Abstract
A new type of standing equatorial wave mode is described that exists in the semi-infinite ocean 0 ⩽ x ⩽ L, −∞ ⩽ y ⩽ ∞. It consists of a finite sum of the meridionally trapped equatorial waves in an infinite x domain. The new mode is thus itself equatorially trapped and requires no energy sources or sinks at |y| = ∞. However, it exists only for a discrete, countable set of pairs of values of the frequency ω and the ocean zonal width L. Previously described standing modes exist for any ocean width, but are infinite sums of trapped equatorial waves and require a continuous energy source in the west at |y| = ∞ to balance the continuous energy sink in the east at |y| = ∞. Several examples of the new type of standing mode are given, and it is shown that as the standing mode period becomes very long, so the zonal scale becomes very short. The effect on the standing modes of bounding the basin meridionally is also described; energy is recycled round the basin by boundary-trapped Kelvin waves along the zonal walls. The amount of energy recycled in the new type of standing mode, however, is exponentially small compared to that recycled in the previously described standing modes.
