class: center, middle # It's not you, it's me: ## Breakup of dipoles and formation of sub-surface anticyclones ### Liam Brannigan, Helen Johnson, Camille Lique, ### Johan Nilsson, Jonas Nycander [Generation of sub-surface anticyclones at Arctic surface fronts due to a surface stress, *in press doi:10.1175/JPO-D-17-0022.1*, JPO.](http://journals.ametsoc.org/doi/abs/10.1175/JPO-D-17-0022.1) --- ## Observed sub-surface eddies in the Arctic
A sub-surface anticyclone observed around Day 143 from an ice-tethered profiler in May 2006. The largest buoyancy anomaly is in the halocline around 50 m depth (b), but there is also a weaker surface buoyancy anomaly (a). The colour scale in (d) is based on that used for (a). --- ## Initial condition used for simulations
The model domain is doubly-periodic and about 90 m deep. There are two independant fronts with opposite orientation. A positive zonal surface stress leads to a downfront stress at the northern front but an upfront stress at the southern front. --- #### Dipole formation with zero surface stress
With zero surface stress (left panels) cyclone-anticyclone dipoles form. They tend to follow curved paths that bring them back to the front. The dipole trajectory is shown by the black dots. --- #### Dipole formation under an upfront stress
With an upfront surface stress (centre panels) dipoles also emerge from the front. However, in this case the mixed-layer cyclone eventually travels south in the direction of the Ekman transport, while the sub-surface anticyclone remains in place as an isolated sub-surface eddy. This is shown in the movie on the next slide. --- #### Dipole formation under an upfront stress
--- #### Dipole formation under a downfront stress
With a constant downfront surface stress (right panels) dipoles do not emerge from the front. This is because the front is advected by the Ekman transport in the same direction as the dipole propagation at a slightly faster rate than the dipole can propagate. --- ## Vertical strucure of dipoles
The vertical structure of the dipoles shows why they are subject to breakup by a surface stress. With no stress (a) the dipole is `tilted', with the cylonic component stronger near the surface and the anticyclonic component stronger near the base of the mixed layer. As such, with an Ekman depth of about 11 m, only the cyclone is subject to the direct effects of the surface stress. --- ## Effect of a surface stress of dipoles The hypothesis developed above is that dipoles can be broken up when the surface cyclone component is subject to an Ekman transport that causes it to travel in the direction of the Ekman flow. We test this hypothesis by restarting the simulation with no surface stress at the point when a dipole has formed. We then apply a surface stress in different directions to see the effect on the dipole propagation. --- ## Effect of a surface stress of dipoles
The dots show the trajectories for the surface cyclone (left panel) and the sub-surface anticyclone (right panel). The colour of the dots corresponds to the arrow showing the direction of the Ekman transport. The black dots show the curved trajectory for the case with zero surface stress. --- ## Effect of a surface stress of dipoles
When the Ekman transport has a component advecting the cyclone away from the anticyclone (blue and red colours), the cyclone travels away from the anticyclone in the direction of the Ekman transport. --- ## Effect of a surface stress of dipoles
When the Ekman transport pushes the cyclone towards the anticyclone (green colours) the entire dipole trajectory is affected. When the Ekman transport is in the direction of the dipole (magenta colours), the dipole remains coherent but follows a less curved path. In both these cases the anticyclone does a fast loop of the cyclone. --- ## Effect of a surface stress of dipoles
An animated version of this plot is shown on the next slide. --- ## Effect of a surface stress of dipoles
--- ## Model of eddy advection due to Ekman transport
We derive a surface quasi-geostrophic (SQG) model for the effect of a surface stress on a mixed layer eddy. This model predicts that when the mixed-layer cyclone is affected only by the Ekman transport, the translation velocity of the cyclone should be the Ekman transport divided by the stratification depth. Comparing this against the cyclone translation velocity in the model shows a good match. --- ## Kinematic model of eddy advection
We also derive a simple kinematic model for the joint effect of dipole self-propagation and the advection due to Ekman transport. This model also captures the basic dynamics of the advection for each component of the dipole. --- ## Conclusions 1. An upfront surface stress *aids* dipole propagation away from fronts while a downfront stress *inhibits* propagation. 2. The surface cyclone component of dipoles is advected by the Ekman transport when the Ekman layer is thinner than the mixed layer. 3. The sub-surface anticyclone is not advected by the Ekman transport when the Ekman layer is thinner than the mixed layer. 4. Sub-surface anticyclones are formed where the cyclonic component is advected *away* from the anticyclone by the Ekman transport. [Generation of sub-surface anticyclones at Arctic surface fronts due to a surface stress, *in press doi:10.1175/JPO-D-17-0022.1*, JPO.](http://journals.ametsoc.org/doi/abs/10.1175/JPO-D-17-0022.1)