Abstract: The particle flow fields inside bubbling beds exhibit strong unsteady flow patterns. Two state-of-the-art analysis methodologies, the proper orthogonal decomposition (POD) and the swirling strength criterion, are applied to the fluctuating particle flow fields predicted by the two-fluid model of a bubbling bed to identify and analyze the dominant spatio-temporal patterns of the particulate phase. The overall objective of this study is to demonstrate the capability of these data analysis methods to enhance our understanding of gas-particle flows in fluidized beds. These methods offer valuable insights into the complex dynamics of fluidized bed systems, particularly in elucidating the spatio-temporal patterns and vortical structures associated with particle motion and mixing phenomena. This study extends our previous investigation of bubbling fluidized beds by applying the POD to a Cartesian bed geometry, building on the findings from our initial analysis of a cylindrical bed. The identified particle vortical motions are characterized by their flat structure. These flat vortex sheets appear to be stable structures in bubbling beds that emerge due to the collective effect of instabilities occurring in the particulate phase, in contrast to single-phase turbulent flows, where the dominant flow structures are tubular; that is, the common attribute of vigorous mixing in bubbling beds primarily arises from the meso-scale unsteady patterns of particles rather than their behavior at the individual particle level. The similarities in the observed particle vortical motions across different geometries suggest that these patterns are a fundamental characteristic of bubbling beds. The ability of POD eigenmodes to reproduce the instantaneous fields is also systematically assessed.