Atmospheric physics has a long history as a serious scientific discipline, extending back at least as far as the late seventeenth century. Today it is a rich and fascinating subject, sustained by detailed global observations and underpinned by solid theoretical foundations. It provides an essential tool for tackling a wide range of environmental questions, on local, regional and global scales. Although the solutions to vital and challenging problems concerning weather forecasting and climate prediction rely heavily on the use of supercomputers, they rely even more on the imaginative application of soundly based physical insights.

This book is intended as an introductory working text for third or fourth-year undergraduates studying atmospheric physics as part of a physics, meteorology or environmental science degree course. It should also be useful for graduate students who are studying atmospheric physics for the first time and for students of applied mathematics, physical chemistry and engineering who have an interest in the atmosphere.

Modern scientific study of the atmosphere draws on many branches of physics. I believe that a balanced introductory course in atmospheric physics should include at least some atmospheric thermodynamics, radiative transfer, atmospheric fluid dynamics and elementary atmospheric chemistry. Armed with some understanding of these topics, the interested student will be able to grasp the essential physics behind important issues of current concern, such as the amplification of the greenhouse effect and associated questions of climatic change, the Antarctic ozone hole and global depletion of ozone, as well as more familiar processes such as the formation of raindrops and the development of weather systems.

In this chapter we consider a small selection of techniques for observing the atmosphere. These techniques have been chosen for two main reasons: (a) they illustrate the use of physical principles, including principles introduced earlier in this book; and (b) they provide crucial data on atmospheric phenomena modelled elsewhere in this book, such as Rossby waves, gravity waves and the Antarctic ozone hole. The topics considered are all examples of remote sounding; we do not attempt to present a balanced account of all observational methods.

In Section 7.1 we briefly list some of the main atmospheric observational methods. In Section 7.2 we outline the principles of remote sounding of the atmosphere from space, focusing on methods that rely on thermal emission from atmospheric gases and on scattering of solar radiation by atmospheric gases. Then in Section 7.3 we discuss three types of ground-based remote sounding, namely the Dobson spectrophotometer, radars and lidars. We omit the details of the instruments' optical and electronic systems, the technicalities of signal processing and the sophisticated statistical methods that may be required in order to extract meaningful physical quantities from the raw measurements.

Atmospheric observations

Quantitative observations of the atmosphere are made in many different ways. Routine meteorological measurements of ground-level temperature and wind are made with simple thermometers and anemometers, respectively, and routine measurements of temperature and humidity through the depth of the troposphere are made with balloon-borne instruments (radiosondes) that transmit information back to the surface by radio.

This chapter describes some aspects of energy transfer by electromagnetic radiation in the atmosphere. In Section 3.1 we introduce the Planck function, the solar spectrum and the concept of local thermodynamic equilibrium. In Section 3.2 we list some formal definitions of radiometric quantities and then derive and solve the radiative-transfer equation, which describes the way in which radiative power is affected by extinction and emission of radiation. In Section 3.3 we present some basic aspects of molecular spectrosopy and give some of the properties of spectral line shapes. In Section 3.4 we introduce the concept of transmittance, the fraction of radiative power that survives propagation from one point to another. In Section 3.5 we consider the absorption and emission of infra-red radiation and the absorption of ultra-violet radiation by gases in the atmosphere. This absorption and emission lead to heating and cooling; the principles of the calculation of heating rates are outlined in Section 3.6. In Section 3.7, we revisit the greenhouse effect, investigating a more realistic model than that described in Section 1.3.2. Finally, in Section 3.8, we discuss a simple model of atmospheric scattering.

The solution of the radiative transfer equation also plays an important role in certain aspects of atmospheric remote sounding. This will be covered in Chapter 7.

It is an unfortunate fact that quantitative calculations of radiative heating rates, for example, involve considerable geometric and algebraic detail, which tend to distract attention from the basic physics of the processes.

The atmosphere is a fluid in which a wide variety of flows occurs. This chapter introduces the basic fluid-dynamical laws that govern these atmospheric flows. The length scales of interest range from metres to thousands of kilometres; these are many orders of magnitude greater than molecular scales such as the mean free path, at least in the lower and middle atmosphere. We may therefore average over many molecules, ignoring individual molecular motions and regarding the fluid as continuous. ‘Local’ values of quantities such as density, temperature and velocity may be defined at length scales that are much greater than the mean free path but much less than the scales on which the meteorological motion varies.

