this is for holding javascript data
Matteo Cantiello edited MLT.tex
over 9 years ago
Commit id: 85131fc4cbc6a6b0783e0e48f400ef9ff4d4d5fe
deletions | additions
diff --git a/MLT.tex b/MLT.tex
index 677a4a8..86dca0b 100644
--- a/MLT.tex
+++ b/MLT.tex
...
We can define the gradients $\nabla \equiv \frac{\D \ln \T}{\D \ln \P}$ 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] r}\bigg].
\end{equation}
Assumin $\T' \simeq \T$, i.e. the temperature is not changing drastically within the distance $\Delta r$, one can write
\begin{equation}
\Delta \T (\Delta r) = \Delta r \T \bigg[ -\frac{\D \ln \T}{\D r}- (-\frac{\D \ln \T'}{\D r})\bigg].
\end{equation}