Cluster-Based Reduced-Order Modeling of Flat Plate Hydrodynamics Near an Air-Water Interface

Leveraging a Cluster-based Reduced-Order Modeling approach, this study investigates how proximity to a deformable free surface alters vortex dynamics and fluid–structure interactions around a flat plate, based on experimentally obtained flow fields. Two configurations are explored: a stationary plate (zero degree of freedom, 0-DOF) and a plate undergoing coupled pitching and plunging oscillations (2-DOF), both positioned near the air–water interface. Time-resolved Particle Image Velocimetry and volumetric Particle Tracking Velocimetry capture the flow evolution. The flow data are reduced in dimensionality using Proper Orthogonal Decomposition, and unsupervised k-means clustering identifies the dominant flow states. Finally, a Markov model describing the dynamic pathways of flow evolution is constructed through analysis of cluster transition probabilities. The results show that proximity to the free surface significantly influences the dominant flow states and transitions, with certain states exhibiting strong vortex interactions with the free surface. For the 2-DOF plate, a cyclic and unidirectional Markov chain indicates a synchronized coupling between vortex shedding and structural motion, while the stationary 0-DOF plate exhibits asymmetric and intermittently branching state transitions. These findings highlight the role of the air–water interface and structural motion in shaping flow states and transition dynamics.