In Section 4.1 we derive the mass-conservation law (often called the continuity equation) for a fluid. In Section 4.2 we introduce the concept of the material derivative and the Eulerian and Lagrangian views of fluid motion. An alternative form of the mass conservation law is given in Section 4.3 and the equation of state for the atmosphere (an ideal gas) is recalled in Section 4.4. Then in Section 4.5 Newton's Second Law is applied to a continuous fluid, giving the Navier–Stokes equation. The Earth's rotation cannot be ignored for large-scale atmospheric flows, so its incorporation into the Navier–Stokes equation is discussed in Section 4.6. The full equations of motion for a spherical Earth and for Cartesian tangent–plane geometry are given in Section 4.7. Simplifications of these equations for large-scale flows are introduced in Section 4.8.

PROLOGUE

This chapter deals with Reynolds number effects in turbulent shear flows with particular emphasis on the canonical zero-pressure-gradient boundary layer and twodimensional channel-flow problems. The Reynolds numbers encountered in many practical situations are typically several orders of magnitude higher than those studied computationally or even experimentally. High-Reynolds-number research facilities are expensive to build and operate, and the few that exist are heavily scheduled with mostly developmental work. For wind tunnels, additional complications due to compressibility effects are introduced at high speeds. Likewise, full computational simulation of high-Reynolds-number flows is beyond the reach of current capabilities. Understanding turbulence and modeling will therefore continue to play vital roles in the computation of high-Reynolds-number practical flows using the Reynolds-averaged Navier–Stokes equations. Because the existing knowledge base, accumulated mostly through physical as well as numerical experiments, is skewed toward the low Reynolds numbers, the key question in such high-Reynolds-number modeling as well as in devising novel flow control strategies is, What are the Reynolds number effects on the mean and statistical turbulence quantities and on the organized motions? Understanding the Reynolds number effects is important for flow control on two counts:

1. A passive or active control device developed in a low-Reynolds-number facility may perform quite differently at high Re.

2. For reactive control, coherent structures are targeted.

PROLOGUE

There is no doubt that rational design (i.e., based on first principles) of flow-control devices is always preferable to a trial and error approach. Rational design of course is not always possible owing to the extreme complexity of the equations involved, but one tries either analytically or, more commonly to date, numerically. The search for useful compliant coatings, discussed in Chapter 7, is a case in point. The window of opportunity for a successful coating is so narrow that the probability of finding the right one by experimenting is near nil. Fortunately, the analytical and numerical tools to guide the initial choice for a transition-delaying compliant surface are currently available. On the other hand, the flowfield associated with a typical, deceivingly simple vortex generator for airplane wings is so complex that its design is still done to date more or less empirically.

The proper first principles for flow control are those for fluid mechanics itself. The principles of conservation of mass, momentum, and energy govern all fluid motions. Additionally, all processes are constrained by the second law of thermodynamics. In general, a set of partial, nonlinear differential equations expresses those principles, and, together with appropriate boundary and initial conditions, constitute a wellposed problem.

PROLOGUE

The subject of flow control is broadly introduced in this first chapter, leaving much of the details to the subsequent chapters of the book. The ability to manipulate a flowfield actively or passively to effect a desired change is of immense technological importance, and this undoubtedly accounts for the subject's being more hotly pursued by scientists and engineers than any other topic in fluid mechanics. The potential benefits of realizing efficient flow-control systems range from saving billions of dollars in annual fuel costs for land, air, and sea vehicles to achieving economically and environmentally more competitive industrial processes involving fluid flows. In this monograph both the classical tools and the more modern strategies of flow control are covered. Methods of control to achieve transition delay, separation postponement, lift enhancement, drag reduction, turbulence augmentation, and noise suppression are considered. The treatment is tutorial at times, which makes the material accessible to the graduate student in the field of fluid mechanics. Emphasis is placed on external boundary-layer flows, although applicability of some of the methods discussed for internal flows as well as free-shear flows will be mentioned.

PROLOGUE

Boundary layer manipulation via reactive control strategies is now in vogue. The payoffs are handsome, but the difficulties involved are daunting. This topic is deferred to the last chapter of the book. There are, however, much simpler alternatives to such sophisticated flow alteration devices, and the present chapter discusses one such alternative: passive compliant walls. We particularly review the important developments in the field of compliant coatings that took place during the past decade or so. During this period, progress in theoretical and computational methods somewhat outpaced that in experimental efforts. There is no doubt that compliant coatings can be rationally designed to delay transition and to suppress noise on marine vehicles as well as other practical hydrodynamic devices. Transition Reynolds numbers that exceed by an order of magnitude those on rigid-surface boundary layers can readily be achieved.

