This study explores the structure of liquid/gas coaxial jets under forced and unforced conditions. The forcing is in the form of a transverse acoustic resonance within the confined space where the mixing occurs. The studied flows are relevant to combustion instabilities which involve an interaction between acoustic waves and reactant mixing. A variety of local and global signal processing methods were applied to digital flow visualization data to identify spatial and temporal features. The unforced case is in particular chaotic and influenced by a broad range of spatial and temporal phenomena. Proper orthogonal decomposition (POD) was able to extract flapping and convecting features, and spectral content of these behaviors is presented. The forced case results in organized structures that emerge above the background turbulence, including harmonics of the forcing frequency and nonlinear interactions between specific frequencies. The dynamic mode decomposition (DMD) performs the best in the forced case, clearly isolating all of these features. Wavelet analysis showed that forcing tended to reorganize energy from longer to shorter time scales. Bicoherence analysis of the data showed that the forcing causes a much different energy exchange in the outer and inner shear layers. The outer-to-inner jet coupling during forced conditions appears to be limited to an axial extent of about one to three inner jet diameters downstream of the jet exit. The recirculation zone between the inner and outer jet, extending about one inner jet diameter downstream, appears to disrupt the influence of forcing on the inner jet.