[lucamirtanini]

Dear all,
I am keep on studying Tenneke's book, in particular I am focusing on the chapter about the Buoyant convection (the extract of the book is attached), which it is very important for my study.

In particular I have a problem with the definition of the Boussinesq approximation.

1. What does it mean "mean temperature of an adiabatic atmosphere"? there is no definition of this
2. It seems that theta (temperature difference) can be defined as "into a mean value and fluctuation"but it is also defined as "the difference between the actual temperature and the adiabatic athmosfphere".
There are lot of temperature definitions here. I cannot understand which of these is the temperature that I can measure directly (maybe the actual temperature that does not have a dedicated sign in this book?) Can you help me to interpret concretely these definitions of temperature?

[LuckyTran]

1. Big Theta (capital theta) is the spatiotemporal average temperature of the (adiabatic) atmosphere. Adiabatic atmosphere means not isothermal. This is important because a lot of people consider the atmosphere to be isothermal.



2. The scripted v symbol is what is being defined as the difference between temperatures which is decomposed into a v with an overbar for the mean and theta for the fluctuation. None of these you can measure directly because they are all calculated quantities.


You would go measure the temperature of the atmosphere everywhere and calculate Theta. Then calculate v which is the local deviation about Theta. Then you'd take the temporal average and that is v bar. And then you find deviation about v bar and that is non-capital theta.

[lucamirtanini]

Thank you for your answers, they are very focused, and I have understand almost everything. Last question!
If adiabatic means not isothermal, why is it used the word adiabatic?
I cannot understand where I can find the concept of adiabatic, i.e. there is no transfer of heat or mass of substances between a thermodynamic system and its surroundings.

[LuckyTran]

Originally Posted by lucamirtanini

If adiabatic means not isothermal, why is it used the word adiabatic?

This is an example of, not everbody uses the terms the same way. I.e. does adiabatic mean no internal heat transfer at all (which would mean isothermal) or does it mean no net external heat transfer?


For example in thermodynamics... If you have gas in a piston and the gas inside the piston is higher pressure than outside then the piston expands. If there is no heat transfer then the gas temperature drops.


The same happens in the atmosphere. As you move up in elevation (you don't add any heat) and the atmospheric temperature drops.

[lucamirtanini]

Ok. So in this case does it mean "no net external heat trasfer"? external to what?

[LuckyTran]

I thought maybe you were just confused between internal and external processes, but it seems to be more systemic. There is an entire wikipedia article on what is an adiabatic process if you are still struggling with this concept. I explained it already. Just stop being reactive and just read it until your understand it. I haven't explained much that was not already in the textbook.


If you want, you can ignore the word adiabatic and forget what it means because they explain exactly what they mean using other words in the same block of text.

[lucamirtanini]

Ok the problem was different.
I was thinking too much to the semantic meaning of the word adiabatic, as definition, but it was referred to the adiabatic process.
Ok I've understand everything now. Thank you