We examine the interactions between two three-dimensional quasi-geostrophic hetons. The hetons are initially translating towards one another. We address the effect of the vertical distance between the two poles (vortices) constituting each heton on the interaction. We also examine the influence of the horizontal separation between the poles within each heton. In this investigation, the two hetons are facing each other. Two configurations are possible depending on the respective locations of the like-signed poles of the hetons. When they lie at the same depth, we refer to the configuration as symmetric; the antisymmetric configuration corresponds to opposite-signed poles at the same depth. The first step in the investigation uses point vortices to represent the poles of the hetons. This approach allows us to rapidly browse the parameter space and to estimate the possible heton trajectories. For a symmetric pair, the hetons either reverse their trajectory or recombine and escape perpendicularly depending of their horizontal and vertical offsets. On the other hand, antisymmetric hetons recombine and escape perpendicularly as same-depth dipoles. In a second part, we focus on finite core hetons (with finite volume poles). These hetons can deform and may be sensitive to horizontal-shear-induced deformations, or to baroclinic instability. These destabilisations depend on the vertical and horizontal offsets between the various poles, as well as on their width-to-height aspect ratios. They can modify the volume of the poles via vortex merger, breaking and/or shearing out; they compete with the advective evolution observed for singular (point) vortices. Importantly, hetons can break down or reconfigure before they can drift away as expected from a point vortex approach. Thus, a large variety of behaviours is observed in the parameter space. Finally, we briefly illustrate the behaviour of tall hetons which can be unstable to an azimuthal mode $l=1$ when many vertical modes of deformation are present on the heton.
Effect of Nonlinear Dissipation on the Basin Boundaries of a Driven Two-Well Modified Rayleigh–Duffing Oscillator
