= Solution
If the lower density $\rho_-$ exceeds the upper density $\rho_+$, <stable density stratification> adds a gravitational restoring term. Including <surface tension> $\gamma$, the same calculation has the schematic dispersion relation
$$
\rho_-\coth(Kh)(\omega-kU)^2+\rho_+\omega^2
=(\rho_--\rho_+)gK+\gamma K^3.
$$
The gravity term dominates the shear term as $K\to0$ and therefore suppresses sufficiently long waves. The capillary term dominates as $K\to\infty$ and suppresses sufficiently short waves. Together they reduce the <Kelvin-Helmholtz instability> growth rate and can leave only a finite unstable band, or eliminate instability if the restoring effects are strong enough.
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