Richard J.A.M. Stevens

Physics of Fluids · University of Twente

Research Highlights

Selected papers across the three connected programme areas: wind-farm–atmosphere interaction, multiscale prediction and physical modelling, and turbulence simulation and high-performance computing. For the complete chronological record, see the publications page.

Large-eddy simulation of turbine wakes in an extended wind farm
Large-eddy simulation of turbulent wakes in an extended wind farm. Such simulations reveal how turbine-scale wakes, farm-scale blockage, and atmospheric-boundary-layer dynamics interact.

The highlights show how the three programme areas — wind-farm–atmosphere interaction, multiscale prediction and physical modelling, and turbulence simulation and high-performance computing — connect fundamental transport physics to predictions of wind-farm performance, atmospheric exchange, flow variability, noise, and heat transport.

Six selected contributions are shown first. Four further recent papers and additional thematic selections remain one step away in expandable sections below.

Featured highlights

Recent highlights

Impact of atmospheric turbulence on performance and loads of wind turbines: knowledge gaps and research challenges

B. Kosović, S. Basu, J. Berg, L.K. Berg, S.E. Haupt, X.G. Larsén, J. Peinke, R.J.A.M. Stevens, P. Veers & S. Watson, Wind Energy Science, 2026

This expert review connects atmospheric turbulence from boundary-layer eddies to mesoscale structures and extreme events with single-turbine power and structural loads. It shows why turbulence intensity alone cannot represent the effects of stability, shear, veer, coherence, intermittency, and length scale.

Key idea: Modern rotors sample vertically and temporally heterogeneous flow that neutral, stationary, homogeneous inflow models only partly represent; better observations, coupled modelling, and validation are needed before more realistic design models can be generalized.

Studied scope: Evidence synthesis rather than a new experiment or meta-analysis; focuses mainly on single-turbine atmospheric inflow, performance, and loads, while wake-generated turbulence and farm control are assigned to a companion review. Quantitative examples come from heterogeneous cited field, wind-tunnel, LES, and failure studies and are not universal response laws.

Mean turbulent momentum fluxes and wind deficits in nocturnal stable atmospheric boundary layers

Z. Shen, L. Liu, X.-Y. Lu & R.J.A.M. Stevens, Journal of Fluid Mechanics, 2025

A reanalysis of 16 nocturnal stable-boundary-layer simulations separates the streamwise and spanwise momentum fluxes and shows how rotation turns the stress vector with height. Total stress alone therefore cannot determine the profile exponent; the result is a model built from an existing simulation database, not an independent validation.

Key idea: Total momentum-flux magnitude alone cannot distinguish the new closure from Nieuwstadt's α = 3/2 model; the spanwise flux and two wind-deficit components provide the discriminating evidence.

Studied scope: Analytical model assessed against 16 previously published wall-modelled LES cases for quasi-steady, barotropic, horizontally homogeneous, flat-surface nocturnal boundary layers with moderate stability. Field data support selected flux profiles, but the wind-deficit validation relies mainly on the same LES family. Very stable, subsiding, heterogeneous, turbine, wake, and wind-farm regimes are not tested.

Four more recent highlights

The global properties of nocturnal stable atmospheric boundary layers

Z. Shen, L. Liu, X. Lu & R.J.A.M. Stevens, Journal of Fluid Mechanics, 2024

Main finding: Across 20 large-eddy simulations, the nocturnal stable-boundary-layer height follows h ∝ √(LfLs), while the two mean wind-gradient components collapse with u*2/(h2f). The resulting geostrophic-drag coefficients reduce to functions of the stability parameter μ.

Key idea: Matching Monin–Obukhov surface-layer profiles to the outer Ekman-layer gradients yields compact drag-law expressions without assuming a separate z-less stratification layer.

Studied scope: Twenty wall-modelled LES cases over a flat, homogeneously rough surface, under quasi-steady, barotropic, horizontally homogeneous conditions, with 16.7 ≤ μ ≤ 193.3. The single-case grid test is a sensitivity check rather than strict convergence. Very stable or intermittent, subsiding, baroclinic, heterogeneous, offshore, turbine, and wind-farm flows are not tested. A 2025 follow-up revises the component-flux exponent from 3/2 to 2 while retaining the global scaling framework.

Simulation and modeling of wind farms in baroclinic atmospheric boundary layers

J.H. Kasper, A. Stieren & R.J.A.M. Stevens, Journal of Renewable and Sustainable Energy, 2024

The article compares four orientations of baroclinic forcing with a barotropic neutral-surface reference and develops a compact wake model. Boussinesq wall-modelled LES uses AMD and filtered actuator disks (C_T=0.75, induction a=0.25). The domain is 102.4 km x 10.24 km x 10 km, resolved by 2048 x 512 x 384 points (50 m x 20 m, 10 m vertically to 1.5 km, stretched to 62 m aloft).

Key idea: Aggregate-wake recovery combines turbulence-controlled wake expansion with an upward displacement of the maximum velocity deficit caused by height-dependent entrainment in a sheared boundary layer. A reduced model needs both effects to reproduce the LES ordering.

