One of the consequences of the global warming is the modification of the hydrological cycle and then of the freshwater flux get by the ocean. These flux have local influence on the sea surface salinity and thus influence the large scale ocean circulation. The ocean circulation, and more accurately the thermohaline circulation, is able to produce some low frequency variability, as the slow part of the climate system. We are going to study the impact of the freshwater flux on the thermohaline circulation and mainly on the decadal to millennial variability.

In the ocean, as in all dynamical systems, two paradigms coexist for the explanation of the observed variability: it can be endogenous or exogenous.
For the first paradigm, the variability comes from internal mode as relaxation oscillation or non-linear saturation of a linear growth mode: This theory is intrinsically linked with non-linear effects.
The second paradigm is based on the existence of an asymptotic stable steady state and of external stimulation sustaining the variability: transient growth of initial perturbations or oscillation sustains by stochastic forcing. Actually, the non-normality of the ocean dynamic allows some strong variability around a steady state even if it is stable.

During this thesis, we sought to identify the variability appearing under different freshwater flux regimes. For this we implemented systematical methods of analysis as linear the stability analysis or the general stability analysis in a hierarchy more and more realistic models (Howard-Malkus loop model, 2D latitude-depth model, planetary-geostrophic model or OPA model in global realistic configuration). These methods allow us to extract the physical mechanisms linked to internal variability modes or forced variability modes.

Some outstanding results appear. During the study of endogenous variability in a 2D latitude-depth model, the growth mechanism and the oscillation one of a centennial mode are analyzed and theirs characteristics are described. This mode, corresponding to a salinity dominated density anomaly advected around the circulation, is feed by the positive salinity feedback on the advection in the freshwater forcing zone.
A millennial oscillation cycle which appears through an infinite-period bifurcation is characterized. The bifurcation is due to higher frequency mode presence during the millennial cycle. Thus, we point out that the centennial oscillation is a precursor of millennial oscillation.

During the study of the exogenous variability, the optimal perturbations of the sea surface salinity influencing the ocean circulation are performed in a latitude-depth model of the thermohaline circulation. We analyzed an optimal finite time growth: an ocean circulation intensity growth, 67 yr after the sea surface salinity perturbation, is not even possible but optimal. The optimal perturbation correspond to a stimulation of the centennial oscillation when this latter is reinforced through the positive salinity feedback on advection in the evaporation-precipitation zone. The optimal perturbation of the freshwater flux confirms the idea that an increase of the intensity flux decreases the ocean circulation in such kind of model. The optimal stochastic perturbation of the freshwater flux shows the strong response less damped linear mode, here the centennial oscillation. The other parts of the ocean spectrum response to the optimal stochastic perturbation correspond to a red noise.
In the same way, 24 yr transient growth is optimal through the multi-decadal oscillation appearing in a planetary-geostrophic model. Optimal stochastic perturbations studies show the strong response at the frequency of the less damped eigenmode with an intensity controlled by the non-normality of the system. Because the variability is strongly controlled the surface boundary condition (i.e. mixed conditions or flux conditions), the shape of the optimal perturbations and their response is too.
Finally, using a primitive equation modem in global realistic configuration, an optimal growth of the meridional ocean circulation intensity and of the meridional heat transport intensity appear respectively at 10.5 yr and 2.2 yr after the sea surface salinity perturbation. These optimal initial perturbations allow us to determine an efficient growth mechanism of the meridional circulation and of the meridional heat transport. A meridional gradient of the sea surface salinity perturbation induces a perturbation of the zonal velocities by the thermal wind relation. This perturbation of the zonal velocities, by interaction with the zonal gradient of temperature, creates a perturbation of the zonal gradient of temperature. This latter induces, by the thermal wind relation, a perturbation of the meridional velocities which modifies the meridional circulation or the meridional heat transport. Moreover the study of optimal perturbations allow us to fix bounds of the circulation variations. By taking a perturbation equivalent to the Great Salinity Anomalies, we obtain modification bounds of 0.75 Sv and 0.03 PW.