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Convection

4.1. The nature of convection

4.1.1. Convection in a shallow fluid

4.1.2. Instability

4.2. Convection in water

4.2.1. Buoyancy

4.2.2. Stability

4.2.3. Energetics

4.2.4. GFD Lab II: Convection

4.3. Dry convection in a compressible atmosphere

4.3.1. The adiabatic lapse rate (in unsaturated air)

4.3.2. Potential temperature

4.4. The atmosphere under stable conditions

4.4.1. Gravity waves

4.4.2. Temperature inversions

4.5. Moist convection

4.5.1. Humidity

4.5.2. Saturated adiabatic lapse rate

4.5.3. Equivalent potential temperature

4.6. Convection in the atmosphere

4.6.1. Types of convection

4.6.2. Where does convection occur?

4.7. Radiative-convective equilibrium

4.8. Further reading

4.9. Problems

We learned in Chapters 2 and 3 that terrestrial radiation emanates to space primarily from the upper troposphere, rather than the ground; much of what radiates from the surface is absorbed within the atmosphere. The surface is thus warmed by both direct solar radiation and downwelling terrestrial radiation from the atmosphere. In consequence, in radiative equilibrium, the surface is warmer than the overlying atmosphere. However, this state is unstable to convective motions that develop, as sketched in Fig. 4.1, and transport heat upward from the surface. In the troposphere, therefore, equilibrium is not established solely by radiative processes. In this chapter, we discuss the nature of the convective process and its role in determining the radiative-convective balance of the troposphere.

FIGURE 4.1. Solar radiation warms the Earth's surface, triggering convection, which carries heat vertically to the emission level from which, because the atmosphere above this level is transparent in the IR spectrum, energy can be radiated out to space. The surface temperature of about 288 K is significantly higher than the temperature at the emission level, 255 K, because the energy flux from the surface must balance not just the incoming solar radiation but also downwelling IR radiation from the atmosphere above. An idealized radiative equilibrium temperature profile, T(z), is superimposed (cf. Fig. 2.11).

FIGURE 4.1. Solar radiation warms the Earth's surface, triggering convection, which carries heat vertically to the emission level from which, because the atmosphere above this level is transparent in the IR spectrum, energy can be radiated out to space. The surface temperature of about 288 K is significantly higher than the temperature at the emission level, 255 K, because the energy flux from the surface must balance not just the incoming solar radiation but also downwelling IR radiation from the atmosphere above. An idealized radiative equilibrium temperature profile, T(z), is superimposed (cf. Fig. 2.11).

As we are about to explore, the conditions under which convection occurs depend on the characteristics of the fluid. The theory appropriate in a moist, compressible atmosphere is somewhat more complicated than in an incompressible medium like water. Accordingly, we will discuss convection in a sequence of cases of increasing complexity. After making some general remarks about the nature of convection, we will describe the incompressible case, using a theoretical approach and a laboratory experiment, in Section 4.2. Convection in an unsaturated compressible atmosphere is discussed in Section 4.3; the effects of latent heat consequent on condensation of moisture are addressed in Section 4.5 following a discussion of the atmosphere under stable conditions in Section 4.4.

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