Measurement of Eulerian vorticity beneath rotating surface waves

Abstract

In this study, we report experimental verification of the existence of an Eulerian contribution to vortices beneath rotating gravity surface waves. We are motivated by recent theoretical predictions regarding the generation of vortices by surface waves. The first prediction indicates that surface waves which produce vortex lattices at the liquid-gas interface can also produce vorticity beneath them and in the liquid bulk. The second prediction is the existence of an Eulerian contribution to the vorticity, owing to the liquid viscosity. First, we establish that we can generate a vortex lattice at the liquid-air interface using rotating waves, resulting from the superposition of two orthogonal phase-shifted standing waves. Using glycerol-water solution as the liquid, we then conduct Particle Image Velocimetry of tracer particles to measure the velocity and vorticity profiles of the flow beneath the interface. We found that vortices are indeed generated beneath these rotating surface waves. To verify the existence of the Eulerian vorticity, we first measure the vorticity at different values of the liquid layer z < 0. After this, we set a reference vorticity value at a specific z closest to the interface that does not intersect with the waves, and get its ratio with respect to the vorticities at other z. We introduce the computation of the normalized density curves of the vorticity ratios, and compare the peak values to the vorticity prefactor ratios obtained using the theoretical predictions. Our results are in close agreement with the theoretical analysis which accounts for this additional contribution. Our experiments shed light on the mechanism of vorticity generation beneath rotating surface waves.