaged conservation equations, in which the turbulent transport terms are described by semi-empirical expressions. A new development has been reported by Brouwers in a number of consecutive papers published over the last 15 years. The new development is that presented descriptions can be obtained through the application of fundamental principles of statistical physics and making use of the asymptotic structure of turbulence at a high Reynolds number. They no longer rely on empirical constructions, minimise calibration factors, and are not limited to specific flow situations. This article updates the contents of these works and presents them in coherent manner. The first derivations are presented as expressions for turbulent diffusion. These are subsequently implemented in a closed set of equations expressing the conservation of mean momentum, mean fluctuating energy, and energy dissipation rate. Predictions from these equations are shown to compare favourably with the results of direct numerical simulations (DNS) of the Navier–Stokes equations of highly anisotropic and inhomogeneous channel flow. The presented model equations provide a solid basis to calculate the main statistical parameters of turbulent flow and dispersion in engineering praxis and environmental analysis. Full article

Sea surface temperature (SST) gradients modulate surface wind variability at the mesoscale O(100 km), with relevant impacts on surface fluxes, rainfall, cloudiness and storms. The dependence of the SST-wind coupling mechanisms on physical environmental conditions has been proven using global ERA5 reanalysis data, regional observations and models. However, recent literature calls for the need of an observational confirmation to overcome the limitations of numerical simulations in representing such turbulent processes. Here, we employ O(10 km) MetOp A observations of surface wind and SST to verify the dependence of the downward momentum mixing (DMM) mechanism on large-scale wind U and atmospheric stability. We propose a simple empirical model describing how the coupling intensity varies as a function of U, where we account for the role of the characteristic SST length scale LSST and the boundary layer height h in determining the balance between the advective and response timescales, and therefore the decoupling of the atmospheric response from the SST forcing due to advection. Fitting such a model to the observations, we retrieve a scaling with U that depends on the atmospheric stability, in agreement with the literature. The physical interpretation from ERA5 is confirmed, albeit relevant discrepancies emerge in stable regimes and specific regional contexts. This suggests that global numerical models are not able to properly reproduce the coupling in certain conditions, which might have important implications for air–sea fluxes. Full article

This study employs Direct Numerical Simulation (DNS) to investigate the flow and heat transfer characteristics in a compressor blade passage at five Reynolds numbers ($Re=1.091\times {10}^5$, $1.229\times {10}^5$, $1.367\times {10}^5$, $1.506\times {10}^5$, and $1.645\times {10}^5$). A recent method based on local inviscid velocity reconstruction is applied to define and calculate boundary layer parameters, whereas the Rortex vortex identification method is used to analyze turbulent vortical structures. Results indicate that $Re$ significantly affects separation bubble size, transition location, and reattachment behavior, thereby altering wall heat transfer characteristics. On the pressure surface, separation and early transition are observed at higher $Re$, with the Nusselt number ($Nu$) remaining high after transition. On the suction surfaces, separation occurs such that large-scale separation at low $Re$ reduces $Nu$, while reattachment combined with turbulent mixing at high $Re$ significantly increases $Nu$. Turbulent vortical structures enhance near-wall fluid mixing through induced ejection and sweep events, thereby promoting momentum and heat transport. As $Re$ increases, the vortical structures become denser with reduced scales and the peaks in heat flux move closer to the wall, thus improving convective heat transfer efficiency. Full article

In an attempt to reconciliate air-sea momentum flux estimates derived from open sea observations, from large eddy simulation output fields, and from wind-wave tank measurements, a series of dedicated experiments were conducted in the wind-wave tank of the Large Air-Sea Facility of Marseille, France. The turbulent friction velocity, upon which the momentum flux depends, was estimated from wind measurements by applying four classical methods including the eddy-covariance method and the inertial-dissipation method. The collected data were used to investigate some characteristics of the wave-influenced boundary layer that were predicted by previous simulations, and to quantify a wave-dependent term of the turbulent kinetic energy equation, the so-called imbalance term ${\varphi }_{\mathrm{imb}}$. Our results show that the turbulent stress decreases toward lower heights where the effect of waves is large, as in the simulations, and that ${\varphi }_{\mathrm{imb}}$ is in the range 0.3 to 0.7, which is comparable to the value found with open sea data (0.4). These preliminary results have to be confirmed with wave-following probes, because the estimated eddy-covariance flux slightly varied with height, thus it could not be strictly considered to be equal to a constant total flux. Full article

This paper investigates the flow dynamics of a turbulent fountain with negative buoyancy using a Computational Fluid Dynamics (CFD) model, developed using OpenFOAM^® and calibrated against laboratory experiments. The simulations effectively replicate the geometry and buoyancy fluxes of the fountain, showing a fairly good agreement between the numerical and experimental velocity fields. These simulations are then used to investigate momentum and buoyancy fluxes for various source fluid densities. We find a dominant out-upward momentum transfer in the body of the fountain, while it is mainly out-downward below the inlet section. Furthermore, the vertical flux is almost twice the radial flux, while the tangential components are negligible on the inner side of the fountain. For small density differences between the fountain and the surrounding environment, we find a greater diffusion of the source fluid, while both the vertical and radial salt fluxes increase with increasing density of the fountain. The data generated serve as a significant resource for the development of future CFD models. Full article