A multifaceted future for wind power: Modern wind turbines already represent a tightly optimized confluence of materials science and aerodynamic engineering. Veers et al. review the challenges and opportunities for further expanding this technology, with an emphasis on the need for interdisciplinary collaboration. They highlight the need to better understand atmospheric physics in the regions where taller turbines will operate as well as the materials constraints associated with the scale-up. The mutual interaction of turbine sites with one another and with the evolving features of the overall electricity grid will furthermore necessitate a systems approach to future development. Science , this issue p. eaau2027

▪ Abstract Relationships between small and large scales of motion in turbulent flows are of much interest in large-eddy simulation of turbulence, in which small scales are not explicitly resolved and must be modeled. This paper reviews models that are based on scale-invariance properties of high-Reynolds-number turbulence in the inertial range. The review starts with the Smagorinsky model, but the focus is on dynamic and similarity subgrid models and on evaluating how well these models reproduce the true impact of the small scales on large-scale physics and how they perform in numerical simulations. Various criteria to evaluate the model performance are discussed, including the so-called a posteriori and a priori studies based on direct numerical simulation and experimental data. Issues are addressed mainly in the context of canonical, incompressible flows, but extensions to scalar-transport, compressible, and reacting flows are also mentioned. Other recent modeling approaches are briefly introduced.

The dynamic model for large-eddy simulation of turbulence samples information from the resolved velocity field in order to optimize subgrid-scale model coefficients. When the method is used in conjunction with the Smagorinsky eddy-viscosity model, and the sampling process is formulated in a spatially local fashion, the resulting coefficient field is highly variable and contains a significant fraction of negative values. Negative eddy viscosity leads to computational instability and as a result the model is always augmented with a stabilization mechanism. In most applications the model is stabilized by averaging the relevant equations over directions of statistical homogeneity. While this approach is effective, and is consistent with the statistical basis underlying the eddy-viscosity model, it is not applicable to complex-geometry inhomogeneous flows. Existing local formulations, intended for inhomogeneous flows, are most commonly stabilized by artificially constraining the coefficient to be positive. In this paper we introduce a new dynamic model formulation, that combines advantages of the statistical and local approaches. We propose to accumulate the required averages over flow pathlines rather than over directions of statistical homogeneity. This procedure allows the application of the dynamic model with averaging to in-homogeneous flows in complex geometries. We analyse direct numerical simulation data to document the effects of such averaging on the Smagorinsky coefficient. The characteristic Lagrangian time scale over which the averaging is performed is chosen based on measurements of the relevant Lagrangian autocorrelation functions, and on the requirement that the model be purely dissipative, guaranteeing numerical stability when coupled with the Smagorinsky model. The formulation is tested in forced and decaying isotropic turbulence and in fully developed and transitional channel flow. In homogeneous flows, the results are similar to those of the volume-averaged dynamic model, while in channel flow, the predictions are slightly superior to those of the spatially (planar) averaged dynamic model. The relationship between the model and vortical structures in isotropic turbulence, as well as ejection events in channel flow, is investigated. Computational overhead is kept small (about 10% above the CPU requirements of the spatially averaged dynamic model) by using an approximate scheme to advance the Lagrangian tracking through first-order Euler time integration and linear interpolation in space.

A simple model is presented for the energy-cascading process in the inertial range that fits remarkably well the entire spectrum of scaling exponents for the dissipation field in fully developed turbulence. The scheme is a special case of weighted curdling and its one-dimensional version is a simple generalized two-scale Cantor set with equal scales but unequal weights (with ratio∼(7/3). This set displays all the measured multifractal properties of one-dimensional sections of the dissipation field.

The intermittency of the rate of turbulent energy dissipation ε is investigated experimentally, with special emphasis on its scale-similar facets. This is done using a general formulation in terms of multifractals, and by interpreting measurements in that light. The concept of multiplicative processes in turbulence is (heuristically) shown to lead to multifractal distributions, whose formalism is described in some detail. To prepare proper ground for the interpretation of experimental results, a variety of cascade models is reviewed and their physical contents are analysed qualitatively. Point-probe measurements of ε are made in several laboratory flows and in the atmospheric surface layer, using Taylor's frozen-flow hypothesis. The multifractal spectrum f(α) of ε is measured using different averaging techniques, and the results are shown to be in essential agreement among themselves and with our earlier ones. Also, long data sets obtained in two laboratory flows are used to obtain the latent part of the f(α) curve, confirming Mandelbrot's idea that it can in principle be obtained from linear cuts through a three-dimensional distribution. The tails of distributions of box-averaged dissipation are found to be of the square-root exponential type, and the implications of this finding for the f(α) distribution are discussed. A comparison of the results to a variety of cascade models shows that binomial models give the simplest possible mechanism that reproduces most of the observations. Generalizations to multinomial models are discussed.

It is well known that when wind turbines are deployed in large arrays, their efficiency decreases due to complex interactions among themselves and with the atmospheric boundary layer (ABL). For wind farms whose length exceeds the height of the ABL by over an order of magnitude, a “fully developed” flow regime can be established. In this asymptotic regime, changes in the streamwise direction can be neglected and the relevant exchanges occur in the vertical direction. Such a fully developed wind-turbine array boundary layer (WTABL) has not been studied systematically before. A suite of large eddy simulations (LES), in which wind turbines are modeled using the classical “drag disk” concept, is performed for various wind-turbine arrangements, turbine loading factors, and surface roughness values. The results are used to quantify the vertical transport of momentum and kinetic energy across the boundary layer. It is shown that the vertical fluxes of kinetic energy are of the same order of magnitude as the power extracted by the forces modeling the wind turbines. In the fully developed WTABL, the kinetic energy extracted by the wind turbines is transported into the wind-turbine region by vertical fluxes associated with turbulence. The results are also used to develop improved models for effective roughness length scales experienced by the ABL. The effective roughness scale is often used to model wind-turbine arrays in simulations of atmospheric dynamics at larger (regional and global) scales. The results from the LES are compared to several existing models for effective roughness lengths. Based on the observed trends, a modified model is proposed, showing improvement in the predicted effective roughness length.