Validation of the k-filtering technique for a signal composed of random phase plane waves and non-random coherent structures

Recent observations of astrophysical magnetic fields have shown the presence of fluctuations being wave-like (propagating in the plasma frame) and those described as being structure-like (advected by the plasma bulk velocity). Typically with single spacecraft missions it is impossible to differentiate between these two fluctuations, due to the inherent spatio-temporal ambiguity associated with a single point measurement. However missions such as Cluster which contain multiple spacecraft have allowed temporal and spatial changes to be resolved, with techniques such as the k-filtering technique. While this technique does not assume Taylor's hypothesis as is necessary with single spacecraft missions, it does require weak stationarity of the time series, and that the fluctuations can be described by a superposition of plane waves with random phase. In this paper we test whether the method can cope with a synthetic signal which is composed of a combination of non-random phase coherent structures with a mean radius d and a mean separation λ, as well as plane waves with random phase.