Numerical study of elliptical modons using a spectral method

Abstract

We study the relationship between dynamical structure and shape for vortex pairs, now usually named ‘modons’. When the boundary between the exterior irrotational flow and the inner core of non-zero vorticity is a circle, an analytical solution is known. Here, we generalize the circular modons to solitary vortex pairs whose vorticity boundary is an ellipse. We find that as the eccentricity of the ellipse increases, the vorticity becomes concentrated in narrow ridges which run just inside the elliptical vorticity boundary and continue just inside the line of zero vorticity which divides the two vortices. Each vortex becomes increasingly ‘hollow’ in the sense that each contains a broad valley of low vorticity which is completely enclosed by the ridge of high vorticity already described. The relationship between vorticity ζ and streak function Ψ, which is linear for the circular modons, becomes strongly nonlinear for highly eccentric modons, qualitatively resembling ζ ∝ Ψe−λΨ for some constant λ. In this study, we neglect the Earth's rotation, but our method is directly applicable to quasi-geostrophic modons, too. An efficient and simple spectral method for modon problems is provided.