Studied scope: One aligned 10 × 6 actuator-disk farm in a conventionally neutral boundary layer, comparing one barotropic case with four directions of baroclinicity at a single shear magnitude while matching hub-height speed and direction. The reported row-power changes and fitted wake constants are case-specific. The three-hour statistics, same-LES model calibration, and absence of grid, field, magnitude, layout, stability, and operational sensitivity prevent general design claims.

Modeling wind farm noise emission and propagation: Effects of flow and layout

J. Colas, A. Emmanuelli, D. Dragna & R.J.A.M. Stevens, Renewable Energy, 2026

In one modeled stable-atmosphere case, a staggered 4 × 4 wind farm produced spatially averaged downwind sound levels about 3 dBA higher than the aligned layout beyond 2 km. The coupled calculation attributes the difference to both layout-dependent turbine source emission and sound propagation through the wind-farm flow.

Key idea: Wake-reduced wind and rotor speed suppress trailing-edge noise downstream, while turbulence-driven inflow noise persists. Superposed wake shear also creates focusing and amplitude-modulation patterns that isolated-turbine propagation misses.

Studied scope: One isolated turbine and one aligned-versus-staggered 4 × 4 comparison in a time-averaged stable atmospheric boundary layer, using inflow- and trailing-edge-noise sources and N × 2D propagation from 50 to 1080 Hz. One ground model, a two-hour mean flow, and no unsteady scattering, fully three-dimensional propagation, numerical-sensitivity study, field validation, layout ensemble, or human-response analysis. Some mapped levels are below a typical 30 dBA rural background; this is a case comparison, not a universal layout rule.

Low-frequency wind speed variations and their impact on wind farm performance

Y. Liu, A. Stieren & R.J.A.M. Stevens, Journal of Renewable and Sustainable Energy, 2026

Conditional numerical evidence for wake-history asymmetry under prescribed speed forcing, not a field-validated mesoscale response law.

Key idea: Wakes carry the history of upstream conditions: acceleration advects weaker wakes produced at lower past speeds, whereas deceleration advects stronger ones. Above-rated changes in turbine thrust can oppose this effect, so wind history alone does not determine the farm response.

Studied scope: One 7 × 4 DTU 10 MW actuator-disk farm at 7D × 5D in a neutral, horizontally homogeneous boundary layer, driven by one six-hour mast-derived speed signal repeated three times and a synthetic frequency scan. Only spatially uniform streamwise-speed forcing was tested. No non-neutral, direction-changing, terrain, layout, controller-dynamics, uncertainty, farm-grid, or field-power validation study was performed. The 3%–5% difference and roughly three-minute transition are case-specific, not operational predictions.

Further highlights by theme

Wind-farm turbulence and wake physics

Wake interaction, farm-scale recovery, and turbulent energy replenishment.

Large wind farms operate in a multiscale turbulent flow. Turbine wakes interact with neighboring turbines, merge into farm-scale wakes, and alter the exchange of momentum between the surface layer and the atmosphere above. We use large-eddy simulation and reduced-order modeling to understand these processes and improve predictive wind-farm models. See also the wind-farm LES and analytical wind-farm modeling pages.

Understanding wind farm power densities

R.J.A.M. Stevens, Journal of Fluid Mechanics, 2023

The paper separates wind-farm power loss into a turbine-scale component from interactions within the array and a farm-scale component from the atmospheric boundary layer's response to aggregate drag. This conceptual split clarifies why layout optimization cannot remove the whole-farm momentum-supply limit.

Key idea: Layout changes can reduce internal turbine interactions, but they cannot remove the atmospheric momentum-supply constraint acting on the whole farm. The article synthesizes earlier theory and LES rather than independently deriving this result.

Studied scope: Neutral, statistically stationary large-farm synthesis; the roughly two-to-one farm-scale/turbine-scale loss ratio is attributed to earlier work, not independently demonstrated here.

Effects of turbine spacing on the power output of extended wind-farms

R.J.A.M. Stevens, D.F. Gayme & C. Meneveau, Wind Energy, 2016

Fully developed power in staggered arrays approximately organizes by the geometric-mean turbine spacing, whereas aligned arrays remain controlled mainly by streamwise spacing; entrance-region and fully developed objectives can therefore favour different layouts.

Key idea: Downward vertical kinetic-energy flux correlated with deep-array power density. Aligned columns concentrated this flux and recovered locally faster, yet staggered arrays generally produced more power because they avoided persistent direct alignment and provided a longer direct-wake recovery distance.

Studied scope: Regular arrays with more than ten rows, 100 m actuator disks at constant thrust, one fixed inflow direction, and discrete streamwise/spanwise spacings from 3.49D to 7.85D. Fully developed quantities use 6–8 km downstream; entrance power uses the first 4 km. The paper includes normalized Horns Rev/Nysted comparisons and a selected two-grid check, but no uncertainty analysis, strict convergence at shorter spacing, restated thermal-regime parameters, operational controls or loads, irregular layouts, or economics. The approximate 5D spanwise result and preferred alignments are case trends, not universal design rules.

