Experimental particle paths and drift velocity in steep waves at finite water depth

The Lagrangian paths, horizontal Lagrangian drift velocity, $U_{L}$, and the Lagrangian excess period, $T_{L}-T_{0}$, where $T_{L}$ is the Lagrangian period and $T_{0}$ the Eulerian linear period, are obtained by particle tracking velocimetry (PTV) in non-breaking periodic laboratory waves at a finite water depth of $h=0.2~\text{m}$, wave height of $H=0.49h$ and wavenumber of $k=0.785/h$. Both $U_{L}$ and $T_{L}-T_{0}$ are functions of the average vertical position of the paths, $\bar{Y}$, where $-1<\bar{Y}/h<0$. The functional relationships $U_{L}(\bar{Y})$ and $T_{L}-T_{0}=f(\bar{Y})$ are very similar. Comparisons to calculations by the inviscid strongly nonlinear Fenton method and the second-order theory show that the streaming velocities in the boundary layers below the wave surface and above the fluid bottom contribute to a strongly enhanced forward drift velocity and excess period. The experimental drift velocity shear becomes more than twice that obtained by the Fenton method, which again is approximately twice that of the second-order theory close to the surface. There is no mass flux of the periodic experimental waves and no pressure gradient. The results from a total number of 80 000 experimental particle paths in the different phases and vertical positions of the waves show a strong collapse. The particle paths are closed at the two vertical positions where $U_{L}=0$.