= Relaxation of a symmetric viscous layer
{title2=$s=\Delta\rho gh_0\kappa/[2\mu(\lambda+2\kappa)]$}
A layer of half-thickness $h_0$, <dynamic viscosity> $\mu$ and density $\rho$, between semi-infinite fluids of viscosity $\lambda\mu$ and densities $\rho\mp\Delta\rho$, relaxes a symmetric thickness <Fourier mode>. In the plug-like <extensional viscosity> regime, <mass conservation> and $4\mu(hu_x)_x=h\Delta\rho gh_x-\sigma_{xz}^+$ together with the <Fourier traction map for a viscous half-space> give the displayed rate, where $\kappa=|k|h_0$. Inner longitudinal extension dominates for $\lambda\ll\kappa$; outer tangential resistance dominates for $\kappa\ll\lambda$ while the plug approximation remains valid.
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