Impact of wind farm wakes on flow structures in and around downstream wind farms

A. Stieren & R.J.A.M. Stevens, Flow, 2022

An upstream wind-farm wake changed power and turbulent transport throughout the downstream farm, not only at its first row. Increasing the gap from 5 to 15 km raised the downstream first-row power from 67% to 87% of the upstream first-row value in the tested staggered cases.

Key idea: Farm-to-farm wake interaction changes power and recovery through multiple downstream rows, not only at the entrance.

Studied scope: Two directly aligned 72-turbine farms in neutral LES, separated by 5–15 km; one turbine model, without stability, yaw, control, terrain, or direction ensembles.

Effect of thrust coefficient on the flow blockage effects in closely-spaced spanwise-infinite turbine arrays

J.M.I. Strickland & R.J.A.M. Stevens, Journal of Physics: Conference Series, 2020

In the tested spanwise-infinite arrays, tight lateral spacing increased first-row power relative to an isolated row, while seven downstream rows decreased it. These opposing layout effects mean that a wind farm's first row is not a neutral reference for blockage or total-farm performance.

Key idea: The first row already contains two opposing neighbor effects, so it is a layout-dependent baseline.

Studied scope: Neutral eight-row, spanwise-periodic arrays with unusually tight lateral spacing; at highest thrust, lateral benefit was 7.6–9.4% versus a 1.0–8.0% downstream penalty.

Large eddy simulations of the effect of vertical staggering in large wind farms

M. Zhang, M.G. Arendshorst & R.J.A.M. Stevens, Wind Energy, 2019

Vertical staggering increased cumulative power in the first two rows by up to 20% in the strongest tested case, but produced little or negative benefit over the last four rows in most cases. The diagnostics are consistent with local wake avoidance improving the entrance without increasing the downward turbulent energy supply to the deep farm.

Key idea: Avoiding wakes near the farm entrance does not necessarily increase the atmospheric energy supply or downstream performance.

Studied scope: Neutral finite-farm LES with alternating hub heights and fixed inflow; total gain reached about 5% only at tight spacing, without loads, yaw, control, or wind-rose averaging.

Comparison of wind farm large eddy simulations using actuator disk and actuator line models with wind tunnel experiments

R.J.A.M. Stevens, L.A. Martínez Tossas & C. Meneveau, Renewable Energy, 2018

The actuator-line model reproduces the near-wake velocity and turbulence profiles better through approximately three rotor diameters. Farther downstream, the mean profiles predicted by the actuator-line and actuator-disk models become increasingly similar. Including nacelle and tower forces further improves the local near-wake prediction.

Key idea: Turbine-model fidelity depends on the wake distance and quantity being evaluated; one representation is not uniformly superior.

Studied scope: Neutral wind-tunnel model and coarse-grid LES; actuator-line advantage was strongest within about 3D, nacelle/tower effects negligible by about 5D, and no farm-power observations were tested.

Atmospheric coupling and wind-energy limits

Stability, low-level jets, geostrophic forcing, and available kinetic energy.

Wind-farm performance is controlled by the atmospheric boundary layer. Stability, low-level jets, baroclinicity, geostrophic forcing, and turbulent momentum transport determine how much kinetic energy is available to the farm and how quickly wakes recover. See also the turbulent boundary layer page.

  • Understanding wind farm power densities - also featured above.
  • The global properties of nocturnal stable atmospheric boundary layers, and Mean turbulent momentum fluxes and wind deficits in nocturnal stable atmospheric boundary layers - also listed under Recent highlights above.

Geostrophic drag law for conventionally neutral atmospheric boundary layers revisited

L. Liu, S.N. Gadde & R.J.A.M. Stevens, Quarterly Journal of the Royal Meteorological Society, 2021

Main finding: Across 24 idealized conventionally neutral atmospheric-boundary-layer LES, the dimensionless 5%-momentum-flux height |f|h/u* decreased systematically as the stratification-to-rotation ratio N/|f| increased from 42 to 1350. A curve fitted within the same simulation campaign organized the cases, while selected field estimates showed broad consistency rather than independent validation.

Key idea: The ratio of free-atmosphere stratification to planetary rotation provides a physically motivated coordinate for organizing the depth of an inversion-capped, conventionally neutral boundary layer.

Studied scope: Twenty-four principal wall-modelled LES with a flat homogeneous surface, zero surface heat flux, fixed 12 m s−1 geostrophic wind and 10−4 m roughness, lapse rates of 1-9 K km−1, and latitudes of 5°-70°. The fitted curve uses the same LES campaign. Endpoint grid and subgrid checks do not establish absolute convergence, and the selected field estimates do not control roughness, thermal state, nonstationarity, or measurement uncertainty. The result is not a universal height law or a direct wind-energy-performance prediction.

