Vertical structure of 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.

Numerical investigation of neutral atmospheric boundary layer flows over flat terrain and three-dimensional hills considering the effects of Coriolis force

In the E – ϵ turbulence model an eddy-exchange coefficient is evaluated from the turbulent kinetic energy E and viscous dissipation ϵ. In this study we will apply the E – ϵ model to the stable and neutral atmospheric boundary layer. A discussion is given on the equation for ϵ, which terms should be included and how we have evaluated the constants. Constant cooling rate results for the stable atmospheric boundary layer are compared with a second-order closure study. For the neutral atmospheric boundary layer a comparison is made with observations, large-eddy simulations and a second-order closure study. It is shown that a small stability effect can change the neutral atmospheric boundary layer quite drastically, and therefore, it will be difficult to observe a neutral boundary layer in the atmosphere.

In this study, a neutral atmospheric boundary layer and wind turbine blades were constructed in a large eddy simulation and actuator line model for conducting a field experiment of a wind turbine. Further, the flow field of the wind turbine was simulated in a neutral atmospheric boundary layer. The evolution of the turbulence in the front and back of the rotor with a neutral atmospheric boundary layer and its correlation with the load were studied by analyzing the continuous wavelets, the spectrum, and the correlation. The results indicate that the coherent structure of the turbulence in the neutral atmospheric boundary layer becomes stronger from one-diameter (1 D ) front of the rotor plane to 1 D back of it. The coherent structure of the turbulence in inflow is affected by the rotation of the rotor. Subsequently, strong small-scale turbulence structures appear in the rotor plane, which are continuously dissipated in the wind direction. The turbulent energy with small scales at 1 D back of rotor is feeble, and the turbulence mainly moves on a large scale. The frequency of the small-scale turbulence is approximately 1.82 Hz at the tip, which corresponds to the passing frequency of the blade and is mainly generated because of the rotation of the rotor. The flapwise load of the blade root is high when the turbulent energy is high. The results of wavelet analysis denote that the turbulence structure at the monitoring points has a good relation with the flapwise load of the blade root, and the flapwise load of the blade root of the wind turbine has obvious response to the turbulent structure of the atmosphere. A multi-resolution analysis of two points at the center and tip of the rotor and the flapwise load of the blade root denotes that the low-frequency turbulent structure at the center of the rotor (B3–B6 frequency band) is dependent on the low-frequency flapwise load of the blade root, whereas the high-frequency turbulent structure (B1–B2 frequency band) has no obvious corresponding relation with the flapwise load of the blade root. The high-frequency turbulent structure at the tip (B1–B2 frequency band) is related to the high-frequency flapwise load of the blade root, whereas the low-frequency turbulent structure (B3–B6 frequency band) has no obvious corresponding relation with the flapwise load of the blade root. Therefore, the low-frequency turbulence structure significantly influences the low-frequency band of the flapwise load of the blade root, whereas the high-frequency turbulence structure significantly influences the high-frequency band of the flapwise load of the blade root. When compared with the high-frequency turbulent structure at the blade root, the high-frequency turbulent structure has a higher frequency and a higher energy at the blade tip, and its influence on the high-frequency band of the flapwise load of the blade root is more obvious, exhibiting a consistent regular periodic variation.

The wind energy industry relies on computationally efficient engineering-type models to design wind farms. Typically these models do not account for the effect of atmospheric stratification in either the boundary layer or the free atmosphere. This study proposes a new analytical model for fully developed wind-turbine arrays in conventionally neutral atmospheric boundary layers frequently encountered in nature. The model captures the effect of the free-atmosphere stratification, Coriolis force, wind farm layout and turbine operating condition on the wind farm performance. The model is developed based on the physical insight derived from large-eddy simulations. We demonstrate that the geostrophic drag law (GDL) for flow over flat terrain can be extended to flow over fully developed wind farm arrays. The presence of a vast wind farm significantly increases the wind farm friction velocity compared with flow over flat terrain, which is modelled by updated coefficients in the GDL. The developed model reliably captures the vertical wind speed profile inside the wind farm. Furthermore, the power production trends observed in simulations are reliably reproduced. The wind farm performance, normalized by the geostrophic wind speed, decreases as the free-atmosphere thermal stability increases or the Coriolis force decreases. In addition, we find that the optimal wind farm performance is obtained at a lower thrust coefficient than the Betz limit, which indicates that optimal operating conditions for turbines in a wind farm are different than for a single turbine.

