Calculations of kinematics underneath measured time histories of steep water waves

Abstract

The present paper is concerned with the problem of estimating fluid particle velocities underneath a measured wave profile at a single spatial position. Second-order calculations are compared with measurements of wave particle kinematics underneath both irregular waves (Skjelbreia et al. (1991) [17]) and focused wave groups (Johannessen & Swan (2001) [16]). It is found that second-order theory is capable of describing the kinematics at the free surface very accurately provided that the local underlying regime of free waves can be identified. At the free surface, estimates of the crest velocities are nearly independent of the cut-off frequency even for broad continuous spectra. Since the velocities at the free surface can be calculated accurately, it is found that the simplest and most reliable method to obtain the velocities below the surface is to use the exponentially decaying velocity potential directly also above the still water level. In a continuous spectrum, the solution will necessarily break down for large enough frequencies but since the velocities at the surface are known, this is strictly an interpolation and the frequency cut-off may be controlled. A directional wave field is not defined uniquely from measurements of the surface elevation at one spatial position. Comparisons between measurements of steep directional wave groups and calculations of unidirectional waves based on the measured surface elevation, however, indicate that the unidirectional case may provide very useful predictions also for short crested wave groups.