PROLOGUE

A particular control strategy is chosen based on the kind of flow and the control goal to be achieved. Flow-control goals are strongly, often adversely, interrelated, and there lies the challenge of making the tough compromises. There are several different ways for classifying control strategies to achieve a desired effect. Presence or lack of walls, Reynolds and Mach numbers, and the character of the flow instabilities are all important considerations for the type of control to be applied. All these seemingly disparate issues are what places the field of flow control in a unified framework. They will be discussed in turn in this chapter.

Control Goals and Their Interrelation

What does the engineer want to achieve when attempting to manipulate a particular flowfield? Typically he or she aims at reducing the drag; at enhancing the lift; at augmenting the mixing of mass, momentum, or energy; at suppressing the flowinduced noise; or at a combination thereof.

PROLOGUE

Drag is the force by which a fluid resists the relative motion of a solid. An equal and opposite reaction force acts on the body surface as a result of the fluid deformation, and drag is the component of this force parallel to the direction of the relative velocity vector. The fluid can be external or internal to the solid boundaries, and the solid surface can be rigid or compliant. Billions of gallons of fossil fuel are used annually to overcome the drag encountered by vehicles moving in air or water and the fluid resistance in gas, water, or oil pipelines. Flow control aims at minimizing this drag force, and the subject is explicitly or implicitly interwoven in every chapter of this book. Delaying laminar-to-turbulence transition (Chapter 6) is usually sought in order to benefit from the much lower skin friction associated with laminar boundary layers. Preventing separation (Chapter 8) means reducing the pressure drag, and when separation is provoked, as for example in delta wings, it is desirable to keep the associated drag penalty to a minimum.

Words are food for thought; utter the right one and you will have created a delicacy to be savored. And so will begin every chapter in this book with the rich words spoken through the ages by the wisest of all men.

The ability to actively or passively manipulate a flow field to effect a desired change is of immense technological importance, and this undoubtedly accounts for the subject's being hotly pursued at present by more scientists and engineers than any other topic in fluid mechanics. The art of flow control is as old as prehistoric man, whose sheer perseverance resulted in the invention of streamlined spears, sickle-shaped boomerangs, and fin-stabilized arrows. The German engineer Ludwig Prandtl pioneered the science of flow control at the beginning of the twentieth century.

The potential benefits of realizing efficient flow-control systems range from saving billions of dollars in fuel cost for land, air, and sea vehicles to achieving economically and environmentally more competitive industrial processes involving fluid flows. The purpose of this book is to provide an up-to-date view of the fundamentals of some basic flows and control practices that can be employed to produce needed effects. Understanding of some basic mechanisms in free and wall-bounded turbulence has increased substantially in the last few years. This understanding suggests that taming of turbulence—the quintessential challenge in the field of flow control—is possible so as to eliminate some of its deleterious effects while enhancing its useful traits.

PROLOGUE

Under certain conditions, wall-bounded flows separate. To improve the performance of natural or man-made flow systems, it may be beneficial to delay or advance this detachment process. This chapter reviews the status and outlook of separation control for steady and unsteady flows. Passive and active techniques to prevent or to provoke flow detachment are considered, and suggestions are made for further research.

Introduction

The Phenomenon of Separation

Fluid particles in a boundary layer are slowed down by wall friction. If the flow is sufficiently retarded, for example, owing to the presence of an adverse pressure gradient, the momentum of those particles will be reduced by both the wall shear and the pressure gradient. In terms of energy principles, the kinetic energy gained at the expense of potential energy in the favorable-pressure-gradient region is depleted by viscous effects within the boundary layer. In the adverse-pressure-gradient region, the remaining kinetic energy is converted to potential energy but is too small to surmount the pressure hill, and the motion of near-wall fluid particles is eventually arrested. At some point (or line), the viscous layer departs or breaks away from the bounding surface. The surface streamline nearest to the wall leaves the body at this point, and the boundary layer is said to separate (Maskell 1955).

Introduction

In terms of mixing, there are two extremes: 1. premixed combustion where fuel and oxidizer are completely mixed prior to their entering the combustion chamber and 2. nonpremixed combustion where fuel and oxidizer enter separately. We have treated these two cases in the preceding two chapters. In technical applications, however, the optimum often lies somewhere between the extremes, trying to profit from advantageous features of both while avoiding their adverse effects. If fuel and oxidizer enter separately, but partially mix by turbulence, combustion takes place in a stratified medium, once the mixture is ignited. Such a mode of combustion has traditionally been called partially premixed combustion.

