arXiv subjects

Richard J. A. M. Stevens

Publications and source records attributed to Richard J. A. M. Stevens.

At least 19 recordsLinked to original sources

arXiv2026

Effect of grid anisotropy, resolution, and subgrid-scale models in pseudo-spectral Large Eddy Simulations of low-level clouds

We investigate the effect due to grid resolution and subgrid-scale model on large-eddy simulations of low-level clouds using a novel framework that combines pseudo-spectral advection with the anisotropic minimum dissipation (AMD) subgrid-scale model. We use two field campaigns as reference, DYCOMS-II RF01 and ASTEX, which cover both non-precipitating and precipitating stratocumulus cloud regimes across different time scales. Our results demonstrate that the AMD model combined with pseudo-spectral advection produces robust and accurate predictions across varying grid resolutions without parameter tuning. We identify a recommended grid anisotropy where vertical spacing is approximately three times finer than horizontal spacing, balancing accuracy and computational efficiency. Finally, an error analysis based on cloud liquid water content and vertical velocity variance reveals good agreement with theoretical predictions for isotropic grids, while grid anisotropy effectively improves convergence rates.

physics.flu-dyn↗

arXiv2026

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

The influence of turbine-turbine interactions on sound propagation is investigated using numerical simulations. Three configurations are examined: turbines aligned downstream of each other, placed side by side, and arranged in a staggered pattern. The simulation framework combines large-eddy simulations for aerodynamic interactions, an aeroacoustic source model to simulate turbine sound emission, and parabolic equation methods for sound propagation. When a second turbine is positioned directly downstream, wake-induced flow focusing enhances sound pressure levels (SPL) and amplitude modulation (AM) by several decibels downwind. In side-by-side and staggered configurations, SPL increases are limited (<2 dBA), and AM is generally reduced due to spatial averaging. Distinct AM patterns emerge in regions where acoustic contributions from both turbines are comparable. For identical rotor speeds, AM is strongly affected by the angular offset between rotors. When rotor speeds differ slightly, beating effects occur, resulting in intermittent AM. These findings highlight the sensitivity of AM to rotor dynamics, a key factor influencing sound perception, with implications for environmental impact and turbine siting.

physics.flu-dyn↗

arXiv2024

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

We provide scaling relations for the Nusselt number $Nu$ and the friction coefficient $C_{S}$ in sheared Rayleigh-Bénard convection, i.e., in Rayleigh-Bénard flow with Couette or Poiseuille type shear forcing, by extending the Grossmann & Lohse (2000,2001,2002,2004) theory to sheared thermal convection. The control parameters for these systems are the Rayleigh number $Ra$, the Prandtl number $Pr$, and the Reynolds number $Re_S$ that characterises the strength of the imposed shear. By direct numerical simulations and theoretical considerations, we show that in turbulent Rayleigh-Bénard convection, the friction coefficients associated with the applied shear and the shear generated by the large-scale convection rolls are both well described by Prandtl's (1932) logarithmic friction law, suggesting some kind of universality between purely shear driven flows and thermal convection. These scaling relations hold well for $10^6 \leq Ra \leq 10^8$, $0.5 \leq Pr \leq 5.0$, and $0 \leq Re_S \leq 10^4$.

physics.flu-dyn↗

arXiv2023

Characterization of natural convection between spherical shells

In this manuscript, it is analysed the onset and evolution of natural convection of an incompressible fluid between spherical shells. The shells are kept at a fixed temperature difference and aspect ratio, and the Rayleigh-Benard convection is driven by different radial gravity profiles. The analysis has been carried out by using a finite difference scheme to solve the three-dimensional Navier-Stokes equations in spherical coordinates. Numerical results are compared with theoretical predictions from linear and non-linear stability analysis, and differ from the expected critical Rayleigh number Ra_c = 1708 by less than 1 percent. In the range of Prandlt numbers Pr studied, and for all the different gravity profiles analysed, the system presents a dependence on its starting condition and flow history. Even in the region just above the onset of convection, two stable states are observed, with qualitative and quantitative differences, and exploring higher values of Ra introduces new modes and time dependency phenomena in the flow. These results are corroborated by spectral analysis.

