Three-dimensional numerical investigations have been carried out to study the unsteady wake behind a sphere performing transverse rotational oscillations. Frequency and amplitude of forced oscillation have been varied and their influence on coherent wake structures and transitions have been presented. These structures have been identified with the help of instantaneous iso-λ2 surfaces and streamline plots. The results reveal presence of different vortex shedding modes that appear over the parametric range. Variations in mean and instantaneous values of hydrodynamic coefficients with amplitude and frequency of forced oscillations have also been reported in this work. Time series signals of these force coefficients have been analysed using Hilbert Huang Transformation and recurrence relations. These techniques shed light on the time dependent behaviour of the wake by providing insights on frequency–time–amplitude distributions of the wake oscillations. Nonlinearities in wake interactions have also been quantified in terms of degree of stationarity. Variation of recurrence quantification parameters with change in forcing frequency has also been presented. © 2019 Elsevier Masson SAS