Turbulent flame propagation in a stratified mixture occurs, for instance, in aircraft gas turbines. Liquid kerosene is fed by an air-blast injector into the gas turbine combustion chamber, where it is mixed with the compressed air. There is typically a pilot injector for idling and a main injector for part load and full load operations. When the main injector is started, an inhomogeneous ignitable mixture is formed at its inlet. When this comes into contact with the hot exhaust gases from the pilot injector, flame propagation takes place from the pilot burner to the main burner through a stratified mixture. This process is difficult to control and modeling of the mixing and of partially premixed combustion poses a main challenge to CFD simulations of gas turbine combustion.

Another example is partially premixed flame propagation in direct injection gasoline engines, where a spray of liquid gasoline is injected directly into the cylinder rather than into the intake manifold as in conventional homogeneous charge spark-ignition engines.

PROLOGUE

Delaying laminar-to-turbulence transition of a boundary layer has many obvious advantages. Depending on the Reynolds number, the skin-friction drag in the laminar state can be as much as an order of magnitude less than that in the turbulent condition (Figure 6.1). For an aircraft or an underwater body, the reduced drag means longer range, reduced fuel cost and volume, or increased speed. Flow-induced noise results from the pressure fluctuations in the turbulent boundary layer and, hence, is virtually nonexistent in the laminar case. Reducing the boundary layer noise is crucial to the proper operation of an underwater sonar. On the other hand, turbulence is an efficient mixer, and rates of mass, momentum, and heat transfer are much lower in the laminar state; thus, early transition may be sought in some applications as, for example, when enhanced heat transfer rates are desired in heat exchangers or when rapid mixing is needed in combustors. This chapter focuses on transition delay, particularly for wall-bounded flows. Transition advancement will be discussed in Chapter 11.

Free-Shear versus Wall-Bounded Flows

Free-shear flows, such as jets, wakes, and mixing layers, are characterized by in- flectional mean-velocity profiles and are therefore susceptible to inviscid instabilities.

PROLOGUE

This chapter is concerned with noise suppression. Noise in the context of this book is undesired sound—particularly that generated by a fluid flow. Although tangential to the primary topics of this monograph, noise control is an important and broad topic and deserves, and is addressed in, its own books. Hence, the treatment here is rather cursory and consists simply of introducing the topic and relating noise control to other flow control topics discussed elsewhere in this book. Particularly for cold subsonic flows, small-scale turbulence fluctuations and unsteady flow oscillations, either in free-shear modes or interacting with solid surfaces, provide the primary sources for the flow-induced sound energy. For hot supersonic flows, the interaction of the turbulence large eddies with the flow is the dominant noise source. In either case, therefore, controlling the flow modulates the sound field favorably or adversely. The goal is of course to reduce noise pollution either for human comfort, for military advantage, or for the prevention of violent structural vibrations. Both passive and active control strategies can be employed to suppress flow-induced noise.

Introduction

In many combustion applications fuel and oxidizer enter separately into the combustion chamber where they mix and burn during continuous interdiffusion. This process is called nonpremixed combustion.

A typical example is combustion in furnaces, which are operated under nonpremixed conditions mainly for safety reasons. Fuel is supplied, for instance, by jets of gaseous fuel, which entrain enough air from the surroundings so that all the fuel can be burned within a certain distance from the nozzle. That distance is called the flame length. Other fuels used in furnaces are coal dust injected with air as a carrier gas, or liquid fuel that is injected as a spray. Since mixing and combustion in jets and sprays occur simultaneously, the formation of large volumes of unburnt flammable mixture can be avoided. In a practical application this requires a control system to make sure that each of the flames in a furnace is burning as long as fuel is supplied.

Other applications of nonpremixed combustion include diesel engines and gas turbines. In diesel engines the air is compressed by the piston before a liquid fuel spray is injected into the combustion chamber. The hot compressed air is entrained into the spray, leading to liquid fuel breakup, evaporation, and finally to auto-ignition. During the combustion phase, at first the premixed fraction of the gas is rapidly consumed, but then combustion takes place under nonpremixed conditions. During this phase most of the formation of NOx and soot is taking place, but it also provides the necessary conditions for soot oxidation.

In aircraft gas turbine engines nonpremixed combustion occurs in the swirlstabilized combustion zone downstream of the spray injector.