#### Title

#### Abstract

A linear stratified model is used to study the response of the equatorial ocean to forcing by the wind at periods from one month to one year. Solutions are represented as double sums of vertical modes (designated by the index *n*) and of the various types of waves associated with each mode (designated by the index *l*). Waves associated with a considerable number of vertical modes contribute to the solutions. They superpose in such a way that energy and phase propagate vertically as well as horizontally. It is useful to isolate the individual contributions of various pieces of the complete solution. One way to do this isolates the response of individual vertical modes (that is, specifies a value for *n*, but carries out the summation over *l*). Pieces of the solution defined in this way tend to focus energy at specific points on the equator. These focal points, however, are not at all visible in the complete solution. Another way isolates the response due to waves of a particular type (that is, fixes a value of *l*, but carries out the summation over *n*). These pieces of the solution form well-defined beams that carry energy into the deep ocean at slopes predicted by inviscid ray theory, and they are visible in the complete solution. Solutions for zonal winds are complicated. A Kelvin beam directly forced by the wind reflects from the eastern boundary of the ocean as a set of *l* = 1,3,5,... Rossby beams. These beams, in turn, reflect from the western boundary as Kelvin beams. All of them reflect efficiently from the ocean surface and bottom. It is the multiple reflection of these beams from basin boundaries that makes the response so complicated. The most visible beams in the solutions are the wind-driven Kelvin beam and a reflected *l* = 1 Rossby beam. The response is strong at frequencies of the order of 2*π* years^{–1} (or lower), and weakens considerably at higher frequencies. Solutions for meridional winds are much simpler. At a frequency of 2*π* months^{–1} a beam of Rossby-gravity waves directly forced by the wind reflects entirely poleward along the eastern boundary as a packet of coastal Kelvin waves, since there are no Rossby waves available for this reflection. The response is strong at frequencies of the order of 2*π* months^{–1}, and weakens markedly at lower frequencies.

#### Recommended Citation

McCreary, Julian P..
1984.
"Equatorial beams."
*Journal of Marine Research*
42,
(2).
https://elischolar.library.yale.edu/journal_of_marine_research/1724