## Geostrophic turbulence

I study geostrophic turbulence—the slowly evolving, large-scale turbulence in the atmosphere and ocean that is modified by Earth’s rotation, with a focus on the turbulence induced by geostrophic boundary buoyancy anomalies (e.g., buoyancy anomalies at the ocean’s surface). My work shows that the density stratification’s vertical structure controls the interaction range of surface buoyancy anomalies and the dispersion of surface-trapped Rossby waves. As a result, the density stratification controls the distribution of energy across horizontal scales as well as the dynamics of surface quasigeostrophic jets.

### The interaction range of surface buoyancy anomalies

The theory for surface buoyancy anomalies is developed in Blumen (1978) and Held et al. (1995). However, this theory assumes that the density stratification does not change with depth. The following animation, which shows the buoyancy anomaly at the ocean’s surface in a 400 km by 400 km domain, illustrates what this turbulence looks like. Red areas indicate lighter fluid whereas blue areas indicate denser fluid.

However the ocean does not have a uniform density stratification. Instead, the ocean’s density stratification is not only depth-dependent but seasonal as well. As a consequence, the theory developed in Blumen (1978) and Held et al. (1995) is only relevant at horizontal scales smaller than 10 km in the mid-latitude open ocean. At larger scales, the ocean’s density stratification must be taken into account. My work generalizes the theory to account for vertically variable density stratification. The resulting difference between summertime and wintertime turbulence is striking.

In summer, the turbulence is diffuse and highly local in space, with buoyancy anomalies exhibiting a short interaction range:

However, in winter, buoyancy anomalies have a longer interaction range and the flow is more non-local. The turbulence is characterized by thin surface buoyancy filaments as well as the presence of vortices with a wide range of sizes:

The dynamics of buoyancy anomalies at the ocean’s surface are therefore inherently seasonal due to the seasonality in upper ocean density stratification. Moreover, this seasonality controls the shape of the surface kinetic energy spectrum implied by surface quasigeostrophic turbulence.

### Buoyancy staircases in surface quasigeostrophic turbulence

Under certain circumstances, the interplay of surface-trapped Rossby waves with geostrophic turbulence results in a spontaneous reorganization of the flow into a surface buoyancy staircase: a meridional buoyancy profile consisting of mixed-zones punctuated by sharp buoyancy gradients, with eastward jets centred at the sharp gradients and weaker westward flows in between.

Moreover, the dynamics of the resulting jets depends on the density stratification’s vertical structure. In uniform stratification, we obtain (where yellow indicated more buoyant fluid and blue less buoyant fluid):

Over decreasing stratification, the dynamics are similar, but with eastward propagating along jet waves.

Finally, over increasing stratification, we obtain meandering jets whose shape evolves in time due to the westward propagation of weakly dispersive along jet waves.