physics.flu-dyn↗

arXiv2023

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

The heat transport in rotating Rayleigh-Bénard convection (RBC) can be significantly enhanced for moderate rotation, i.e., for an intermediate range of Rossby numbers $Ro$, compared to the non-rotating case. At Rayleigh numbers $Ra\lesssim5\cdot10^8$, the largest heat transport enhancement (HTE) is achieved when the thicknesses of kinetic and thermal boundary layer are equal. However, experimental and numerical observations show that, at larger $Ra$ ($\gtrsim5\cdot10^8$), the maximal HTE starts to deviate from the expected optimal boundary layer ratio and its amplitude decreases drastically. We present data from direct numerical simulations of rotating RBC in a periodic domain in the range of $10^7\leq Ra\leq10^{10}$ and $0\leq Ro^{-1}\leq40$ for Prandtl number $Pr=4.38$ and $6.4$ to identify the reason for the transition to this large $Ra$ regime of HTE. Our analysis reveals that the transition occurs once the bulk flow at the optimal boundary layer ratio changes to geostrophic turbulence for large $Ra$. In that flow state, the vertically coherent vortices, which support HTE by Ekman pumping at smaller $Ra$, dissolve into vertically decorrelated structures in the bulk, such that the enhancing effect of Ekman pumping and the influence of the boundary layer ratio become small. Additionally, more heat leaks out of the Ekman vortices as the fraction of thermal dissipation in the bulk increases. We find that the rotation induced shearing at the plates helps to increase the thermal dissipation in the bulk, and thus acts as a limiting factor for HTE at large $Ra$: beyond a certain ratio of wall shear stress to vortex strength, the heat transport decreases irrespectively of the boundary layer ratio. This $Pr$ dependent threshold, which roughly corresponds to a bulk accounting for $\approx1/3$ of the total thermal dissipation, sets the maximal HTE and the optimal rotation rate at large $Ra$.

physics.flu-dyn↗

arXiv2023

The mean wind and potential temperature flux profiles in convective boundary layers

We develop innovative analytical expressions for the mean wind and potential temperature flux profiles in convective boundary layers (CBLs). CBLs are frequently observed during daytime as the Earth's surface is warmed by solar radiation. Therefore, their modeling is relevant for weather forecasting, climate modeling, and wind energy applications. For CBLs in the convective-roll dominated regime, the mean velocity and potential temperature in the bulk region of the mixed layer are approximately uniform. We propose an analytical expression for the normalized potential temperature flux profile as a function of height, using a perturbation method approach in which we employ the horizontally homogeneous and quasi-stationary characteristics of the surface and inversion layers. The velocity profile in the mixed layer and the entrainment zone is constructed based on insights obtained from the proposed potential temperature flux profile and the convective logarithmic friction law. Combining this with the well-known Monin-Obukhov similarity theory allows us to capture the velocity profile over the entire boundary layer height. The proposed profiles agree excellently with large-eddy simulation results over the range of $-L/z_0 \in [3.6\times10^2, 0.7 \times 10^5]$, where $L$ is the Obukhov length and $z_0$ is the roughness length.

physics.flu-dyn↗

arXiv2022

A three-dimensional dynamic mode decomposition analysis of wind farm flow aerodynamics

High-fidelity large-eddy simulations are suitable to obtain insight into the complex flow dynamics in extended wind farms. In order to better understand these flow dynamics, we use dynamic mode decomposition (DMD) to analyze and reconstruct the flow field in large-scale numerically simulated wind farms by large-eddy simulations (LES). Different wind farm layouts are considered, and we find that a combination of horizontal and vertical staggering leads to improved wind farm performance compared to traditional horizontal staggering. We analyze the wind farm flows using the amplitude selection (AP) and sparsity-promoting (SP method) DMD approach. We find that the AP method tends to select modes with a small length scale and a high frequency, while the SP method selects large coherent structures with low frequency. The latter are somewhat reminiscent of modes obtained using proper orthogonal decomposition (POD). We find that a relatively limited number of SP-DMD modes is sufficient to accurately reconstruct the flow field in the entire wind farm, whereas the AP-DMD method requires more modes to achieve an accurate reconstruction. Thus, the SP-DMD method has a smaller performance loss compared to the AP-DMD method in terms of the reconstruction of the flow field.

physics.flu-dyn↗

arXiv2022

Evaluating the accuracy of the actuator line model against blade element momentum theory in uniform inflow

