this is for holding javascript data
Matteo Cantiello edited Gradients.tex
over 9 years ago
Commit id: 4abf181268f7fd8f66c89be6165072b5e0f332df
deletions | additions
diff --git a/Gradients.tex b/Gradients.tex
index f0df851..63be352 100644
--- a/Gradients.tex
+++ b/Gradients.tex
...
\subsection{Gradients}
We can define the gradients $\nabla \equiv \frac{\D \ln \T}{\D \ln
\P}$ \p}$ and $\nabla' \equiv \frac{\D \ln \T'}{\D \ln \P}$. Here $\nabla$ represents the average temperature gradient with respect to pressure of all matter at a given level, while $\nabla'$ is the temperature gradient with respect to pressure of a rising/falling fluid element.
At first order the temperature excess of such fluid elements can therefore be written as
\begin{equation}
\Delta \T (\Delta r) = \T'(r + \Delta r) - \T(r + \delta r) \simeq \Delta r \bigg[ \frac{\D \T'}{\D r}-\frac{\D \T}{\D r}\bigg].