The large-scale rotating flow structure in an engine cylinder exhibits features that can be described in generic terms of tumble and swirl. The structural details, nevertheless, vary from cycle to cycle due to fluctuating initial and boundary conditions of the flow. Typical analysis of the flow field cyclic variability — by simple root-mean-square, or additional spatial or temporal filtering, or proper orthogonal decomposition — is based on pointwise deviation of the instantaneous velocity from the ensemble mean. However, that analysis approach is not amenable to the evaluation of spatial variation of the flow structure, in position and orientation, within the flow field. To this end, other studies in the past focused instead on quantifying the variation of the vortex center for the dominant tumble or swirl pattern within the flow field. Yet there is no attempt in the literature to analyze both translational and rotational variations of more complex in-cylinder flow patterns, such as a counter-rotating tumble vortex pair generated during intake. In this paper, the technique of complex moment normalization from pattern recognition applications is extended to enable such an analysis. The algebraic properties of complex moments are introduced and related to the geometric and physical properties of two-dimensional flow fields. Complex moment normalization is then used to analyze a set of in-cylinder flow fields obtained by high-speed particle image velocimetry in the middle tumble plane of an optical engine. The cycle-to-cycle variation of the large-scale tumble flow structure — in magnitude, position, and orientation — are quantified and discussed.