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We introduce an analytical model that describes the vertical structure of Ekman boundary layer flows coupled to the Monin-Obukhov Similarity Theory (MOST) surface layer repre- sentation, which is valid for conventionally neutral (CNBL) and stable (SBL) atmospheric conditions. The model is based on a self-similar profile of horizontal stress for both CNBL and SBL flows that merges the classic 3/2 power law profile with a MOST-consistent stress profile in the surface layer. The velocity profiles are then obtained from the Ekman momentum balance equation. The same stress model is used to derive a new self-consistent Geostrophic Drag Law (GDL). We determine the ABL height (h) using an equilibrium boundary layer height model and parameterize the surface heat flux for quasi-steady SBL flows as a function of a prescribed surface temperature cooling rate. The ABL height and GDL equations can then be solved together to obtain the friction velocity (u∗) and the cross-isobaric angle (α0) as a function of known input parameters such as the Geostrophic wind speed and surface roughness (z0). We show that the model predictions agree well with simulation data from the literature and newly generated Large Eddy Simulations (LES). These results indicate that the proposed model provides an efficient and relatively accurate self-consistent approach for predicting the mean wind velocity distribution in CNBL and SBL flows. 

Two common definitions of the spatially local rate of kinetic energy cascade at some scale$\ell$in turbulent flows are (i) the cubic velocity difference term appearing in the ‘scale-integrated local Kolmogorov–Hill’ equation (structure-function approach), and (ii) the subfilter-scale energy flux term in the transport equation for subgrid-scale kinetic energy (filtering approach). We perform a comparative study of both quantities based on direct numerical simulation data of isotropic turbulence at Taylor-scale Reynolds number 1250. While in the past observations of negative subfilter-scale energy flux (backscatter) have led to debates regarding interpretation and relevance of such observations, we argue that the interpretation of the local structure-function-based cascade rate definition is unambiguous since it arises from a divergence term in scale space. Conditional averaging is used to explore the relationship between the local cascade rate and the local filtered viscous dissipation rate as well as filtered velocity gradient tensor properties such as its invariants. We find statistically robust evidence of inverse cascade when both the large-scale rotation rate is strong and the large-scale strain rate is weak. Even stronger net inverse cascading is observed in the ‘vortex compression’$R>0$,$Q>0$quadrant, where$R$and$Q$are velocity gradient invariants. Qualitatively similar but quantitatively much weaker trends are observed for the conditionally averaged subfilter-scale energy flux. Flow visualizations show consistent trends, namely that spatially, the inverse cascade events appear to be located within large-scale vortices, specifically in subregions when$R$is large.

 

Drag for wall-bounded flows is directly related to the spatial flux of spanwise vorticity outward from the wall. In turbulent flows a key contribution to this wall-normal flux arises from nonlinear advection and stretching of vorticity, interpretable as a cascade. We study this process using numerical simulation data of turbulent channel flow at friction Reynolds number$Re_\tau =1000$. The net transfer from the wall of spanwise vorticity created by downstream pressure drop is due to two large opposing fluxes, one which is ‘down-gradient’ or outward from the wall, where most vorticity concentrates, and the other which is ‘up-gradient’ or toward the wall and acting against strong viscous diffusion in the near-wall region. We present evidence that the up-gradient/down-gradient transport occurs by a mechanism of correlated inflow/outflow and spanwise vortex stretching/contraction that was proposed by Lighthill. This mechanism is essentially Lagrangian, but we explicate its relation to the Eulerian anti-symmetric vorticity flux tensor. As evidence for the mechanism, we study (i) statistical correlations of the wall-normal velocity and of wall-normal flux of spanwise vorticity, (ii) vorticity flux cospectra identifying eddies involved in nonlinear vorticity transport in the two opposing directions and (iii) visualizations of coherent vortex structures which contribute to the transport. The ‘D-type’ vortices contributing to down-gradient transport in the log layer are found to be attached, hairpin-type vortices. However, the ‘U-type’ vortices contributing to up-gradient transport are detached, wall-parallel, pancake-shaped vortices with strong spanwise vorticity, as expected by Lighthill's mechanism. We discuss modifications to the attached eddy model and implications for turbulent drag reduction.

 

Based on a generalized local Kolmogorov–Hill equation expressing the evolution of kinetic energy integrated over spheres of size$\ell$in the inertial range of fluid turbulence, we examine a possible definition of entropy and entropy generation for turbulence. Its measurement from direct numerical simulations in isotropic turbulence leads to confirmation of the validity of the fluctuation relation (FR) from non-equilibrium thermodynamics in the inertial range of turbulent flows. Specifically, the ratio of probability densities of forward and inverse cascade at scale$\ell$is shown to follow exponential behaviour with the entropy generation rate if the latter is defined by including an appropriately defined notion of ‘temperature of turbulence’ proportional to the kinetic energy at scale$\ell$.

 

Recent high-resolution large-eddy simulations (LES) of a stable atmospheric boundary layer (SBL) with mesh sizes N=(5123,10243,20483) or mesh spacings ▵=(0.78,0.39,0.2) m are analyzed. The LES solutions are judged to be converged based on the good collapse of vertical profiles of mean winds, temperature, and low-order turbulence moments, i.e., fluxes and variances, with increasing N. The largest discrepancy is in the stably stratified region above the low-level jet. Subfilter-scale (SFS) motions are extracted from the LES with N=20483 and are compared to sonic anemometer fields from the horizontal array turbulence study (HATS) and its sequel over the ocean (OHATS). The results from the simulation and observations are compared using the dimensionless resolution ratio Λw/▵f where ▵f is the filter width and Λw is a characteristic scale of the energy-containing eddies in vertical velocity. The SFS motions from the observations and LES span the ranges 0.1<Λw/▵f<20 and are in good agreement. The small, medium, and large range of Λw/▵f correspond to Reynolds-averaged Navier–Stokes (RANS), the gray zone (a.k.a. “Terra Incognita”), and fine-resolution LES. The gray zone cuts across the peak in the energy spectrum and then flux parameterizations need to be adaptive and account for partially resolved flux but also “stochastic” flux fluctuations that represent the turbulent correlation between the fluctuating rate of strain and SFS flux tensors. LES data with mesh 20483 will be made available to the research community through the web and tools provided by the Johns Hopkins University Turbulence Database.

 

The filtered lifting line theory is an analytical approach used to solve the equations of flow subjected to body forces with a Gaussian distribution, such as used in the actuator line model. In the original formulation, the changes in chord length along the blade were assumed to be small. This assumption can lead to errors in the induced velocities predicted by the theory compared to full solutions of the equations. In this work, we revisit the original derivation and provide a more general formulation that can account for significant changes in chord along the blade. The revised formulation can be applied to wings with significant changes in chord along the span, such as wind turbine blades.

 

This paper presents a graph‐based dynamic yaw model to predict the dynamic response of the hub‐height velocities and the power of a wind farm to a change in yaw. The model builds on previous work where the turbines define the nodes of the graph and the edges represent the interactions between turbines. Advances associated with the dynamic yaw model include a novel analytical description of the deformation of wind turbine wakes under yaw to represent the velocity deficits and a more accurate representation of the interturbine travel time of wakes. The accuracy of the model is improved by coupling it with time‐ and space‐dependent estimates of the wind farm inflow based on real‐time data from the wind farm. The model is validated both statically and dynamically using large‐eddy simulations. An application of the model is presented that incorporates the model into an optimal control loop to control the farm power output.