During the last twenty years, measurements of the ocean surface properties by satellite instruments have significantly increased our knowledge of ocean dynamics.

One of these instruments is an altimeter that measures the topography of the ocean surface with a resolution of a quarter of degree. This surface topography can be decomposed into two fields: a *mean field* independent of time, plus an *anomaly field*. The mean field is the signature of the mean oceanic circulation, such as the well-known Gulf Stream, but here we only focus on the anomalies. An example of what the anomaly field looks like is shown in Figure 1. On this figure positive and negative anomalies are observed with very different spatial scales: some are large, others are small. The small scales, called mesoscales, range from 50 to 200 or 300 km and are associated with eddies whose driving mechanism is an instability of the mean currents. This is a remarkable property of geophysical fluids: under certain circumstances, the mean currents can spontaneously creates small scale anomalies.

*Figure 1.** Snapshot of sea surface height anomalies (in centimetres) on 14 October 1992*

Here we are interested in larger scales, between 500 and 2000 km. At these scales, non-linearities that were previously very strong can now be neglected, currents behave linearly. It is generally agreed that the large-scale anomalies are observed in every oceanic basins and that their displacement velocity is directed to the west. One exception is in the Antarctic Circumpolar Current where the mean flow is so strong toward the east that the large scale anomalies move eastward as well. The dynamic of these large-scale anomalies is usually described as Rossby waves. Rossby waves owe their existence to the meridional variation of the Coriolis force which is itself the result of the sphericity and rotation of the Earth.

**What are the driving mechanisms of these Rossby waves ?
**The two main mechanisms that are usually used to explain Rossby waves formation are large-scale wind anomalies and propagating waves along eastern coasts. In fact, Rossby waves are the main response of the ocean to large-scale forcing, and as such, any process that introduces a large-scale perturbation in the ocean is likely to produce Rossby waves.

Here we ask ourselves if large-scale instability of the mean currents can create Rossby waves.

We saw above that instability of the mean currents mostly creates mesoscale anomalies with scales between 50 and 200 or 300 km. In fact instability creates anomalies at all scales but the growth is generally faster at small scales than at larger scales. However if the growth is faster at small scales it is not zero at large scales. Here we first investigate the rate of this large-scale growth as a function of the vertical structure of the mean currents and then calculate the growth rate of large-scale anomalies on *in situ* mean current data.

**Results
**Our results first show that the growth rate is very sensitive to the vertical structure of the zonal mean flow. Just as a sound can be decomposed into different sinusoidal components, we decompose the vertical structure of the mean zonal flow into different components, although this time not sinusoidal. We found that the largest growth happens when the component with two signs reversal on the vertical has a westward surface velocity.

*Figure 2.** Growth time (years) of the large-scale anomalies. White regions are regions with no data.*

Figure 2 shows the growth rates in years of the large-scale anomalies calculated on real mean flow data extracted from a database constructed with ARGO float displacements. Growth rates smaller than a year are found in all oceanic basins at low latitudes and in some regions of the Antarctic Circumpolar Current. Further comparison between the phase speed of the theoretical growing anomalies and the observed anomalies have shown that mean circulation is likely to produce large scale anomalies at low latitudes.

Our future calculations should include the horizontal variation of the mean flow.

**Reference**

Antoine Hochet, Thierry Huck, and Alain Colin de Verdière, 2015. Large-scale baroclinic instability of the mean oceanic circulation: A local approach. *J. Phys. Oceanogr.*, **45**, 2738–2754.