= Growing mode of power-law plume similarity
{title2=$\det(\lambda I-J)=\lambda^3+(q+2m+f)\lambda^2+(3qm/2+qf+2mf)\lambda+qmf$}
The linearized relative-flux matrix is $J=[(-q,q/2,0);(m,-2m,m);(f,0,-f)]$. Its <characteristic polynomial> has constant term $qmf<0$ for physical positive-buoyancy similarity, so at least one real <eigenvalue> is positive. The growing mode behaves as $z^\lambda$ and makes the similarity trajectory unstable with increasing height, rather than with physical time.
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