Equatorial Solitary Waves. Part 3: Westward-Traveling Modons

Abstract

Boyd's previous work on equatorial Rossby solitary waves which derivedthe Korteweg-deVries equation using the method of multiple scalesis here extended in several ways. First, the perturbation theoryis carried, to the next highest order to (i) assess the accuracyand limitations of the zeroth-order theory and (ii) analyticallyexplore solitons of moderate amplitude. Second, using the refinedtheory, it is shown that Rossby solitary waves will carry a regionof closed recirculating fluid along with the wave as it propagatesprovided that the amplitude of the wave is greater than some (moderate)threshold. The presence of such closed ?streaklines?, i.e., closedstreamlines in a coordinate system moving with the wave, is an importantproperty of modons in the theory of Flieri, McWilliams and others.The ?closed-streakline? Rossby waves have many other properties incommon with modons including (i) phase speed outside the linear range,(ii) two vortex centers of equal magnitude and opposite sign, (iii)vortex centers aligned due north-south, (iv) propagation east-westonly and (v) a roughly circular shape for the outermost closed streakline,which bounds the region of recirculating fluid. Because of thesesimilarities, it seems reasonable to use ?equatorial modon? as ashorthand for ?closed-streakline, moderate amplitude equatorial Rossbysoliton,? but it should not be inferred that the relationship betweenmidlatitude modons and equatorial solitary waves is fully understoodor that all aspects of their behavior are qualitatively the same.Kindle's numerical experiments which showed that small amplitudeRossby solitons readily appear in El Niño simulations, suggest?butdo not prove?that the very large El Niño of 1982 could have generatedequatorial modons.