= Convective amplification length
{title2=$\ell_a=c/\sigma_r$}
If a disturbance grows in time as $e^{\sigma_rt}$ while it is transported at positive speed $c$, the distance for one e-fold of growth is $\ell_a=c/\sigma_r$. Traversing distance $d$ gives exponent $\sigma_rd/c=d/\ell_a$, so $d\ll\ell_a$ produces little growth. This estimate compares a temporal <growth rate> with transport; it does not by itself determine the full spatial <dispersion relation> or stability of a finite domain with feedback.
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