Equatorial Solitary Waves. Part V: Initial Value Experiments, Coexisting Branches, and Tilted-Pair Instability

Abstract

A series of high-resolution numerical experiments, augmented by theory, to further explore the dynamics of equatorial dipole vortices (Rossby solitary waves) is performed. When the amplitude is sufficiently large so that the vortices trap fluid internally, the solitary waves for a given phase speed are not unique. The potential vorticity–streak function (q–Ψ) relationship is everywhere linear for one branch, but highly nonlinear in the recirculation region for the second branch. Westward-traveling vortex pairs are highly unstable on the midlatitude beta plane, but the equatorial wave guide stabilizes vortex pairs that straddle the equator, even when given a strong initial tilt. As discovered by Williams and Wilson and explained theoretically by Boyd, the author confirms that higher latitudinal mode solitary waves are weakly nonlocal through radiation of sinusoidal Rossby waves of lower latitudinal mode number. The amplitude and wavelength of the radiation are in good agreement with nonlocal soliton theory. It is sometimes said that the great discovery of the nineteenth century was that the equations of nature were linear, and the great discovery of the twentieth century is that they are not.—Thomas Körner, Fourier Analysis (1988, p. 99)