 Oscillatory drift of an attenuated internal-wave beam

In the prescribed along-beam scalar model $U=A(\xi )\cos \omega t$ with $A=U_0{e}^{-\lambda \xi }$, the first-order fluid displacement is $A\sin \omega t/\omega$. Its leading sampled-velocity correction is $-\lambda A^2\sin (2\omega t)/(2\omega )$, whose period average vanishes. This result concerns the supplied component model and does not determine an Eulerian mean streaming flow.