The interaction between two oppositely travelling, horizontally offset, antisymmetric quasi-geostrophic hetons

Abstract

We investigate numerically the nonlinear interactions between hetons. Hetons are baroclinic structures consisting of two vortices of opposite sign lying at different depths. Hetons are long-lived. They most often translate (they can sometimes rotate) and therefore they can noticeably contribute to the transport of scalar properties in the oceans. Heton interactions can interrupt this translation and thus this transport, by inducing a reconfiguration of interacting hetons into more complex baroclinic multipoles. More specifically, we study here the general case of two hetons, which collide with an offset between their translation axes. For this purpose, we use the point vortex theory, the ellipsoidal vortex model and direct simulations in the three-dimensional quasi-geostrophic, contour surgery model. More specifically, this paper shows that there are in general three regimes for the interaction. For small horizontal offsets between the hetons, their vortices recombine as same-depth dipoles which escape at an angle. The angle depends in particular on the horizontal offset. It is a right angle for no offset, and the angle is shallower for small but finite offsets. The second limiting regime is for large horizontal offsets where the two hetons remain the same hetonic structures but are deflected by the weaker mutual interaction. Finally the intermediate regime is for moderate offsets. This is the regime where the formation of a meta-stable quadrupole is possible. The formation of this quadrupole greatly restrains transport. Indeed, it constrains the vortices to reside in a closed area. It is shown that the formation of such structures is enhanced by the quasi periodic deformation of the vortices. Indeed, these structures are nearly unobtainable for singular vortices (point vortices) but may be obtained using deformable, finite-core vortices.

Hetonic quartets in a two-layer quasi-geostrophic flow: V-states and stability

“…The discrepancy between the values of σ r is attributed to horizontal spreading and/or to overlapping of the finite-core vortices, as mentioned above. Finally, we note that a similar instability has been observed for three-dimensional quartets in a continuous stratification 32 .…”

Three-dimensional quasi-geostrophic vortex equilibria with -fold symmetry

“…There are n m = 2m modes for the m-vortex problem or n m = 2m + 2 modes for the m + 1-vortex problem. This approach is the same as the one used in different contexts in Reinaud & Carton (2015, 2016 and is further described in Appendix A. Figure 2 shows the maximum growth rate σ max = max 1 j nm {σ r j } versus the number of peripheral vortices m. For comparison, similar results for two-dimensional vortices are included.…”

Coriolis effect on centrifugal buoyancy-driven convection in a thin cylindrical shell

“…The material derivative of a property implies the rate of change of that property as we track a cyclone or anticyclone. We recast (3.3 a – d ) in terms of stream function () and as follows: A similar set of equations is solved for quasi-geostrophic flows to study the interaction of cyclones and anticyclones with themselves (Reinaud, Dritschel & Koudella 2003; Dritschel, Reinaud & McKiver 2004; Reinaud & Carton 2016) or with the wall (Deremble, Johnson & Dewar 2017; Venaille 2020). Equation (3.4 c ) justifies figure 14( b – g ); the temperature of cyclone and anticyclones does not change with time.…”

“…A similar set of equations is solved for quasi-geostrophic flows to study the interaction of cyclones and anticyclones with themselves (Reinaud, Dritschel & Koudella 2003;Dritschel, Reinaud & McKiver 2004;Reinaud & Carton 2016) or with the wall (Deremble, Johnson & Dewar 2017;Venaille 2020). Equation (3.4c) justifies figure 14(b-g); the temperature of cyclone and anticyclones does not change with time.…”