Time-frequency analysis of phase coherence of solar wind turbulence

Several observations in space plasmas have reported the presence of coherent structures at different plasma scales. Structure formation is believed to be a direct consequence of nonlinear interactions between plasma modes that depend strongly on the phase synchronization of those modes. Analysing directly Fourier phases is however very tricky due to their dependence on an arbitrary time origin and to their 2π periodicity (which makes the phases appear completely mixed/random, even when they are not!). A method, based on Surrogate data, has been developed recently to solve this problem and to allow one to systematically detect coherent structures in turbulent signals [Sahraoui, PRE, 2008]. This 1-D method, however, suffers the weakness that it can estimate the scale of the structures but only over the whole used time series. Here we present a new version of the method that makes a 2-D analysis of the time series, i.e., in the time and the scale (frequency) domains. This makes possible the estimation of the size of the structures and their localisation in time. After validating the new method on synthetic data, we will show applications to the Cluster data. In particular, we will present recent results on coherent structures at small/electron scales in the solar wind. A discussion of the consequence of such observations on theoretical modeling of solar wind turbulence (e.g., weak versus strong, intermittency) will be discussed.