Quantitative relationship between hydrodynamic forces and flow structures for rectangular cylinders with varying aspect ratios

Establishing a quantitative mapping between local flow structures and global hydrodynamic forces is crucial for uncovering the physical mechanisms of flow-induced vibrations, yet it remains a significant challenge using traditional integral methods. This study introduces a field-based force reconstruction framework utilizing the Derivative-Moment Transformation (DMT) method to address this issue. The proposed approach explicitly decomposes instantaneous hydrodynamic forces into diffusive, unsteady, and convective components based solely on velocity and vorticity fields, bypassing the need for pressure data. To validate the framework and demonstrate its diagnostic capabilities, numerical simulations are performed for flows past rectangular cylinders with aspect ratios (AR) of 1, 5, 8, and 10 at a Reynolds number of 300. The results demonstrate that the reconstructed forces agreed closely with those obtained from direct numerical integration. Furthermore, the decomposition reveals the distinct physical origins of the hydrodynamic loads: the unsteady component is identified as the primary driver of lift fluctuations during vortex shedding, while the convective component captures the effects of shear layer reattachment processes. These findings confirm that the proposed framework provides a robust and insightful tool for interpreting the complex relationship between fluid motions and hydrodynamic loads in ocean engineering applications.