Turbulent flow is an important branch of fluid mechanics with wide-ranging occurrences and applications, from the formation of tropical cyclones to the stirring of a cup of coffee. Turbulence results in increased skin friction and heat transfer across surfaces, as well as enhanced mixing. As such, it is of practical significance, and there is a need to establish predictive methods to quantify turbulent flows. Equally important is a physical understanding of turbulent flows to guide strategies to model and control turbulence-driven phenomena. We focus on the study of turbulent flows and draw on theoretical developments, experimental measurements, and results from numerical simulations. Turbulent flows are governed by the Navier-Stokes equations. The solution of these equations for turbulent flows displays chaotic and multiscale behavior. When averaged, the nonlinear terms in the Navier-Stokes equations lead to the so-called closure problem, where additional unknowns are introduced in the mean flow equations. These unknowns are typically modeled using intuition, experience, and dimensional arguments. We present the scaling and dimensional analysis necessary for model development.

Virtually all technologically relevant applications involve interactions of turbulent flows with solid walls, including flows over aircrafts and automobiles. We study these interactions using canonical wall-bounded flows, including fully developed channels, pipes, and flat-plate boundary layers, with a focus on channel flow. A common scaling may be employed in the near-wall region using the friction velocity and viscous length scale to derive the so-called wall units. In this region, which comprises the viscous sublayer, buffer layer, and overlap layer, the law of the wall governs the mean velocity profile, and the constant-stress-layer assumption is often employed. We discuss key features of the mean velocity profile, particularly the log law in the overlap region, which stands as a celebrated result in turbulence theory. Away from the wall, the outer layer scales with the boundary-layer thickness and freestream velocity. We discuss the skin friction and wake laws to describe the mean outer velocity profile and introduce the Clauser chart method. We also examine in more detail the scales and structural features of turbulence near a wall, including streaks and hairpin vortices.

In turbulent free-shear flows, fluid streams interact to generate regions of turbulence that evolve without being limited or confined by solid boundaries. Such interactions create mean shear, which is a source of turbulent kinetic energy that results in enhanced flow mixing. Far downstream, the flow retains little memory of its origins and exhibits self-similar behavior. Its mean velocity profile, turbulence intensities, and Reynolds stresses, when scaled appropriately, become independent of downstream distance as it freely expands into its surroundings. Free-shear flows occur in combustors, vehicle wakes, and jet engine exhaust. We focus our attention on three canonical categories of such flows: jets, wakes, and mixing layers. A detailed similarity analysis of the plane jet is provided alongside summarized results for the plane wake and mixing layer. We introduce examples involving turbines in wind farms and drag on wake-generating bodies. The notion of entrainment, which is central to the expansion of free-shear flows, is discussed. We also examine the scales and structural features of turbulent free-shear flows, including streamwise rib vortices and spanwise rollers.

In many practical applications, one is interested only in the average or expected value of flow quantities, such as aerodynamic forces and heat transfer. Governing equations for these mean flow quantities may be derived by averaging the Navier-Stokes and temperature or scalar transport equations. Reynolds averaging introduces additional unknowns owing to the nonlinearity of the equations, which is known as the closure problem in the turbulence literature. Turbulence models for the unclosed terms in the averaged equations are a way to manage the closure problem, for they close the equations with phenomenological models that relate the unknown terms to the solution variables. It is important that these models do not alter the conservation and invariance properties of the original equations of motion. We take a closer look at the equations of motion to understand these fundamental qualities in more depth. We describe averaging operators for canonical turbulent flows at the core of basic turbulence research and modeling efforts, and discuss homogeneity and stationarity. We also examine the Galilean invariance of the equations of motion and the role of vorticity in turbulence dynamics.

This chapter focuses on experimental techniques in the micro/nanoscale thermal radiation. The contents in the chapter are divided into two parts based on either far- or near-field measurement. The contents mainly involve far-field Fourier transform infrared microscopes, near-filed scanning thermal microscopy, and near-field thermal radiation instrument. We will review some outstanding experiments performed by different research groups for measuring the properties of micro/nanoscale thermal radiation. This chapter can be served as a guideline for researchers to design the experimental setups.

These years, we have witnessed great progress in manipulating radiative properties of thermal radiation, including angular, spectral, and polarized responses, via tailoring the light–matter interaction by taking advantages of designed nanostructures, metamaterials or metasurfaces, novel 2D materials, or even anisotropic materials. This chapter will review and give a detailed introduction of several manipulating mechanisms based on different types of materials, giving a comprehensive view of recent progress of radiative property engineering.

This chapter will focus on some important theories in micro/nanoscale thermal radiation, which are the basis of this area and become the fundamentals of other chapters in the books. The contents mainly involve electromagnetic wave theory, fluctuation dissipation theorem, and near-field thermal radiation. Brief derivation, solving the process and analysis method will be presented.

This chapter will cover a variety of methods, especially numerical methods of rigorous coupled-wave analysis and finite-difference time-domain solution. These methods are widely used in solving the problems of the micro/nanoscale thermal radiation. It is important and will give students hands-on experience in numerical simulations.