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Brian Jackson edited As_it_travels_on_the__.tex
over 8 years ago
Commit id: 56b158f9635be64c5eb1b7f9df50885e7db2e432
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\label{eqn:dust_devil_area}
A = \pi b_{\rm max}^2 + \upsilon \tau b_{\rm max} = \left( \Gamma_{\rm act}/2 \right) \sqrt{ \dfrac{P_{\rm act} - P_{\rm min}}{P_{\rm min}} } \left[ \pi \left( \Gamma_{\rm act}/2 \right) \sqrt{ \dfrac{P_{\rm act} - P_{\rm min}}{P_{\rm min}} } + \upsilon \tau \right].
\end{equation}
The probability to recover a devil is proportional to this total area. Thus devils with deeper and wider pressure profiles are more likely to be recovered.
As illustrated in Using the lifetime scaling from \citet{Lorenz_2014}, Figure
\ref{fig:relative_areas}, \ref{fig:relative_areas} shows taht the second term dominates over the first term for all but the smallest, slowest dust devils, so, for simplicity, we'll neglect the first term, giving
\begin{equation}
A \approx \left( \Gamma_{\rm act}/2 \right) \sqrt{ \dfrac{P_{\rm act} - P_{\rm min}}{P_{\rm min}} } \upsilon \tau.
\end{equation}