Universal Wind Profile for Conventionally Neutral Atmospheric Boundary Layers

L. Liu, S.N. Gadde & R.J.A.M. Stevens, Physical Review Letters, 2021

The study supplies a compact and physically motivated representation that is strongly consistent with its calibration LES. It does not provide independent evidence for a universal wind profile, a parameter-free derivation, or transfer beyond the sampled CNBL family.

Key idea: Zero potential-temperature flux at the surface does not make buoyancy irrelevant throughout an inversion-capped boundary layer. Entrainment near the capping inversion creates a local flux that modifies the wind profile above the surface layer.

Studied scope: Six flat, horizontally periodic, quasistationary LES cases on a 2883 grid, spanning Rossby numbers 4.5 × 104 to 2.7 × 107 and Zilitinkevich numbers 51.2–153.6, with statistics averaged over one inertial period. Model constants were inferred from the same LES family; the final wind-profile comparison shows two representative cases. Earlier numerical datasets support the flux-profile shape, but the paper provides no field-profile, held-out-case, uncertainty, or grid-sensitivity validation and does not test transient or heterogeneous flows, turbines, wakes, or farm power. The cited supplement was not present in the supplied corpus.

Impact of Negative Geostrophic Wind Shear on Wind Farm Performance

A. Stieren, J.H. Kasper, S.N. Gadde & R.J.A.M. Stevens, PRX Energy, 2022

The paper tests how a prescribed negative vertical gradient of geostrophic wind changes stable- and neutral-boundary-layer wind-farm performance. Wall-modelled Boussinesq LES uses the AMD SGS closure, concurrent precursor inflow, and actuator-line NREL 5-MW turbines. The 15.36 km x 4.8 km x 4 km domain has 1280 x 640 x 384 points, 12 m x 7.5 m horizontal resolution, 5 m vertical resolution below 1.5 km, and stretching aloft.

Key idea: Additional turbulence aloft is not necessarily beneficial. Negative shear above the low-level jet generated upward turbulent momentum transport that opposed the downward transport supplying the wind farm.

Studied scope: Six stable or neutral LES cases with prescribed, direction-preserving linear negative shear, an aligned 10 × 5 NREL 5-MW farm at 7D × 5D spacing, and three-hour statistics on a 1280 × 640 × 384 grid. The stable and neutral forcing changes were 4 m/s over 200 m and 3 m/s over 1000 m, respectively. No case reached fully developed farm flow. The study tests one turbine, layout, hub-height direction, and offshore roughness, with no field comparison, uncertainty analysis, strict grid convergence, positive or direction-changing shear, thermal advection, or time-dependent forcing. Baroclinicity changed several inflow properties together, so the results do not define a universal power penalty or benefit.

Effect of low-level jet height on wind farm performance

S.N. Gadde & R.J.A.M. Stevens, Journal of Renewable and Sustainable Energy, 2021

The article asks how a fixed stable-boundary-layer LLJ behaves when it lies above, across, or below a farm's rotor-swept area. Boussinesq LES uses a Lagrangian dynamic SGS closure, Monin–Obukhov wall fluxes, filtered actuator disks, concurrent precursor inflow, two-direction fringe layers, Rayleigh damping, and local turbine yaw control. The moderately stable inflow has G=8 m s^-1, f=1.159e-4 s^-1, offshore z_0=0.002 m, surface cooling 0.5 K h^-1, z_i=131.6 m, z_jet approximately 125 m, u_jet/G=1.21, and z_i/L=2.95.

Key idea: A jet below the rotor caused a severe early-row loss because the negative-shear region had little atmospheric turbulence. Farther downstream, wake-generated turbulence enabled an upward flux from the jet and relative power began to recover.

Studied scope: LES of one moderately stable offshore boundary layer with a fixed jet at approximately 125 m. Three main cases moved an aligned 10 × 4 actuator-disk farm vertically relative to the jet using 80-m rotors at 7D × 5D spacing; two larger-rotor cases also changed hub height and normalized spacing. Statistics cover the final hour after an eight-hour precursor spin-up and one preceding hour of turbine operation. Power is normalized by each case's first row, so the study tests downstream recovery, not absolute power, annual energy, or an optimal hub height. It provides no field comparison, uncertainty analysis, independent realization, strict grid convergence, turbine-control or load assessment, transient jet, or other stability regime.

Multiscale wind-farm variability

Power fluctuations driven by atmospheric and array-scale motions.

Wind-farm power varies over seconds, minutes, hours, and longer atmospheric time scales. We study how coherent atmospheric motions, turbulent structures, and turbine-array interactions shape aggregate power fluctuations.

Temporal structure of aggregate power fluctuations in large-eddy simulations of extended wind-farms

R.J.A.M. Stevens & C. Meneveau, Journal of Renewable and Sustainable Energy, 2014

Spanwise turbine signals are nearly uncorrelated, while downstream signals are correlated with an advection-time delay. Streamwise and whole-farm aggregation suppresses intermediate frequencies more strongly than an independent 1/N expectation because delayed correlated signals partially cancel.

