A comparison of optical techniques for free-surface measurements along wave- and turbulence-driven flows*

The free surface at an air-water interface has been shown to relay information about inner-flow characteristics, including the manifestation of turbulence through rising coherent structures. We explore existing optical techniques that enable free-surface reconstruction in a cost-effective and efficient manner. These techniques measure the apparent distortions of a reflected or refracted reference pattern that vary linearly with the gradient of the surface elevation. We compare the performance of three imaging techniques (Free-Surface Synthetic Schlieren, Total Internal Reflection-Deflectometry, Moon-Glade Background Oriented Schlieren) to characterize the perturbations along a dynamic free-surface. Surface reconstruction is performed using an optical flow algorithm that provides an improvement over cross-correlation techniques. This is in part due to the higher spatial resolution of the resulting displacement field coupled with a superior performance in computing larger displacements with higher straining/dilatation of the background reference pattern. Surface motions are induced in two ways: 1) turbulent free-shear flow emanating from a submerged jet that impinges the underside of the free-surface and 2) gravity-capillary waves that arise from flow across an overspill weir. These two flow conditions simulate surface dynamics in an open-channel flow where the bottom roughness triggers coherent structures that impact the free surface. The physics of each technique is assessed, and the surface reconstruction results are compared to one another. We will discuss the advantages and drawbacks of each technique in terms of accuracy and practicality. Finally, we use the surface elevation results to untangle the gravity-capillary wave mechanics in terms of their dispersive properties as well as to investigate the manifestation of turbulence within the energetic and random surface roughness that is generated from the submerged jet.