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Brian Jackson edited subsection_The_Pressure_Signal_Full__.tex
almost 9 years ago
Commit id: 8a135802e356ee27bfb887f9b7341946dd60d014
deletions | additions
diff --git a/subsection_The_Pressure_Signal_Full__.tex b/subsection_The_Pressure_Signal_Full__.tex
index 9d5de3b..5084ed9 100644
--- a/subsection_The_Pressure_Signal_Full__.tex
+++ b/subsection_The_Pressure_Signal_Full__.tex
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\end{equation}
where we've suppressed the constant factor involving the pressures.
Likewise, non-central encounters with a dust devil will distort the observed profile full-width/half-max $\Gamma_{\rm obs}$. Having passed through its minimum at the devil's closest approach distance, the observed pressure signal reaches half its value when the center of the devil is a radial distance from the barometer $r = \dfrac{\Gamma_{\rm obs}}{2}$, giving
$\frac{1}{2} P_{\rm obs} =\dfrac{P_{\rm act}}{1 + \left( \upsilon \Gamma_{\rm obs}/\Gamma_{\rm act} \right)^2}$. We can solve this for $\Gamma_{\rm obs}$:
\begin{equation}
\frac{1}{2} P_{\rm obs} =\dfrac{P_{\rm act}}{1 + \left( \upsilon \Gamma_{\rm obs}/\Gamma_{\rm act} \right)^2}.
\end{equation}
The figure below compares the pressure signals for $b = 0$ and $b = \Gamma_{\rm act}$, for which $P(r = b) = \frac{1}{5} P_{\rm act}$ and $\left( \upsilon \Gamma_{\rm obs} \right) = 3 \Gamma_{\rm act}$.
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