Key idea: Farm aggregation is not simple independent averaging: wake and atmospheric structures travel downstream, phase-shifting correlated turbine signals. The peak shifted with downstream spacing and was smoothed by changing wind direction.

Studied scope: Neutral, flat-terrain actuator-disk LES with 100-m rotors in aligned and staggered periodic farms containing 4–64 turbines streamwise and six spanwise at fixed sparseness, plus one aligned 13 × 6 finite farm. Most periodic cases ran for about 27 h, with the first 5.4 h discarded; resolution, domain length, slowly varying speed, fixed direction, and two dynamic-direction cases were tested. Power conversion assumes operating regime II. The study contains no stability, terrain, field, controller, electromechanical, grid, uncertainty, or independent- realization validation. The f−5/3 range is approximate and its origin remains unresolved; it is not a universal forecasting or grid-balancing law.

A wavenumber-frequency spectral model for atmospheric boundary layers

M. Wilczek, R.J.A.M. Stevens, Y. Narita & C. Meneveau, Journal of Physics: Conference Series, 2014

This paper establishes an economical leading-order ABL spectral representation and documents its failure modes. It does not establish a complete dynamical model, quantitative prediction error, or wind-farm transfer.

Key idea: Mean flow sets the Doppler shift; random sweeping by larger eddies gives each spatial scale a range of observed frequencies. The simple model underestimates low-wavenumber scatter, where scale separation and omitted dynamics matter most.

Studied scope: One pressure-driven, horizontally periodic, neutral boundary-layer LES in a 4π × 2π × H domain on a 512 × 256 × 128 grid, with the published comparisons focused on z = 0.15H. The model treats only streamwise advection of streamwise velocity, assumes Gaussian sweeping and scale separation, and neglects intrinsic small-scale evolution and transverse or vertical effects. Agreement is qualitative, with no uncertainty, sensitivity, field, or independent validation. The 100-m rotor scale is an illustrative mapping only: no turbine, power, fatigue-load, farm, or forecasting calculation is made.

Wind-farm noise and environmental impact

Wake, layout, terrain, and atmospheric effects on sound.

Wind-farm flow physics affects more than power production. Wakes, turbine layout, atmospheric turbulence, and rotor operating conditions influence noise emission, propagation, and amplitude modulation.

  • Modeling wind farm noise emission and propagation: Effects of flow and layout - also listed under Recent highlights above.

Wake-induced variations in noise levels and amplitude modulation for two interacting wind turbines

J. Colas, A. Emmanuelli, D. Dragna & R.J.A.M. Stevens, Journal of the Acoustical Society of America, 2026

The paper demonstrates that predicted pair AM is structurally sensitive to geometry and timing inputs. Its 400 s beat is an illustrative sensitivity experiment, not evidence that staggered layouts generate that physical timescale.

Key idea: Pair orientation separately changes source strength, wake refraction, and rotor-timing effects; these are numerical case results, not a universal siting rule.

Three-dimensional effects of the wake on wind turbine sound propagation using parabolic equation

H. Bommidala, J. Colas, A. Emmanuelli, D. Dragna, C. Khodr, B. Cotté & R.J.A.M. Stevens, Journal of Sound and Vibration, 2025

The paper makes 3D horizontal refraction a load-bearing modelling concern for long, laterally sheared wakes. It does not validate the focal magnitudes or establish a general stability or annoyance rule.

Key idea: Independent vertical propagation planes capture vertical focusing but can miss horizontal wake refraction and strongly underpredict stable-condition focal levels and modulation.

Impact of a Two-Dimensional Steep Hill on Wind Turbine Noise Propagation

J. Colas, A. Emmanuelli, D. Dragna, P. Blanc-Benon, B. Cotté & R.J.A.M. Stevens, Wind Energy Science, 2024

Main finding: In one neutral, idealized 100 m ridge calculation, placing the turbine immediately upstream produced a strong modeled OASPL dip roughly 250-600 m downwind, but hill-wake refraction restored levels near 700 m to about the flat-case value; farther downwind, levels were about 4 dBA lower than flat. This coupled LES/source/acoustic result is case-specific, not a general siting rule or field validation.

Key idea: Terrain is not only an acoustic barrier: by reshaping the mean flow and turbine wake, it can create new focusing zones, so source emission, shielding, and refraction must be separated.

Studied scope: Six coupled numerical cases compare flat terrain, a turbine immediately upstream of one 100 m-high idealized ridge, and a hilltop turbine, with and without the turbine wake in the propagation mean field. The truly neutral, constant-temperature calculation uses actuator-disk LES, an extended moving source, and independent vertical-plane acoustic propagation. It omits transverse refraction, wind veer, unsteady turbulent scattering, terrain-dependent source turbulence, a terrain ensemble, displayed grid/source-height convergence, field validation, and human-response evidence.

High-performance simulation and open-source tools

Scalable LES and DNS for wind farms and canonical turbulence.

High-fidelity turbulence simulations require scalable numerical methods and efficient use of modern supercomputers. We develop and use simulation tools for wind-farm LES and canonical DNS, including the open-source AFiD framework.

