A current stake for numerical ocean models is to adequately represent meso- and small-scale activity, in order to simulate its crucial role in the general ocean circulation and energy budget. It is therefore also a challenge for data assimilation (DA) methods to control these scales. However this small-scale activity is strongly linked to the nonlinear or turbulent character of the flow, whereas DA methods are generally much less efficient in such contexts than in (almost) linear ones. For variational DA methods as incremental 4DVAR, non-linearities imply convergence difficulty, the cost functions to be minimised presenting multiple local minima. The purpose of this thesis is to address this problem specifically, by exploring the behaviour of variational DA methods in a non-linear ocean model. To achieve this objective, a series of "twin" experiments assimilating simulated altimeter data, following the characteristics of altimetric satellite Jason-1 and SARAL/AltiKA, are analyzed. We also find different ways to improve efficiency of variational algorithms applied to turbulent circulations. This work is based on oceanic modelisation software called NEMO, including a idealized turbulent oceanic basin configuration, SEABASS, and DA components (e.g. Observation operator, Linear Tangent and Adjoint Models). Thanks to NEMO-ASSIM research platform, we have used and developed this set of tools. The used variational DA system itself is NEMOVAR. We present results characterizing scales and structures of the analysis error along the assimilation process, as well as tentative links with small scale activity. To study both the algorithm convergence and the analysis and forecast errors in a qualitative and quantitative way, a large spectrum of systematic diagnostics has been employed, e.g. spatial and temporal RMSE, cost function characteristics, projection of error fields on EOFs, validity of the tangent linear hypothesis, PSD of error fields. In our experiments, it appears that the incremental 4DVAR algorithm proved to be quite robust for long DA windows at eddy-permitting resolution. When the model horizontal resolution increases, the convergence of the minimisation algorithm is poorer but the 4DVAR method still controls efficiently analysis error. It has also been shown that the 4DVAR algorithm is clearly more performant than 3DFGAT for both considered resolutions. Moreover we investigate some strategies for DA in such nonlinear contexts, with the aim of reducing the analysis error. We performed so-called progressive incremental 4DVAR to improve the algorithm convergence for longer assimilation windows. Finally, we show that the adequation in represented flow scales between the model and the altimetric sampling is crucial to obtain the best error analysis reduction.
