A unifying mechanistic framework linking fluid loads on moving bodies to flow field

Over the past several decades, multiple methods have been developed to relate fluid dynamic forces on submerged bodies to the surrounding volumetric flow fields. These approaches ranging from force partitioning methods using divergence-free filters based on potential flow, to reciprocal-theorem-based techniques connecting actual flows to auxiliary viscous potential fields, to impulse and vorticity-moment methods grounded in global momentum conservation offer different perspectives for identifying links between flow features and hydrodynamic forces. In this work, we present a unifying mechanistic framework that integrates these seemingly disparate approaches under a single methodological umbrella, enabling consistent interpretation and comparison of their predictions. The framework is validated and demonstrated across canonical vortex-dominated flows, including two-dimensional and oscillating cylinders, oscillating spheres, prolate spheroids, and carangiform swimmers, highlighting its versatility and diagnostic power for analyzing complex hydrodynamic interactions.