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Rotating flow inside an internal combustion engine cylinder is deliberately engineered for improved fuel-air mixing and combustion. The details of the rotating flow structure vary temporally over an engine cycle as well as cyclically at the same engine phase. Algorithms in the literature to identify these structural details of the rotating flow invariably focus on locating its center and, on occasion, measuring its rotational strength and spatial extent. In this paper, these flow structure parameters are evaluated by means of complex moments, which have been adapted from image (scalar field) recognition applications to two-dimensional flow pattern (vector field) analysis. Several additional detailed characteristics of the rotating flow pattern - the type and extent of its deviation from the ideal circular pattern, its rotational and reflectional symmetry (if exists), and thus its orientation - are also shown to be related to the first few low-order complex moments of the flow pattern.