The balance requirement approach covered in Part II provides a reasonable explanation of how the atmosphere satisfies the various budget constraints imposed by the conservation of mass, momentum, total energy, and mechanical energy, but it does not go very far in addressing such questions as:

• Why is there a single pair of tropospheric jet streams located around 30∘N/S?

• Why do the eddies transport angular momentum poleward, across 30∘N/S, maintaining the trade‐wind and westerly wind belts?

• Why do the diagnoses based on the angular momentum balance in Chapter 3 and the energy balance in Chapter 5 yield the same configuration of mean meridional circulations?

The realization that correlation statistics could provide useful information on the three‐dimensional structure and evolution of the transients (i.e., variations about the seasonally varying climatological mean state) dates back al least 100 years, but at that time studies based on this methodology were largely restricted to the analysis of seasonal or annual mean time series at individual stations. Notable examples include studies of Exner, and Walker and Bliss.

The middle atmosphere encompasses the stratosphere and the mesosphere. Its geometric midpoint at ∼50 km corresponds roughly to the stratopause, the top of the stratosphere and the level of strongest heating (per unit mass) due to the absorption of solar ultraviolet radiation by ozone molecules.

In motion systems with timescales ranging from hours up to and including the diurnal cycle, gravity and inertio‐gravity waves are dominant. The influence of the Earth’s rotation is discernible, but geostrophic balance does not prevail and Rossby wave propagation and dispersion do not play a dominant role in the dynamics.

Tropical weather systems with timescales shorter than a few weeks can be divided into three broad categories: equatorially trapped waves, off‐equatorial waves, and tropical vortices.

Some of the most influential general circulation papers in the late 1940s, 1950s, and 1960s involved the formulation and diagnosis of balance requirements that can be applied to any scalar, conserved quantity.

The prominence of the stratosphere in general circulation research derives from

• its role as a reservoir for dangerous radioactive debris from nuclear explosions and reflective sulfate aerosols from volcanic eruptions,

• its role in mediating ozone photochemistry, which shields life on Earth from harmful effects of solar ultraviolet radiation,

• its distinctive low frequency variability, which is seen as a possible vehicle for extending the range of useful weather prediction,

• its relative simplicity as a dynamical system in which the interactions between waves and the zonally symmetric flow play a central role.

This chapter introduces influence of density change on a flow, i.e., the compressible flow theory. Strictly speaking, any gas flow is both viscous and compressible. In tradition the influence of viscosity and compressibility are dealt with separately to make things easy. In this book, the chapter 6 deals with viscosity, and the chapter 7 deals with compressibility. Sound speed and Mach number are introduced in the beginning, then the equations for steady isentropic flow are derived with statics and total parameters introduced. Some gas dynamic functions are derived that use coefficient of velocity in replace of Mach number. Propagation mode of pressure waves are discussed next, and expansion and compression waves are introduced. Shock wave, as a strong compression wave, is discussed in depth. In the end, transonic and supersonic flow in a variable cross-section pipe is discussed, especially the characteristics of the flow in a Laval nozzle.

In this chapter, basic concepts in fluid mechanics are introduced. Firstly, the definition of a fluid is discussed in depth with the conclusion that a fluid is such a substance that cannot generate internal shear stresses by static deformation alone. Secondly, some important properties of fluids are discussed, which includes viscosity of fluids, surface tension of liquids, equation of state for gases, compressibility of gases, and thermal conductivity of gases. Lastly, some important concepts in fluid mechanics are discussed, which includes the concept of continuum and forces in a fluid. Within these discussions, fluid is compared to solid in both microscopic and macroscopic to reveal the mechanism of its mechanical property. Viscosity of fluid is compared to friction and elasticity of solid to give readers a better idea how it works microscopically. Forces is classified as body force and surface force for further analysis. Finally, continuum hypothesis is introduced to deem the fluid as continuously separable, which tells the reader that fluid mechanics is a kind of macroscopic mechanics that conforms Newtonian mechanics and thermodynamics.

In this chapter, the basic equations of fluid dynamics are derived and their physical significances are discussed in depth and in examples. Both integral and differential forms of the continuity equation, momentum equation, and energy equation are derived. In addition, Bernoulli’s equation, angular momentum equation, enthalpy equation and entropy equation are also introduced. Finally, several analytical solutions of these governing equations are shown, and the mathematical properties of the equations are discussed. Besides the fundamental equations, some important concepts are explained in this chapter, such as the shaft work in integral energy equation and its origin in differential equations, the viscous dissipation term in the differential energy equation and its relation with stress and deformation, and the method to increase total enthalpy of a fluid isentropically.

This chapter introduces the description of fluid motion, that is, the fluid kinematics. At first, the Lagrangian and Eulerian method is compared to emphasize that most problems in fluid mechanics is more suitable for Eulerian method. Secondly, the concepts of pathlines and streamlines are introduced. Next, Acceleration equation and substantial derivative are derived in Eulerian coordinates and their physical significance is discussed in depth and in examples. Reynolds transport theorem is then introduced and compared with substantial derivative to demonstrate that they are the same relation in integral and differential form respectively. Deformation of a finite fluid element is discussed in the next. Linear deformation, rotation, angular deformation equations are derived individually with equations and illustrations. These knowledges are the key to derive the differential equations of a flow, which will be introduced in chapter 4.

In this chapter, twenty-five carefully selected flow-related phenomena are analyzed, with the purpose of consolidating the understanding of the subject and strengthening the ability to link theory with practice. These flow phenomena include some interesting examples such as the principle of lift, the thrust of a water rocket, the mechanism of a faucet et al. Another type of the examples includes those with controversial explains in some popular science books or websites, such as the pressure of jet flow, the pressure change by a passing train, the reason why the water does not spill when a cup is upside-down et al.