# 3.3: Frameworks

The First Law of Thermodynamics is a powerful tool that we can apply to different frameworks.

# 3.3.1. Lagrangian vs. Eulerian

One framework, called Eulerian, is fixed relative to a position on the Earth’s surface. Thus, if there is a wind, then the air blows through this framework, so we need to be concerned about what heat is carried in by the wind. Weather forecasts for specific points on a map utilize this framework.

Another framework is called Lagrangian. It moves with the air — its position is constantly changing. This is handy for investigating what happens to air as it rises or sinks.

Eulerian and Lagrangian frameworks can be used for a variety of budget equations:

• Heat Budget (First Law of Thermo)
• Momentum Budget (Newton’s Second Law)
• Moisture Budget (conservation of water), We will use these frameworks in other chapters too.

# 3.3.2. Air Parcels

Sometimes a large cluster of air molecules will move together through the atmosphere, as if they were enclosed by a hypothetical balloon about the diameter of two city blocks. We can use a Lagrangian framework that moves with this cluster or “blob”, in order to study changes of its temperature, momentum, and moisture.

When these air blobs move through the atmosphere, myriad eddies (swirls of turbulent motion) tend to mix some of the outside air with the air just inside the blob (such as the mixing you see in smoke rising from a campfire). Thus, warmer or colder air could be added to (entrained in through the sides of) the blob, and some air from inside could be lost (detrained) to the surrounding atmosphere. Also, in the real atmosphere, atmospheric radiation can heat or cool the air blob. These processes complicate the thermodynamic study of real air blobs.

But to gain some insight into the thermodynamics of air, we can imagine a simplified situation where radiative effects are relatively small, and where the turbulent entrainment/detrainment happens only in the outer portions of the air blob, leaving an inner core somewhat protected. This is indeed observed in the real atmosphere. So consider the protected inner core (about the diameter of a city block) as an air parcel.

Whenever you see discussions regarding air parcels, you should immediately associated them with Lagrangian frameworks. This is the case for the next section.