AFiD direct numerical simulation of Rayleigh-Bénard convection

AFiD-GPU: a versatile Navier-Stokes Solver for Wall-Bounded Turbulent Flows on GPU Clusters

X. Zhu et al., Computer Physics Communications, 2018

AFiD-GPU is a high-performance implementation of the AFiD incompressible Navier-Stokes solver for GPU clusters. It enables large-scale simulations of canonical turbulent flows such as Rayleigh-Bénard convection, Taylor-Couette flow, channel flow, and plane Couette flow.

Studied scope: Structured-grid GPU/CPU comparison on 2017-era systems, with Rayleigh–Bénard validation at Pr = 1 and 107 ≤ Ra ≤ 1011, plus one plane-Couette case at Rec = 3,000; the reported speedups are hardware-specific, not current-platform guarantees.

Key idea: Open, scalable simulation tools are essential for connecting fundamental turbulence physics with high-resolution numerical experiments.

Comparison of computational codes for direct numerical simulations of turbulent Rayleigh-Bénard convection

G.L. Kooij, M.A. Botchev, E.M.A. Frederix, B.J. Geurts, S. Horn, D. Lohse, E.P. van der Poel, O. Shishkina, R.J.A.M. Stevens & R. Verzicco, Computers & Fluids, 2018

This is credible cross-implementation validation of global heat transport and a strong negative demonstration against Nu-only fidelity checks. It is not cross-code validation of the earlier local boundary-layer profile claims or a hardware-independent code leaderboard.

Key idea: Agreement in a global heat-transfer number is not sufficient evidence of a resolved DNS: deliberately under-resolved higher-Rayleigh-number runs retain plausible Nusselt values while their near-wall temperature fields show grid-imprinted artifacts.

Studied scope: AFID/RBflow, Goldfish, Nek5000, and one standard OpenFOAM configuration; one converged Rayleigh number, Pr = 1, three simple geometries, 300-free-fall-time averaging, and CPU-cost comparisons on Cartesius and SuperMUC. No current-code or hardware rerun, archived input set, formal timing uncertainty, or full cross-code comparison of higher-order statistics.

Canonical turbulence and thermal convection

Transport, coherent structures, and scaling in controlled turbulent flows.

Canonical turbulent flows provide controlled systems for studying transport, coherent structures, and scaling behavior. These studies support the physical understanding and numerical methods used across our work on wind-energy and environmental flows. See also the thermal convection page.

Normalized heat transport versus inverse Rossby number at Prandtl numbers 4.38 and 6.4, showing weaker maxima and lower optimal rotation at Rayleigh number 10 to the tenth

Optimal heat transport in rotating Rayleigh-Bénard convection at large Rayleigh numbers

R. Hartmann, G.S. Yerragolam, R. Verzicco, D. Lohse & R.J.A.M. Stevens, Physical Review Fluids, 2023

Across the tested rotating-convection DNS, the inverse Rossby number giving the sampled maximum normalized heat transport first increased and then decreased with Rayleigh number. For Pr = 4.38 and 6.4, the maximum enhancement fell from roughly 20%–30% at lower Rayleigh number to about 5% by Ra = 10¹⁰.

Key idea: The low-Rayleigh-number boundary-layer rule stops locating the optimum after the simulated vortices lose vertical coherence. The associated pseudo-shear threshold is a correlated indicator, not an independently isolated cause.

Studied scope: Horizontally periodic rotating-convection DNS over 10⁷ ≤ Ra ≤ 10¹⁰, 0 ≤ Ro−1 ≤ 40, and Pr = 4.38 or 6.4. The dataset combines 81 new simulations with reused 2020 points; the Pr = 6.4, Ra = 10¹⁰ normalization is estimated, and the broad maxima retain sampling uncertainty.

Normalized heat transport across sampled inverse Rossby number and inverse aspect ratio at Rayleigh number 7 times 10 to the eighth, with three maxima labelled A, B, and C

Multiple heat transport maxima in confined-rotating Rayleigh-Bénard convection

R. Hartmann, R. Verzicco, L. Klein Kranenbarg, D. Lohse & R.J.A.M. Stevens, Journal of Fluid Mechanics, 2022

At Ra = 7 × 10⁸ and Pr = 4.38, the sampled rotation-confinement DNS map contained three separated normalized heat-transport maxima: confinement-only, double-vortex, and single-vortex states. Across the four-Rayleigh-number matrix, the double-vortex maximum reached about 50% enhancement at lower Ra but less than 20% at the two higher Ra. The discrete, interpolated cylinder dataset does not define universal optima or uniquely isolate a mechanism.

Key idea: Rotation and confinement are both stabilizing controls, but their joint heat-transport response is nonadditive because different combinations support different domain-spanning flow states. The boundary-layer and state diagnostics organize the response without uniquely partitioning its cause.

