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.Comment: 12 pages, 6 figure

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 $\psi = -c_\psi (z/L)^{1/2}$, where $c_\psi = 4.2$ 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.Comment: 11 pages, 6 figures, the article has been accepted by Physical Review Letters, see https://journals.aps.org/prl/accepted/2807bYecI411db78409a3879761405c3a75de2a0

Instabilities driven by diffusio-phoretic flow on catalytic surfaces

We theoretically and numerically investigate the instabilities driven by diffusiophoretic flow, caused by a solutal concentration gradient along a reacting surface. The important control parameter is the Peclet number Pe, which quantifies the ratio of the solutal advection rate to the diffusion rate. First, we study the diffusiophoretic flow on a catalytic plane in two dimensions. From a linear stability analysis, we obtain that for Pe larger than 8pi, mass transport by convection overtakes that by diffusion, and a symmetry-breaking mode arises, which is consistent with numerical results. For even larger Pe, non-linear terms become important. For Pe larger than 16pi, multiple concentration plumes are emitted from the catalytic plane, which eventually merges into a single larger one. When Pe is even larger, there are continuous emissions and merging events of the concentration plumes. This newly-found flow state reflects the non-linear saturation of the system. The critical Peclet number for the transition to this state depends on Schmidt number Sc. In the second part of the paper, we conduct three-dimensional simulations for spherical catalytic particles, and beyond a critical Peclet number again find continuous plume emission and plume merging, now leading to chaotic motion of the phoretic particle. Our results thus help to understand the experimentally observed chaotic motion of catalytic particles in the high Pe regime

A grouping strategy for reinforcement learning-based collective yaw control of wind farms

Reinforcement learning (RL) algorithms are expected to become the next generation of wind farm control methods. However, as wind farms continue to grow in size, the computational complexity of collective wind farm control will exponentially increase with the growth of action and state spaces, limiting its potential in practical applications. In this Letter, we employ a RL-based wind farm control approach with multi-agent deep deterministic policy gradient to optimize the yaw manoeuvre of grouped wind turbines in wind farms. To reduce the computational complexity, the turbines in the wind farm are grouped according to the strength of the wake interaction. Meanwhile, to improve the control efficiency, each subgroup is treated as a whole and controlled by a single agent. Optimized results show that the proposed method can not only increase the power production of the wind farm but also significantly improve the control efficiency

Vertical structure of conventionally neutral atmospheric boundary layers

SignificanceThe presented model describes the vertical structure of conventionally neutral atmospheric boundary layers. Due to the complicated interplay between buoyancy, shear, and Coriolis effects, analytical descriptions have been limited to the mean wind speed. We introduce an analytical approach based on the Ekman equations and the basis function of the universal potential temperature flux profile that allows one to describe the wind and turbulent shear stress profiles and hence capture features like the wind veer profile. The analytical profiles are validated against high-fidelity large-eddy simulations and atmospheric measurements. Our findings contribute to the scientific community's fundamental understanding of atmospheric turbulence with direct relevance for weather forecasting, climate modeling, and wind energy applications

Effects of atmospheric stability on the performance of a wind turbine located behind a three-dimensional hill

Understanding the effect of thermal stratification on wind turbine wakes in complex terrain is essential to optimize wind farm design. The effect of a three-dimensional hill on the performance of a downwind turbine is studied by performing large eddy simulations for different atmospheric conditions. The distance between the hill and the turbine is six times the turbine diameter, and the hill height is equal to the hub height. It is shown that the hill wake reduces the power production of the downstream turbine by 35% for the convective boundary layer case under consideration. However, surprisingly, the wind turbine power production is increased by about 24% for the stable boundary layer case considered here. This phenomenon results from the entrainment of kinetic energy from the low-level jet due to the increased mixing induced by the hill wake. This effect strongly depends on the Coriolis force-induced wind veer. The increased turbulence intensity by the hill results in a strong increase in the forces experienced by the blades, which suggest the turbine is experiencing much higher unsteady turbulence loading. It is shown that the increase in the power fluctuations may not fully reflect the increase in the force fluctuations on the blades

Numerical validation and physical explanation of the universal force theory of three-dimensional steady viscous and compressible flow

In a recent paper, Liu et al. ["Lift and drag in three-dimensional steady viscous and compressible flow", Phys. Fluids 29, 116105 (2017)] obtained a universal theory for the aerodynamic force on a body in three-dimensional steady flow, effective from incompressible all the way to supersonic regimes. In this theory, the total aerodynamic force can be determined solely with the vorticity distribution on a single wake plane locating in the steady linear far field. Despite the vital importance of this result, its validity and performance in practice has not been investigated yet. In this paper, we performed Reynolds-averaged Navier-Stokes simulations of subsonic, transonic, and supersonic flows over a three-dimensional wing. The aerodynamic forces obtained from the universal force theory are compared with those from the standard wall-stress integrals. The agreement between these two formulas confirms for the first time the validity of the theory in three-dimensional steady viscous and compressible flow. The good performance of the universal formula is mainly due to the fact that the turbulent viscosity in the wake is much larger than the molecular viscosity therein, which can reduce significantly the distance of the steady linear far field from the body. To further confirm the correctness of the theory, comparisons are made for the flow structures on the wake plane obtained from the analytical results and numerical simulations. The underlying physics relevant to the universality of the theory is explained by identifying different sources of vorticity in the wake