= Two-beam radiation from a localized oscillating boundary
{title2=$Z_\pm=z\pm\alpha x,\quad\alpha=\omega/\sqrt{N^2-\omega^2}$}
For a nonrotating uniform-stratification fluid under the <Boussinesq approximation> driven at $0<\omega<N$ by a localized vertical-wall <velocity>, positive vertical <wavenumbers> radiate down and right and negative ones up and right. The real <velocity> separates into functions of $Z_+$ and $Z_-$. Its in-phase component is half the imposed boundary profile on each beam; the quadrature component is its <Hilbert transform> partner. Thus compact localization at maximum boundary speed does not imply compact localization of all components at every phase. A finite-duration source contains several frequencies and spreads <energy> over their different ray angles and group speeds.
Back to article page