Studied scope: 323 cylindrical Boussinesq DNS at Pr = 4.38, four Rayleigh numbers from 2 × 108 to 7 × 109, 0 ≤ Ro−1 ≤ 40, and 2 ≤ Γ−1 ≤ 32. The sampling is nonuniform and interpolated; no universal optimum, formal location uncertainty, hysteresis/initial-state ensemble, alternate solver, or experimental validation is established.

Passive scalar transport in Couette flow

G.S. Yerragolam, R.J.A.M. Stevens, R. Verzicco, D. Lohse & O. Shishkina, Journal of Fluid Mechanics, 2022

Passive-scalar transport in smooth turbulent Couette flow followed Nu ≈ 0.015 Pr^(1/2) Re_b^(3/4) over the tested intermediate range. The scaling is consistent with a Reynolds-analogy link between scalar flux and wall stress, not a universal high-Reynolds-number asymptote.

Key idea: Coupling scalar transfer to measured wall friction explains the observed three-quarter-power dependence in this smooth-Couette DNS range; the exponent is conditional on that finite-range friction scaling.

Studied scope: Smooth passive-scalar plane-Couette DNS, 81 ≤ Reb ≤ 22,361 and 0.1 ≤ Pr ≤ 10; the fit is finite-range, and a domain-size check changed global quantities by less than 1%.

Strong alignment of prolate ellipsoids in Taylor-Couette flow

M.P.A. Assen, C.S. Ng, J.B. Will, R.J.A.M. Stevens, D. Lohse & R. Verzicco, Journal of Fluid Mechanics, 2022

In the tested Taylor-vortex flows, larger prolate ellipsoids clustered near vortex cores and developed a sharp tangential alignment. The strongest alignment coincided with low local axial vorticity and reduced particle rotation, but causality was not independently isolated.

Key idea: Coherent Taylor vortices organize both where finite-size particles accumulate and how they orient, but the coupled particle size, loading, response, and flow-regime changes prevent a causal attribution to any one factor.

Studied scope: Interface-resolved DNS of 16 dilute, neutrally buoyant aspect-ratio-4 ellipsoids in two coupled size/loading cases; alignment minima occurred near Ta ≈ 7 × 105 and 4 × 105.

Calculation of the mean velocity profile for strongly turbulent Taylor-Couette flow at arbitrary radius ratios

P. Berghout, R. Verzicco, R.J.A.M. Stevens, D. Lohse & D. Chung, Journal of Fluid Mechanics, 2020

Across the tested radius ratios, a curvature length organized the transition from a near-wall shear-dominated logarithmic layer to a curvature-affected layer and an approximately constant-angular-momentum bulk.

Key idea: Curvature introduces a second profile scale, but the fitted regions require sufficient scale separation and are not observed at every tested radius ratio and driving strength.

Studied scope: Smooth-wall, inner-cylinder-only Taylor–Couette experiments and DNS at radius ratios 0.5, 0.716, and 0.909; the fit used 0.20 < y/Lc < 0.65 with λ ≈ 0.64.

Direct numerical simulations of spiral Taylor-Couette turbulence

P. Berghout, R.J. Dingemans, X. Zhu, R. Verzicco, R.J.A.M. Stevens, W. van Saarloos & D. Lohse, Journal of Fluid Mechanics, 2020

Near the simulated laminar–turbulent transition, spiral Taylor–Couette turbulence followed finite-wavelength Ginzburg–Landau-type amplitude scaling. The preferred axial wavelength was 41 ± 2 gap widths at radius ratio 0.91, and the spiral traveled with the domain-mean angular velocity rather than the arithmetic mean cylinder speed.

Key idea: A finite-wavelength instability organizes turbulent–laminar spirals, while their wavelength changes turbulent fraction and angular-momentum transport in the tested periodic system.

Studied scope: Counter-rotating periodic DNS near the spiral bifurcation at radius ratio 0.91, axial aspect ratios 42–125, 400 ≤ Rei ≤ 1,200, and −2,000 ≤ Reo ≤ −1,000.

Direct numerical simulations of Taylor-Couette turbulence: the effects of sand grain roughness

P. Berghout, X. Zhu, D. Chung, R. Verzicco, R.J.A.M. Stevens & D. Lohse, Journal of Fluid Mechanics, 2019

Modeled sand-grain roughness on the inner cylinder increased plume activity, angular-momentum transport, and torque. For this surface, the equivalent sand-grain height was 1.33 times the nominal roughness height and the roughness-sublayer height was 2.78 times the equivalent height.

Key idea: Roughness changes both the near-wall structures and the global angular-momentum flux, but the fitted roughness constants remain surface-specific.

Studied scope: Immersed-boundary DNS at radius ratio 0.714 with modeled monodisperse roughness on the inner cylinder, a smooth outer cylinder, 107 ≤ Ta ≤ 109, and 5 ≤ k+ ≤ 92.

