Applying image velocimetry on curved free‑surface geometries of known shape such as spillways or free-nappe: the OrthoCyd method.

Ensuring the safety of spillways during flood events is a critical challenge for dam operators and public authorities. Accurate knowledge of flow velocities along spillways and downstream of ski jumps is essential for assessing the erosive potential of high‑velocity flows and preventing structural damage. However, intrusive velocity measurement techniques are unsuitable in such configurations due to limited accessibility and the very high flow speeds involved. Image‑based velocimetry offers an attractive alternative, providing instantaneous, spatially distributed velocity fields from a single viewpoint. Yet, conventional image-based techniques rely on the assumption of a planar free surface, which becomes invalid for curved flows such as those encountered on spillway chutes or nappe flows. Surface curvature induces geometric distortions in ortho‑rectified images, leading to significant velocity errors.

Stereo‑vision systems can be used to reconstruct non‑planar free surfaces, but their deployment on full‑scale spillways is complex and costly as it requires synchronized cameras with high spatial and temporal resolution. To overcome these limitations, we propose OrthoCyd, a novel single‑camera orthorectification method dedicated to flows whose free‑surface geometry is known a priori and corresponds to a right‑cylindrical surface (i.e., a planar surface which is curved along the longitudinal dimension). This approach is well suited to spillway chutes, with the assumption that the free surface follows the underlying curved geometry. OrthoCyd enable consistent displacement measurements with any image-velocimetry method (block matching, tracking, optical flow, spatio-temporal approach). This method extends the applicability of image‑based velocimetry to non‑planar free‑surface flows while maintaining the simplicity and practicality of single‑camera acquisition systems.

Two applications illustrate the method: a laboratory experiment on a free‑nappe flow, and a field application on an operating spillway. These examples demonstrate that OrthoCyd provides reliable velocity measurements in both controlled and full‑scale conditions.