Predicting wave run-up on vertical columns based on thermal stereography measurements

• The study employed the thermal stereography to achieve more accurate wave run-up measurements on circular and square columns. • A correction was made to the coefficient m in an existing formula for circular columns, resulting in predictions that agreed well with experimental data. • A new empirical formula for predicting wave run-up on square columns was developed based on the velocity stagnation head theory. • The wave run-up profiles for circular and square columns were compared, revealing significant differences in wave behaviour. Accurate estimation of wave run-up is crucial for the design and safety of marine structures. To facilitate more precise and convenient predictions of wave run-up on vertical columns, including circular and square columns, many empirical formulas have been proposed. However, those derived from wave probe measurements typically underestimate the maximum wave run-up height due to the inability of wire-type wave gauges to closely adhere to the column surface. This study employed the non-contact wave measurement technology based on thermal stereography to measure the wave run-up distributions on vertical columns under regular waves, providing a more accurate measurements of wave run-up closer to the column surface. Utilizing the measurements, a modified formula was proposed to predict the wave run-up on circular columns. Additionally, considering the effects of scattering parameter ( kD ) and wave steepness ( k η m a x ), a new empirical formula for predicting the wave run-up on square columns was developed based on the velocity stagnation head theory. These formulas were validated using the experimental data from the present study and the literature, demonstrating their ability to provide satisfactory wave run-up predictions. Furthermore, the spatiotemporal wave evolution for circular and square columns were compared. The wave profile in front of the circular cylinder at a half diameter tends to flatten, with water flowing along the cylinder surface to the sides, leading to a significantly lower wave run-up height ratio compared to the square column. This study provides the valuable insights for predicting the wave run-up on vertical columns, contributing to the design and safety assurance of marine structures.