A model characterizing a turbulent wind field, consistent with neutral atmospheric boundary layer attributes, was developed for a field-based experimental wind turbine using stochastic processes combined with shear flow profiles. By incorporating interactions of vertical thermal exchange, terrain-induced surface roughness, and Coriolis forces, the model simulates environmental impacts. A sequence of wind turbines situated within the atmospheric wind field underwent computational analysis leveraging Large Eddy Simulation (LES) alongside an Actuator Line Model (ALM) to examine atmospheric turbulence alterations both preceding and following the turbines. Analysis of the power spectra concerning wind velocity, turbulence intensity, and components of Reynolds stress upwind and downwind demonstrated the turbines’ blade effects on surrounding turbulence patterns. The research demonstrated that turbulence kinetic energy experienced enhancement in downwind turbines as a result of the upwind turbine’s impact, particularly evident in the lower-frequency spectrum. Augmenting the distance between turbines initially aids in the wake’s turbulent structure restoration, with a marked effect on tip vortices that hold greater amounts of high-frequency energy.

In this paper, we consider the reconstruction of 3D turbulent flow fields from a time series of lidar data in a conventionally neutral atmospheric boundary layer (CNBL). For the reconstruction we use the maximum a posteriori estimate of the flow field. This corresponds to an optimization problem, with a cost function that has two contributions; a first term originating from the prior belief on the probability of having a certain turbulent flow field without any observations. Flow field fluctuations are assumed normally distributed and thus statistically fully determined by the mean and two-point covariance of the velocity field. The second term, is related to the likelyhood of the observations, influenced by model and measurement uncertainties. The two-point covariance is computed and found to be significantly altered by the Coriolis force, breaking up longer streamwise velocity streaks and veering spanwise structures by ∼ 45° with respect to the mean flow direction. For the reconstruction, we consider two different scanning modes, a plan position indicator (PPI) mode and a trajectory which is based on a Lissajous curve. For the PPI scanning mode we find that the mean squared error of the reconstructed velocity field is around 10% of the background variance in the scanning plane, and quickly increases outside this region. The Lissajous curve on the other hand attains an average error of 40% over the scanning region, which spans almost the whole BL height.

Generating an artificially thickened boundary layer to simulate the neutral atmospheric boundary layer

Wind turbines operate in the atmospheric boundary layer (ABL), where Coriolis effects are present. As wind turbines with larger rotor diameters are deployed, the wake structures that they create in the ABL also increase in length. Contemporary utility-scale wind turbines operate at rotor diameter-based Rossby numbers, the non-dimensional ratio between inertial and Coriolis forces, of $\mathcal {O}(100)$ where Coriolis effects become increasingly relevant. Coriolis forces provide a direct forcing on the wake, but also affect the ABL base flow, which indirectly influences wake evolution. These effects may constructively or destructively interfere because both the magnitude and sign of the direct and indirect Coriolis effects depend on the Rossby number, turbulence and buoyancy effects in the ABL. Using large eddy simulations, we investigate wake evolution over a wide range of Rossby numbers relevant to offshore wind turbines. Through an analysis of the streamwise and lateral momentum budgets, we show that Coriolis effects have a small impact on the wake recovery rate, but Coriolis effects induce significant wake deflections which can be parsed into two regimes. For high Rossby numbers (weak Coriolis forcing), wakes deflect clockwise in the northern hemisphere. By contrast, for low Rossby numbers (strong Coriolis forcing), wakes deflect anti-clockwise. Decreasing the Rossby number results in increasingly anti-clockwise wake deflections. The transition point between clockwise and anti-clockwise deflection depends on the direct Coriolis forcing, pressure gradients and turbulent fluxes in the wake. At a Rossby number of 125, Coriolis deflections are comparable to wake deflections induced by ${\sim} 20^{\circ }$ of yaw misalignment.

Abstract. Strategies for wake loss mitigation through the use of dynamic closed-loop wake steering are investigated using large eddy simulations of conventionally neutral atmospheric boundary layer conditions in which the neutral boundary layer is capped by an inversion and a stable free atmosphere. The closed-loop controller synthesized in this study consists of a physics-based lifting line wake model combined with a data-driven ensemble Kalman filter (EnKF) state estimation technique to calibrate the wake model as a function of time in a generalized transient atmospheric flow environment. Computationally efficient gradient ascent yaw misalignment selection along with efficient state estimation enables the dynamic yaw calculation for real-time wind farm control. The wake steering controller is tested in a six-turbine array embedded in a statistically quasi-stationary, conventionally neutral flow with geostrophic forcing and Coriolis effects included. The controller statistically significantly increases power production compared to the baseline, greedy, yaw-aligned control provided that the EnKF estimation is constrained and informed with a physics-based prior belief of the wake model parameters. The influence of the model for the coefficient of power Cp as a function of the yaw misalignment is characterized. Errors in estimation of the power reduction as a function of yaw misalignment are shown to result in yaw steering configurations that underperform the baseline yaw-aligned configuration. Overestimating the power reduction due to yaw misalignment leads to increased power over the greedy operation, while underestimating the power reduction leads to decreased power; therefore, in an application where the influence of yaw misalignment on Cp is unknown, a conservative estimate should be taken. The EnKF-augmented wake model predicts the power production in yaw misalignment with a mean absolute error over the turbines in the farm of 0.02P1, with P1 as the power of the leading turbine at the farm. A standard wake model with wake spreading based on an empirical turbulence intensity relationship leads to a mean absolute error of 0.11P1, demonstrating that state estimation improves the predictive capabilities of simplified wake models.