We evaluate the accuracy of the actuator line model (ALM) approach by performing simulations for the NREL~5~MW wind turbine in uniform inflow using three large eddy simulation codes. The power and thrust coefficients obtained using the three codes agrees within $1\%$ when the grid spacing $Δ_{\rm grid} \le 5.25$~m, and are cross-validated against blade element momentum (BEM) theory. We find that the results of ALM converge towards BEM theory without the need for tip correction when the numerical resolution is increased. For $Δ_{\rm grid}=0.98$~m the difference between the power and thrust coefficient obtained using ALM and BEM is $4.5\%$ and $2.1\%$, respectively, although we note that no absolute convergence between ALM and BEM can be obtained as both models use different assumptions, such as the use of a force projection method in the ALM. The difference in the local axial and tangential forces along the blades obtained from ALM simulations using $Δ_{\rm grid} = 1.97$~m and $Δ_{\rm grid} = 0.98$~m can be as large as $10\%$. The effect of the number of actuator points on the obtained turbine power and thrust coefficients is limited as the results converge when the spacing between the actuator points is about three times the grid spacing. This insight on the required number of blade points can be used to improve the efficiency of actuator line simulations.

physics.flu-dyn↗

arXiv2021

Diffusion-free scaling in rotating spherical Rayleigh-Bénard convection

Direct numerical simulations are employed to reveal three distinctly different flow regions in rotating spherical Rayleigh-Bénard convection. In the low-latitude region $\mathrm{I}$ vertical (parallel to the axis of rotation) convective columns are generated between the hot inner and the cold outer sphere. The mid-latitude region $\mathrm{II}$ is dominated by vertically aligned convective columns formed between the Northern and Southern hemispheres of the outer sphere. The diffusion-free scaling, which indicates bulk-dominated convection, originates from this mid-latitude region. In the equator region $\mathrm{III}$ the vortices are affected by the outer spherical boundary and are much shorter than in region $\mathrm{II}$. Thermally driven turbulence with background rotation in spherical Rayleigh-Bénard convection is found to be characterized by three distinctly different flow regions. The diffusion-free scaling, which indicates the heat transfer is bulk-dominated, originates from the mid-latitude region in which vertically aligned vortices are stretched between the Northern and Southern hemispheres of the outer sphere.\ These results show that the flow physics in rotating convection are qualitatively different in planar and spherical geometries. This finding underlines that it is crucial to study convection in spherical geometries to better understand geophysical and astrophysical flow phenomena.

physics.flu-dyn↗

arXiv2021

Enhanced wind-farm performance using windbreaks

The flow speed-up generated by windbreaks can be used to increase the power production of wind turbines. However, due to the increased drag imposed by the windbreaks, their use in large wind turbine arrays has been questioned. We use large eddy simulations to show that windbreaks can increase the power production of large wind farms. A crucial finding is that windbreaks in a wind farm should be much lower than for a single turbine case. In fact, the optimal windbreak for an isolated turbine can reduce wind farm performance. The optimal windbreak height in a wind farm namely depends on the right balance between flow speed-up over the windbreak and the drag imposed by all windbreaks in the farm. The increased performance is a result of the favorable total pressure flux created by the windbreaks.

physics.flu-dyn↗

arXiv2021

Strong alignment of prolate ellipsoids in Taylor-Couette flow

We report on the mobility and orientation of finite-size, neutrally buoyant prolate ellipsoids (of aspect ratio $Λ=4$) in Taylor-Couette flow, using interface resolved numerical simulations. The setup consists of a particle-laden flow in between a rotating inner and a stationary outer cylinder. We simulate two particle sizes $\ell/d=0.1$ and $\ell/d=0.2$, $\ell$ denoting the particle major axis and $d$ the gap-width between the cylinders. The volume fractions are $0.01\%$ and $0.07\%$, respectively. The particles, which are initially randomly positioned, ultimately display characteristic spatial distributions which can be categorised into four modes. Modes $(i)$ to $(iii)$ are observed in the Taylor vortex flow regime, while mode ($iv$) encompasses both the wavy vortex, and turbulent Taylor vortex flow regimes. Mode $(i)$ corresponds to stable orbits away from the vortex cores. Remarkably, in a narrow $\textit{Ta}$ range, particles get trapped in the Taylor vortex cores (mode ($ii$)). Mode $(iii)$ is the transition when both modes $(i)$ and $(ii)$ are observed. For mode $(iv)$, particles distribute throughout the domain due to flow instabilities. All four modes show characteristic orientational statistics. We find the particle clustering for mode ($ii$) to be size-dependent, with two main observations. Firstly, particle agglomeration at the core is much higher for $\ell/d=0.2$ compared to $\ell/d=0.1$. Secondly, the $\textit{Ta}$ range for which clustering is observed depends on the particle size. For this mode $(ii)$ we observe particles to align strongly with the local cylinder tangent. The most pronounced particle alignment is observed for $\ell/d=0.2$ around $\textit{Ta}=4.2\times10^5$. This observation is found to closely correspond to a minimum of axial vorticity at the Taylor vortex core ($\textit{Ta}=6\times10^5$) and we explain why.

