In this chapter, we will focus on the statistical spectral dynamics which are paramount to understanding the development of the integrated mixing quantities described in Chapter 5. Reynolds flow averaging and the turbulent kinetic energy are introduced. In addition, I will discuss how the energy of the flows is transferred from large scale to small scale modes, as well as the impact of the shockwave and gravity on the isotropy of the flows. The flow spectra allow several important length scales to be defined. Numeric simulations and experimental data will be offered to provide insights on the mixing processes.

This chapter is an overview of wind power meterorology at a relatively simple level without too much mathematical complexity. The origins of the wind are explained in the action of solar thermal radiation on the atmosphere, and the equation is given for the geostrophic wind at the top of the earth’s boundary layer. The role of the boundary layer in creating wind shear and turbulence near the earth’s surface is explained, and appropriate engineering equations given to allow wind speed and turbulence to be estimated. Surface roughness and its relationship to turbulence and shear are explained. Experimental measurements are used to illustrate shear and turbulence for a range of different terrain types. The time and space dependency of wind speeds is also illustrated with site measurements, showing the long-term dependability of annual wind speeds, through the more variable monthly averages, to short-term turbulent variation. Gust factor is explained and illustrated as a function of turbulence intensity. The chapter includes high-resolution wind measurements taken during a storm in the Scottish Outer Hebrides, illustrating the extreme levels of turbulence arising in complex terrain.

Chapter 9 on siting and installation considers some of the key steps leading to the successful installation of a wind energy project, whether a single machine or large array. A section on resource assessment considers site wind measurements, the IEC Wind Classification system, and the measure-correlate-predict (MCP) procedure for establishing long-term characteristics at a prospective site. Array interactions are described in terms of energy loss and increased turbulence: empirical models are given for predicting both effects and wake influence is illustrated with field measurements from large and small arrays. The civil engineering aspects of project construction are examined, with description of different foundation types; simple rules are given for conventional gravity base design, with illustrations. The construction and environmental advantages of rock anchor foundations are described, and some examples given. Transport, access, and crane operations are discussed. The use of winch erection is illustrated with the example of a 50kW machine. The chapter concludes with a short summary of the necessary electrical infrastructure between a wind turbine and the external grid network.

Turbulent flow is a notoriously difficult topic in its own right because it is a truly multi-scale problem with strong nonlinearities. However, in this chapter, I will provide a framework for the key concepts, statistical measurements, and implications for the mixing process, so that the reader can better understand this issue. Both the classic engineering treatment of turbulence as well as the modern statistical closure theories will be introduced and brought together to show the reader how they can be synthesized to describe turbulence mixing induced by hydrodynamic instability driven flows. Some of the key concepts that I will elaborate on include energy transfer and interacting scales. The energy spectrum, and its applicability to RMI and RTI flow, is discussed.

The fractal nature in avalanching systems with SOC is investigated here for phenomena in the solar photosphere and transition region. In the standard SOC model, the fractal Hausdorff dimension is expected to cover the range of [1, 2], with a mean of for 2-D observations projected in the plane-of-sky, and the range of [2, 3], with a mean of for real-world 3-D structures. Observations of magnetograms and with IRIS reveal four groups: (i) photospheric granulation with a low fractal dimension of ; (ii) transition region plages with a low fractal dimension of ; (iii) sunspots at transition region heights with an average fractal dimension of ; and (iv) active regions at photospheric heights with an average fractal dimension of . Phenomena with a low fractal dimension indicate sparse curvilinear flows, while high fractal dimensions indicate near space-filling flows. Investigating the SOC parameters, we find a good agreement for the event areas and mean radiated fluxes in events in transition region plages.

The size distribution of waiting times are found to have an exponential distribution in the case of a stationary Poissonian process. In reality, however, the waiting time distributions reveal power law-like distribution functions, which can be modeled in terms of non-stationary Poisson processes by a superposition of Poissonian distribution functions with time-varying event rates. We model the time evolution of such waiting time distributions by polynomial, sinusoidal, and Gaussian functions, which have exact analytical solutions in terms of the incomplete Gamma function, as well as in terms of the Pareto type-II approximation, which has a power law slope of , where represents the linear time evolution, or with representing nonlinear growth rates, which have a power law slope of . Our mathematical modeling confirms the existence of significant deviations from ideal power law size distributions (of waiting times), but no correlation or significant interval–size relationship exists, as would be expected for a simple (linear) energy storage-dissipation model.

Can we claim that the dynamics of the solar wind is consistent with a SOC system? Observationally we find that magnetic field and kinetic energy fluctuations measured in the solar wind exhibit power law distributions, which is consistent with a SOC system. What about the driver, instability, and avalanches expected in a SOC system? The driver mechanism is the acceleration of the solar wind in the solar corona itself, a process that basically follows the hydrodynamic model of Parker (1958), and may be additionally complicated by the presence of nonlinear wave–particle interactions, such as ion-cyclotron resonance. Then, the instability threshold, triggering extreme bursts of magnetic field fluctuations, the avalanches of solar wind SOC events, can be caused by dissipation of Alfven waves, onset of turbulence, or by the ion-cyclotron instability. Thus, in principle the generalized SOC concept can be applied to the solar wind, if there is a system-wide threshold for an instability that causes extreme magnetic field fluctuations.

We focus on the statistics of SOC-related solar flare parameters in soft X-ray wavelengths, including their size and waiting time distributions. An early SOC model assumed a linear increase of the energy storage, but this pioneering model is not consistent with the expected correlation between the waiting time interval and the subsequently dissipated energy. The Neupert effect in solar flares implies a correlation between the hard X-ray fluence and the soft X-ray flux, which predicts identical size distributions for these two parameters. Quantifying of thermal flare energies in soft X-ray emitting plasma needs also to include radiative and conductive losses. The intermittency and bursty variability of the solar dynamo implies a nonstationary SOC driver, which yields a universal value for the power law slope of fluxes, but the power law slopes of waiting times vary with the flare rate. While our focus encompasses primarily SOC models, alternative models in terms of MHD turbulence can explain some characteristics of SOC features also, such as size distribution functions, Fourier spectra, and structure functions.

Part one gives a description of the characteristics of the wind field over the ocean, including wind shear, turbulence and coherence. It shows how these parameters are modeled and used as an input to wind turbine analyses. The long-term statistics of the mean wind speed are discussed as well as the most common principles for wind speed measurements. In part two, the kinematics and dynamics of ocean waves are given in a form which in subsequent chapters is used in computing wave loads on structures, both in time and frequency domain. Long- and short-term wave statistics are discussed.

This chapter provides an overview of the key elements of turbulent flow. First, the basic averaging approach and examples of turbulent flow decompositions are discussed. Using these techniques, the average transport equations for mass, momentum, and species with closure models are given, followed by advanced numerical techniques for turbulent flows. Turbulent time and length scales as well as the kinetic energy cascade are overviewed, and theoretical turbulent species diffusion is treated.

The chapter sums up the discussion in the previous three chapters, addressing the question of where we are now in the transition process between CAPE and modernity. Was the transition short, as the material side of the story might suggest, or longer, as the social side of the story suggests? Are we now in modernity proper, or are we still in the transition? The chapter proceeds by looking for significant clusters of events, both material and social, that can give guidance as to how these questions might be answered. It argues that the unfolding contradiction between unrestrained development and the limits of planetary carrying capacity is emerging as the key dialectic for the future of humankind.