Abstract. The sensitivities of idealized large-eddy simulations (LESs) to variations of model configuration and forcing parameters on quantities of interest to wind power applications are examined. Simulated wind speed, turbulent fluxes, spectra and cospectra are assessed in relation to variations in two physical factors, geostrophic wind speed and surface roughness length, and several model configuration choices, including mesh size and grid aspect ratio, turbulence model, and numerical discretization schemes, in three different code bases. Two case studies representing nearly steady neutral and convective atmospheric boundary layer (ABL) flow conditions over nearly flat and homogeneous terrain were used to force and assess idealized LESs, using periodic lateral boundary conditions. Comparison with fast-response velocity measurements at 10 heights within the lowest 100 m indicates that most model configurations performed similarly overall, with differences between observed and predicted wind speed generally smaller than measurement variability. Simulations of convective conditions produced turbulence quantities and spectra that matched the observations well, while those of neutral simulations produced good predictions of stress, but smaller than observed magnitudes of turbulence kinetic energy, likely due to tower wakes influencing the measurements. While sensitivities to model configuration choices and variability in forcing can be considerable, idealized LESs are shown to reliably reproduce quantities of interest to wind energy applications within the lower ABL during quasi-ideal, nearly steady neutral and convective conditions over nearly flat and homogeneous terrain.

A detailed experimental investigation of the hydrodynamics of large-scale, bore-driven swash on steep permeable, rough beaches is described. The experiments were carried out on two permeable, but fixed rough beaches, made of 1.3mm sand and 8.4mm gravel, respectively. The large-scale discrete swash event was produced by the collapse of a dam break-generated bore on the beach. Simultaneous depths and velocities were measured using laser-induced fluorescence (LIF), and particle image velocimetry (PIV), respectively. Depth time series, instantaneous velocity profiles, depth-averaged velocities, instantaneous turbulent kinetic energy profiles, depth-averaged turbulent kinetic energy, turbulent shear stress profiles and bed shear stresses are presented for several cross-shore measurement locations in the swash. The effect of beach permeability is investigated by comparing new experimental results with previously published data for impermeable beaches with identical surface roughness (Kikkert et al., 2012). The detailed data can be used to test and develop advanced numerical models for bore-driven swash on rough permeable beaches.

—The Craya–Curtet number for the isothermal confined double concentric jet system has been derived. Velocity, turbulent shear stress and intensity of turbulence profiles have been measured for different operating conditions, corresponding to different values of Craya–Curtet number. Essential flow features of the system such as radial profiles of mean axial velocity and recirculation have been found to be correlated with the Craya–Curtet number. The turbulent shear stress profiles have been found to depend on position in the flow field, and the Reynolds numbers of the primary and secondary streams. The intensity of radial turbulence has been found to be approximately half the value of the intensity of axial turbulence. Experimentally measured velocity profiles have been compared with those predicted by solving the equations of motion by the finite difference technique. Two types of effective viscosity values have been used in these calculations, one based on a simple turbulence model and the other...

The actual title of this chapter could be the application of simple climate models to the great climatic events. In the previous chapters, we have acquired tools that should enable us to study the evolution of climate on the Earth (and also on the other planets), at least for the most important features. A typical example is the ice age problem, which helps us to understand the complexity of the climate system and the nature of the different forcing and feedback. However, considering the ongoing debate on global warming, some attention is also given to main tool of the practitioners that is General Circulation Models (GCM).

Proper simulation and modelling of geophysical flows is crucial to the study of numerical weather prediction, wind energy and many other applications. When simulating the atmospheric boundary layer, Coriolis forces act as a result of Earth’s rotation. The horizontal component of Earth’s rotation, which is often neglected, influences the balance of vertical momentum. The horizontal component results in systematic differences in the structure and statistics of stratified atmospheric boundary layers as a function of the direction of the geostrophic velocity. These differences are particularly relevant to atmospheric flows which include inhomogeneous roughness elements such as drag disks or wind turbines since the presence of these drag elements alters the balance between turbulent stresses and the Coriolis contributions in Reynolds stress budgets. Even at latitudes as high as , changing the geostrophic wind velocity vector direction alone changes the magnitude of shear stress, and therefore vertical transport of kinetic energy, in the conventionally neutral atmospheric boundary layer up to . As such, the boundary layer height, shear and veer profiles, surface friction velocity and other key features are affected by the direction of the geostrophic wind. The influence of the horizontal component of Earth’s rotation in stable nocturnal boundary layers depends on the strength of the stratification as there is a strong influence in the present study and a weak influence in the GEWEX Atmospheric Boundary Layer Study (GABLS) case. A model of the effect of the horizontal component on the boundary layer shear stress is also proposed and verified with the present simulations. While not studied here, the present observations are also relevant to the oceanic Ekman boundary layer.