= Solution
Both <eigenvalues> of the linear generator, $-1/R$ and $-1/(4R)$, are negative. Nevertheless the <non-normal matrix> transfers the slowly decaying second component into the first before viscous decay wins. \b[Modal decay coexists with energy amplification of order $R^2$ over a time of order $R$.]
This illustrates <transient growth from non-normal modes>: large <Reynolds number> permits much greater disturbance amplification even though the <linear stability analysis> finds no unstable <eigenvalue>. The <energy-neutral rotational nonlinearity> can redirect the amplified state and affect its subsequent evolution. The linear gain alone establishes neither sustained nonlinear instability nor a nonlinear transition threshold.
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