physics.flu-dyn↗

arXiv2021

Off-center gravity induces large-scale flow patterns in spherical Rayleigh-Bénard

Inspired by the hemispherical asymmetry observed in the Earth's inner core, we perform direct numerical simulations to study the effect of the gravity center offset in spherical Rayleigh-Bénard convection. We find that even a minimal shift of the gravity center has a pronounced influence on the flow structures. When the gravity center is shifted towards the South, the co-latitudinal buoyancy component creates an energetic jet on the Northern side of the inner sphere that is directed towards the outer sphere. As a result, a large-scale meridional circulation is formed. However, surprisingly, the global heat flux is not affected by the changes in the large-scale flow organization induced by the gravity center offset. Our results suggest that the hemispherical core asymmetry is key to model the flow phenomena in the Earth's outer core and mantle.

physics.flu-dyn↗

arXiv2021

Universal Wind Profile for Conventionally Neutral Atmospheric Boundary Layers

Conventionally neutral atmospheric boundary layers (CNBLs), which are characterized with zero surface potential temperature flux and capped by an inversion of potential temperature, are frequently encountered in nature. Therefore, predicting the wind speed profiles of CNBLs is relevant for weather forecasting, climate modeling, and wind energy applications. However, previous attempts to predict the velocity profiles in CNBLs have had limited success due to the complicated interplay between buoyancy, shear, and Coriolis effects. Here, we utilize ideas from the classical Monin-Obukhov similarity theory in combination with a local scaling hypothesis to derive an analytic expression for the stability correction function $ψ= -c_ψ(z/L)^{1/2}$, where $c_ψ= 4.2$ is an empirical constant, $z$ is the height above ground, and $L$ is the local Obukhov length based on potential temperature flux at that height, for CNBLs. An analytic expression for this flux is also derived using dimensional analysis and a perturbation method approach. We find that the derived profile agrees excellently with the velocity profile in the entire boundary layer obtained from high-fidelity large eddy simulations of typical CNBLs.

physics.ao-ph↗

arXiv2021

Effect of low-level jet height on wind farm performance

Low-level jets (LLJs) are the wind maxima in the lowest 50 to 1000 m of atmospheric boundary layers. Due to their significant influence on the power production of wind farms it is crucial to understand the interaction between LLJs and wind farms. In the presence of an LLJ, there are positive and negative shear regions in the velocity profile. The positive shear regions of LLJs are continuously turbulent, while the negative shear regions have limited turbulence. We present large-eddy simulations of wind farms in which the LLJ is above, below, or in the middle of the turbine rotor swept area. We find that the wakes recover relatively fast when the LLJ is above the turbines. This is due to the high turbulence below the LLJ and the downward vertical entrainment created by the momentum deficit due to the wind farm power production. This harvests the jet's energy and aids wake recovery. However, when the LLJ is below the turbine rotor swept area, the wake recovery is very slow due to the low atmospheric turbulence above the LLJ. The energy budget analysis reveals that the entrainment fluxes are maximum and minimum when the LLJ is above and in the middle of the turbine rotor swept area, respectively. Surprisingly, we find that the negative shear creates a significant entrainment flux upward when the LLJ is below the turbine rotor swept area. This facilitates energy extraction from the jet, which is beneficial for the performance of downwind turbines.

physics.flu-dyn↗

arXiv2020

Interaction between low-level jets and wind farms in a stable atmospheric boundary layer

Low-level jets (LLJs) are the wind maxima in the lower regions of the atmosphere with a high wind energy potential. Here we use large-eddy simulations to study the effect of LLJ height on the flow dynamics in a wind farm with $10\times4$ turbines. We change the LLJ height and atmospheric thermal stratification by varying the surface cooling rate. We find that the first row power production is higher in the presence of a LLJ compared to a neutral reference case without LLJ. Besides, we show that the first row power production increases with decreasing LLJ height. Due to the higher turbulence intensity, the wind turbine wakes recover faster in a neutral boundary layer than in a stably stratified one. However, for strong thermal stratification with a low-height LLJ, the wake recovery can be faster than for the neutral reference case as energy can be entrained from the LLJ. Flow visualizations reveal that under stable stratification the growth of wind farm's internal boundary layer is restricted and the wind flows around the wind farm. Wind farms extract energy from LLJs through wake meandering and turbulent entrainment depending on the LLJ height. Both effects are advantageous for wake recovery, which is beneficial for the performance of downwind turbines. This finding is confirmed by an energy budget analysis, which reveals a significant increase in the kinetic energy flux in the presence of a LLJ. The jet strength reduces as it passes through consecutive turbine rows. For strong stratification, the combined effect of buoyancy destruction and turbulence dissipation is larger than the turbulent entrainment. Therefore, the power production of turbines in the back of the wind farm is relatively low for strong atmospheric stratifications.

