= Viscous penetration depth
{title2=$\delta=\sqrt{2\eta/(\rho\omega)}$}
The <viscous penetration depth> is the distance over which a time-periodic shear <velocity> driven by an oscillating boundary decays by $1/e$ in a semi-infinite <Newtonian fluid>. The <momentum diffusion> equation gives $u=U_0e^{-z/\delta}\cos(\omega t-z/\delta)$. Both attenuation and phase lag are controlled by $z/\delta$. The corresponding fluid-displacement amplitude has the same spatial decay, because dividing each velocity amplitude by the common <angular frequency> does not change their ratio.
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