Temperature field showing turbulent thermal superstructures in Rayleigh-Bénard convection

Turbulent thermal superstructures in Rayleigh-Bénard convection

R.J.A.M. Stevens, A. Blass, X. Zhu, R. Verzicco & D. Lohse, Physical Review Fluids, 2018

Thermal superstructures persist through Ra=10^9 in the sampled Pr=1 simulations; no weakening with Ra is found over this finite range. Approximate large-domain thresholds reported are Γ≈4 for Nu and volume Reynolds number, 8 for horizontally averaged higher moments and temperature–vertical-velocity correlation, 32 for integral scales, and 64 for spectral peak locations.

Key idea: Heat transport can appear converged in a domain that is still too narrow to reproduce the largest flow structures.

Studied scope: 33 AFiD DNS with no-slip isothermal plates, horizontal periodicity, Pr = 1, three Rayleigh numbers, and Γ up to 128. No sidewalls, laboratory validation, reported averaging durations, independent realizations, or uncertainty intervals; the higher-order statistics were explicitly less converged.

Mid-height temperature snapshots across cylindrical Rayleigh-Bénard cells from aspect ratio 0.5 to 32, showing confined circulation giving way to multiple turbulent structures

How wide must Rayleigh–Bénard cells be to prevent finite aspect ratio effects in turbulent flow?

R.J.A.M. Stevens, R. Hartmann, R. Verzicco & D. Lohse, Journal of Fluid Mechanics, 2024

Required width is observable specific—about four for selected integrals but up to 16 for variance/local organization here. No universal width or ultimate-regime sufficiency follows.

Key idea: A converged Nusselt number does not guarantee that large-scale flow organization is free of finite-domain effects.

Studied scope: Cylindrical DNS over 0.075 ≤ Γ ≤ 32 with no-slip isothermal plates and a no-slip adiabatic sidewall, compared with previously published periodic-domain DNS. The study does not reach the ultimate regime; slow superstructure motion limits higher-order statistics, and no laboratory or uncertainty-qualified validation is supplied.

Time-averaged temperature field and velocity streamlines in sheared Rayleigh-Bénard convection, showing spanwise plume reorientation and streamwise sweeping with an x-z section below

Scaling relations for heat and momentum transport in sheared Rayleigh-Bénard convection

G.S. Yerragolam, C.J. Howland, R.J.A.M. Stevens, R. Verzicco, O. Shishkina & D. Lohse, Journal of Fluid Mechanics, 2024

Across the tested Couette- and Poiseuille-forced DNS, ReS/ReR organized a common non-monotonic response: moderate shear reoriented and swept thermal plumes, lowering Nu by 18%–26% at the sampled minima, whereas stronger shear produced recovery or enhancement and a friction response consistent with Prandtl's logarithmic law.

Key idea: The competition between imposed shear and the convection-generated wind, rather than imposed shear alone, organizes the transport crossover.

Studied scope: AFiD DNS and a Grossmann–Lohse-style theory for horizontally periodic smooth-wall cells, validated mainly over 106 ≤ Ra ≤ 108, 0.5 ≤ Pr ≤ 5, and 0 ≤ ReS ≤ 104. The normalized relations require unsheared reference values; no experiment, independent solver, confidence intervals, or exact averaging durations are supplied, and the proposed high-Ra pure-convection friction law remains exploratory.

Related work also covers rotating Rayleigh-Bénard convection and Taylor-Couette turbulence; see those research pages and the publications list for the corresponding papers.

Public-facing results

Accessible examples of the practical consequences of flow physics.

Some results provide especially clear examples of why wind-farm flow physics matters beyond specialist turbulence research.

  • Effect of low-level jet height on wind farm performance, and Modeling wind farm noise emission and propagation - also listed above.
Modeled total wind-farm power relative to the no-windbreak reference versus turbine distance behind the windbreak, for four windbreak heights; low barriers improve power while taller barriers become detrimental

Enhanced wind-farm performance using windbreaks

L. Liu & R.J.A.M. Stevens, Physical Review Fluids, 2021. © 2021 American Physical Society.

Low windbreaks (h/z_h=0.12) increase total six-row farm power by about 10–14% and first-row power by about 20–25% across the tested distances. Intermediate windbreaks (h/z_h=0.24) can produce larger gains at close placement but become strongly distance dependent; high windbreaks (0.36–0.48) often reduce total farm power.

Key idea: A barrier's local turbine benefit is not a farm-level design criterion. The added horizontal total-pressure flux must outweigh barrier drag, slower wake recovery, reduced vertical energy transport, and dissipation.

Studied scope: Wall-modeled LES of a six-row aligned array with 100 m actuator disks at 8D × 5D spacing in one neutral, flat-terrain inflow. The 39 cases sampled h/zh = 0.12–0.48, four offsets, selected widths and porosities, and one to six barriers; statistics used the final 11 of 54 flow-through times. The principal results use extremely dense idealized screens (η = 0.03), although the drag relation was checked only at η = 0.5 and is stated to be uncertain for dense screens. The study provides no farm-scale field validation, stability or wind-direction ensemble, terrain, turbine-control or load model, economic assessment, or evidence for an indefinitely large farm.

For the complete chronological list of peer-reviewed articles, see the publications page.