Convection

Now we are ready to weave our seeming disparate threads of story together into a picture of what controls the temperature as a function of altitude in the atmosphere. The pieces are assembled into a process called convection. Convection takes its place among conduction and radiation, which we have already discussed, as a means of carrying heat in the environment. Convection occurs when a fluid medium is heated from the bottom or cooled from the top, and the heavy water atop light water causes the fluid to circulate. Imagine a lava lamp, in which the fluid is heated from below by a light bulb (a ridiculous energy-wasting incandescent bulb; you could never make a lava lamp work with a nice, efficient, compact fluorescent bulb because fluorescent bulbs do not generate so much waste heat). The fluid at the bottom becomes warmer than the fluid overlying it. Warmer molecules bounce around more energetically, pushing all of the molecules somewhat farther apart from each other. For this reason the fluid expands as its temperature increases. As it expands, its density (mass per volume) decreases. If we stack some fluids of different density together in a column, the stable configuration is to have the densest ones on the bottom. Think of oil and water; the oil always floats on the water because it is less dense. So our expanding parcel of fluid at

Temperature

Fig. 5.7 The effect of convection on the temperature in a pan of water on a stove. In (a: static stability) the water in the pan is well mixed, the same temperature throughout. After the burner is turned on, the water at the bottom of the pan warms, which makes it less dense than the water above it (b: convectively unstable). Either this water can rise to the top without mixing (c: stratified) or it can mix with the water above it, raising the temperature of the entire pan of water (d: new static stability). The atmosphere tends to mix when it convects, as in (d).

the bottom of the lamp begins to rise. It floats to the top of the lamp until it cools and sinks back to the bottom again.

Forget the lava lamp now and think of a pan of water on a stove, which is a simpler case because there is only one fluid instead of two. Figure 5.7 plots the temperature of the water as a function of the height in the pan, which we call a temperature profile. If we thoroughly mix the water, the temperature will be the same throughout the pan of water. This sounds obvious but we'll find in a moment that when we mix a column of air, the temperature is not uniform throughout. A well-mixed, uniform temperature water column is called statically stable because if the fluid is left alone, it won't feel any need to circulate. Any parcel of water has the same density as its neighbors.

Next we'll turn on the burner, warming and expanding the water at the bottom of the pan. Buoyant water at the bottom tends to rise: this situation is called convectively unstable. The buoyant water from the bottom could rise to the top like the lava in the lava lamp, in which case we would end up with denser water underlying lighter water, which we call stratified. Pubs in Ireland serve a concoction called a black and tan, with warm dark Guinness Porter overlying cold Bass Ale. The two types of beer remain unmixed because they are stratified by temperature. Alternatively (back to the pan analogy, alas) the rising warm water could mix with the rest of the water, as generally occurs to a large extent in the atmosphere and ocean. In this case we end up with a second statically stable profile at a higher temperature than the first.

Convection in a compressible gas is analogous to convection in an incompressible fluid like our pan of water (Fig. 5.8). We begin from the temperature profile of static

(a) Temperature

(b) Temperature

(b) Temperature

Fig. 5.8 Convection in a compressible fluid like air. (a) is the statically stable configuration, analogous to (a) in Fig. 5.7. The temperature decreases with altitude because the gas expands, and therefore cools. This temperature profile is what you would see in a well-mixed column of air. (b) is the effect of heating from below, analogous to (b) in Fig. 5.7.

stability. As for the water column, we can construct a statically stable temperature profile by mixing the gas thoroughly. No gas parcel will be more or less dense than its neighbors because it is all the same stuff. The pressure decreases as you ascend the gas column, and so a gas parcel raised from the bottom of the column expands, and its temperature drops. After it does so, our parcel finds that it is still exactly the same temperature as the gas it finds itself surrounded by. The parcel was neutrally buoyant at the bottom of the column, and it is neutrally buoyant aloft.

Convection is driven by heating at the bottom of the column, such as by sunlight hitting the ground. The warmed air parcel from the ground finds itself warmer than the air immediately above it, even when it has expanded to the pressure of the air above it. The rising parcel follows its own adiabat, which is higher than the temperature profile of the gas column, and so the rising parcel has the ability to rise to the top of the gas column if it does not mix with other gas on the way up. If the gas does mix, the temperature profile of the entire column will rise to a new adiabat, all completely analogous to the incompressible case of the pan of water.