physics.flu-dyn↗

arXiv2020

The effect of Prandtl number on turbulent sheared thermal convection

In turbulent wall sheared thermal convection, there are three different flow regimes, depending on the relative relevance of thermal forcing and wall shear. In this paper we report the results of direct numerical simulations of such sheared Rayleigh-Bénard convection, at fixed Rayleigh number $Ra=10^6$, varying the wall Reynolds number in the range $0 \leq Re_w \leq 4000$ and Prandtl number $0.22 \leq Pr \leq 4.6$, extending our prior work by Blass et al. (2020), where $Pr$ was kept constant at unity and the thermal forcing ($Ra$) varied. We cover a wide span of bulk Richardson numbers $0.014 \leq Ri \leq 100$ and show that the Prandtl number strongly influences the morphology and dynamics of the flow structures. In particular, at fixed $Ra$ and $Re_w$, a high Prandtl number causes stronger momentum transport from the walls and therefore yields a greater impact of the wall shear on the flow structures, resulting in an increased effect of $Re_w$ on the Nusselt number. Furthermore, we analyse the thermal and kinetic boundary layer thicknesses and relate their behaviour to the resulting flow regimes. For the largest shear rates and $Pr$ numbers, we observe the emergence of a Prandtl-von Karman log-layer, signalling the onset of turbulent dynamics in the boundary layer. Finally, our results allow to extend the Grossmann-Lohse theory for heat transport in Rayleigh-Bénard convection to the sheared case, universally describing $Nu(Ra,Pr,Re_w)$.

physics.flu-dyn↗

arXiv2020

Wall modeled immersed boundary method for high Reynolds number flow over complex terrain

Modeling the effect of complex terrain on high Reynolds number flows is important to improve our understanding of flow dynamics in wind farms and the dispersion of pollen and pollutants in hilly or mountainous terrain as well as the flow in urban areas. Unfortunately, simulating high Reynolds number flows over complex terrain is still a big challenge. Therefore, we present a simplified version of the wall modeled immersed boundary method by Chester et al. (J. Comput. Phys. 2007; 225: 427-448). By preventing the extrapolation and iteration steps in the original method, the proposed approach is much easier to implement and more computationally efficient. Furthermore, the proposed method only requires information that is available to each processor and thus is much more efficient for simulations performed on a large number of cores. These are crucial considerations for algorithms that are deployed on modern supercomputers and will allow much higher grid resolutions to be considered. We validate our method against wind tunnel measurements for turbulent flows over wall-mounted cubes, a two dimensional ridge, and a three-dimensional hill. We find very good agreement between the simulation results and the measurement data, which shows this method is suitable to model high Reynolds number flows over complex terrain.

physics.comp-ph↗

arXiv2020

Flow organization in laterally unconfined Rayleigh-Bénard turbulence

We investigate the large-scale circulation (LSC) of turbulent Rayleigh-Bénard convection in a large box of aspect ratio $Γ=32$ for Rayleigh numbers up to $Ra=10^9$ and at a fixed Prandtl number $Pr=1$. A conditional averaging technique allows us to extract statistics of the LSC even though the number and the orientation of the structures vary throughout the domain. We find that various properties of the LSC obtained here, such as the wall-shear stress distribution, the boundary layer thicknesses and the wind Reynolds number, do not differ significantly from results in confined domains ($Γ\approx 1$). This is remarkable given that the size of the structures (as measured by the width of a single convection roll) more than doubles at the highest $Ra$ as the confinement is removed. An extrapolation towards the critical shear Reynolds number of $Re_s^{\textrm{crit}} \approx 420$, at which the boundary layer (BL) typically becomes turbulent, predicts that the transition to the ultimate regime is expected at $Ra_{\textrm{crit}} \approx \mathcal{O}(10^{15})$ in unconfined geometries. This result is in line with the Göttingen experimental observations. Furthermore, we confirm that the local heat transport close to the wall is highest in the plume impacting region, where the thermal BL is thinnest, and lowest in the plume emitting region, where the thermal BL is thickest. This trend, however, weakens with increasing $Ra$.

physics.flu-dyn↗