In this chapter, we turn to the problem of completing the set of equations presented in Section 4.8 by introducing specific constitutive equations. They are material-specific and thus depend upon the constitution of the material.

We close this book with a brief discussion of one of the most important and challenging unsolved problems in the mechanics of fluids: turbulence. As it remains as much descriptive art as predictive science, it is appropriate to call upon visual and poetic sources for inspiration to examine this daunting subject. In the visual realm, the subject has been illustrated with a well-known sketch from da Vinci, seen in Fig. 14.1.

Here we consider some standard problems in multi-dimensional viscous flow. As for one-dimensional viscous flow, application areas are widespread and can include ordinary pipe flows as well as microscale fluid mechanics. We will restrict attention to problems that are steady and laminar. Most of the problems will be incompressible, except for one dealing with a problem in natural convection, Section 11.2.6, and another in compressible boundary layers, Section 11.2.7.

The term atmospheric general circulation, as used in this book, connotes a statistical representation of the three‐dimensional, time varying flow in the global atmosphere, including the cycling of zonal momentum, energy, water vapor, and other trace constituents.

In this chapter, we revisit one of the classical topics of atmospheric dynamics: the maintenance of the zonal mean zonal flow $\left[u\right]$ relative to the rotating Earth.

On a rotating planet, the zonally symmetric zonal wind and temperature fields are in thermal wind balance. By applying this dynamical constraint, it is possible to go beyond the consistency arguments for steady state balances in Eqs. (3.21) and (5.20) and deduce how the flow will evolve in response to specified, time varying distributions of diabatic heating rate, frictional drag, and the eddy transports of zonal momentum and heat. In this zonally averaged version of the primitive equations, which dates back to Eliassen,1 the mean meridional circulations play a critical role in enforcing the constraint that the zonal wind and temperature fields remain in thermal wind balance as the flow evolves.

In Chapter 1, we presented a survey of the general circulation encompassing both Northern and Southern Hemispheres and winter and summer seasons. In this chapter, we focus on the Northern Hemisphere winter season DJF, which arguably exhibits the most distinctive patterns in terms of zonally varying jets, storm tracks, and climatological‐mean stationary waves.

This chapter documents and offers a dynamical interpretation of the annual mean tropical circulation. It is made up of six sections. The first documents the patterns of rain rate, vertical velocity, and low cloud coverage. The second and third document and interpret the upper and lower tropospheric circulations in terms of equatorially trapped planetary waves introduced in Chapter 10 and relate them to the observed rain rate distribution.

In this chapter, we consider the leading mode of year‐to‐year climate variability, the El Niño–Southern Oscillation phenomenon, widely referred to as ENSO. El Niño connotes the episodic weakening of the equatorial Pacific SST cold tongue.1 Southern Oscillation refers to a “seesaw” in sea‐level pressure (SLP) between the eastern and western ends of the tropical Pacific Ocean.

From a global perspective, the dynamics of wave–mean flow interaction in the stratosphere is dominated by Rossby waves, as described in the previous chapter. However, the tropical stratosphere is a notable exception, which merits a chapter of its own.

This chapter introduces some of the fundamental concepts that underlie our understanding of the general circulation of planetary atmospheres: radiative–convective equilibrium, a mechanical energy cycle, a thermodynamic heat engine, stratification – how it develops and why it matters, the dynamical response to horizontal and vertical heating gradients, the influence of rotation, the far‐reaching effects of frictional drag.

Wave–mean flow interaction has played a central role in studies of the general circulation, dating back to the foundational works of Rossby, Starr, and collaborators. In the early studies the waves were usually referred to as “eddies” (as in “turbulent eddies”) without regard for the specific kind of instability or forcing mechanism that gave rise to them. Starr was particularly intrigued with the countergradient transports of angular momentum equatorward of the tropospheric jet stream.1

Parts II, III, and IV are exclusively concerned with the zonally averaged circulation. All representations of the eddies and the transports that they produce are based on zonally averaged statistics.