# If the atmosphere is (very nearly) an ideal gas, how can it ever be barotropic?

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?

• Possibly better suited for Chemistry SE?
– L.B.
Mar 10, 2017 at 19:06
• @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. Mar 10, 2017 at 21:21

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.