This paper describes a comprehensive kinematic decomposition of unstructured Lagrangian data from volumetric particle tracking velocimetry measurements. The method uses particle location data at an arbitrary time t and calculates linear affine mappings at a later time \(t+{\text{d}}t\) . The transformation produces the full velocity gradient tensor, which can then be further analyzed to identify the four types of fluid motion (i.e., translation, rotation, dilatation, and shear) without using spatial derivatives. The methodology provides insights into the underlying kinematics and facilitates the identification of coherent structures using, for example, the Q-criterion, within the flow without resorting to numerical differentiation or data assimilation methods. The method is first validated using analytical solutions and direct numerical simulations and then applied to experimental subsonic jet measurements. The method’s accuracy is discussed, and leading-order error sources are presented.
