<p>You are correct, the atmosphere cannot ever be barotropic. It is important to note that the ideal gas law is relevant only as a state equation; it does not describe the gas as a whole. The barotropic assumption effectively states $P=\rho RT_0$. Effectively, it says "hold temperature constant" You may note this is particularly important when discussing the hydrostatic and hypsometric/barometric equations.</p>

<p>On that note, the atmosphere is never entirely barotropic; the atmosphere cannot undergo entirely adiabatic motions; the wind can never stay geostrophic, etc. There are assumptions that are bad, and we know they are (take a class in micrometeorology dealing with similarity theory). But in the words of George Box, "All models are wrong, but some are useful." These simple models teach us about basic atmospheric behavior.</p>

<p>It is also worth noting that the ideal gas law is not the only equation of state. The Boussinesq and anelastic approximations can lead to interesting other formulations of the equation of state.</p>

CC BY-SA 3.0
2017-03-10T17:59:29.833Z
The hydrostatic equation (dP/dz=-rho*g), on first glance, also describes a barotropic atmosphere.
BarocliniCplusplus
CC BY-SA 3.0
2017-03-10T17:50:06.883Z
2017-03-10T17:50:06.883Z
BarocliniCplusplus
<p>A barotropic fluid is a fluid whose density is a function of pressure only, i.e. $\rho=\rho(p)$. My understanding is that, in the atmosphere, in general, the tropics are barotropic whereas the extratropics are baroclinic.</p>

<p>If the atmosphere is an ideal gas, then $\rho =p/R T$. Therefore, density is a function of pressure <em>and</em> temperature. How, then, can the atmosphere ever be barotropic?</p>

CC BY-SA 3.0
2017-03-10T19:06:11.690Z
Possibly better suited for Chemistry SE?
L.B.
CC BY-SA 3.0
2017-03-10T21:21:23.917Z
@L.B. I disagree. If this was primarily a question about thermodynamics, I would agree. However, the barotropic assumption is usually made in atmospheric dynamics.
BarocliniCplusplus
<meteorology><atmosphere>
If the atmosphere is (very nearly) an ideal gas, how can it ever be barotropic?
Sam Hatfield
# If the atmosphere is (very nearly) an ideal gas, how can it ever be barotropic?

(Asked by: username_0 on 2017-03-10)

A barotropic fluid is a fluid whose density is a function of pressure only, i.e. $\rho=\rho(p)$. My understanding is that, in the atmosphere, in general, the tropics are barotropic whereas the extratropics are baroclinic.

If the atmosphere is an ideal gas, then $\rho =p/R T$. Therefore, density is a function of pressure *and* temperature. How, then, can the atmosphere ever be barotropic?

**Tags:** meteorology, atmosphere

> **Comments:**
> **username_1**: Possibly better suited for Chemistry SE?  
> **username_2**: @L.B. I disagree. If this was primarily a question about thermodynamics, I would agree. However, the barotropic assumption is usually made in atmospheric dynamics.  

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## 1 answers

### Answer by username_2 on 2017-03-10. Score: 3 | Accepted answer

You are correct, the atmosphere cannot ever be barotropic. It is important to note that the ideal gas law is relevant only as a state equation; it does not describe the gas as a whole. The barotropic assumption effectively states $P=\rho RT\_0$. Effectively, it says "hold temperature constant" You may note this is particularly important when discussing the hydrostatic and hypsometric/barometric equations.

On that note, the atmosphere is never entirely barotropic; the atmosphere cannot undergo entirely adiabatic motions; the wind can never stay geostrophic, etc. There are assumptions that are bad, and we know they are (take a class in micrometeorology dealing with similarity theory). But in the words of George Box, "All models are wrong, but some are useful." These simple models teach us about basic atmospheric behavior.

It is also worth noting that the ideal gas law is not the only equation of state. The Boussinesq and anelastic approximations can lead to interesting other formulations of the equation of state.

> **Comments:**
> **username_2**: The hydrostatic equation (dP/dz=-rho*g), on first glance, also describes a barotropic atmosphere.  

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