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1

Yes, the wind cells are just a toy model, where we can suppose that the homogenity of the Earth and other things. But there are other things and Earth isn't same on the all points, so the instantaneous winds don't follow their cells. Of course, it is possible (by pure statistics) that sometimes in the Earth history, the majority of the winds was aligned with ...


3

First, let's acknowledge this fact: $$c_p=R+c_v \tag{1}$$, where $R$ is the specific gas constant. This means that $x=R/c_p$. Rearranging the equation, we can see that $$P+I=\int{c_p\left(\frac{P}{P_{00}}\right)^{R/c_p}\Theta dM}\tag{2}$$ Notice that $\left(\frac{P}{P_{00}}\right)^{R/c_p}$ is the Exner function. By extension,$$P+I=\int{c_p T dM}\tag{3}$$ If ...


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