Mike van Meerkerk

We present an experimental study on the variation in wave impact location and present a mechanism for the development of free surface instabilities on the wave crest for repeatable plunging wave impacts on a vertical wall. The existence of free surface instabilities on an impacting wave is well known, but their characteristics and formation mechanism are relatively unknown. The development of the global wave shape is measured using a visualization camera, whereas the local wave shape is measured with an accurate stereo-planar laser-induced fluorescence technique. A repeatable wave is generated with negligible system variability. The global wave behavior resembles that of a plunging breaker, with a gas pocket cross-sectional area defined by an ellipse of constant aspect ratio. The variability of the local wave profile increases significantly as it approaches the wall. The impact location varies by ∼0.5% of the wave height or more than a typical pressure sensor diameter. Additionally, the wave tip accelerates to a velocity of $1.5\sqrt{g{h}_0}$ compared to the global wave velocity of $1.2\sqrt{g{h}_0}$ . The difference in impact location and velocity can result in a pressure variation of ∼25%. A mechanism for instability development is observed as the wave tip becomes thinner and elongates when it approaches the wall. A flapping liquid sheet develops that accelerates the wave tip locally and this triggers a spanwise Rayleigh–Taylor instability.

In this work, we extend a planar laser-induced fluorescence method for free surface measurements to a three-dimensional domain using a stereo-camera system, a scanning light sheet, and a modified self-calibration procedure. The stereo-camera set-up enables a versatile measurement domain with self-calibration, improved accuracy, and redundancy (e.g., possibility to overcome occlusions). Fluid properties are not significantly altered by the fluorescent dye, which results in a non-intrusive measurement technique. The technique is validated by determining the free surface of a hydraulic flow over an obstacle and circular waves generated after droplet impact. Free surface waves can be accurately determined over a height of $$L=100$$L=100 mm in a large two-dimensional domain ( $$y(x,z) = 120\times 62$$y(x,z)=120×62 mm $$^2$$2 ), with sufficient accuracy to determine small amplitude variations ( $$\eta \approx 0.2$$η≈0.2 mm). The temporal resolution ( $${\varDelta }t = 19$$Δt=19 ms) is only limited by the available scanning equipment ( $$f = 1$$f=1 kHz rate). For other applications, this domain can be scaled as needed. Graphic abstract