 Cross-wave Stokes drift

Two plane internal gravity waves can each have zero Stokes drift but give a nonzero drift through interference. The displacement of one wave need not be perpendicular to the other wave's wave vector. For upward waves with wave vectors $(\kappa ,-\kappa )$ and $(-\kappa ,-\kappa )$ and vertical amplitudes $W$, the cross-wave drift is $(0,-2\kappa W^2\cos (2\kappa x)/\omega )$ with $\omega =N/\sqrt{2}$. It has zero spatially averaged vertical flux. It cannot on its own satisfy an impermeable oscillating boundary: the second-order Eulerian mean velocity supplies the necessary normal correction there.