Differing Aspects of Free and Bound Waves in Obtaining Orbital Velocities from Surface Wave Records

Abstract

In coastal zones, the accurate calculation of orbital particle velocities from surface wave measurements is quite important for estimating sediment transport, which is essentially controlled by the near-bottom velocity field. The main difficulty in obtaining orbital velocities from surface wave profiles is associated with the simultaneous existence of free and bound waves of the second harmonic with the same frequencies but different wave numbers. In a laboratory experiment, a discrepancy between the orbital velocities measured at different depths and the velocities obtained from synchronous wave records with the widely used transfer function of the linear theory was shown. The main reason for this was the different attenuations of free and bound waves with depth. Modeling with high spatial resolution made it possible to separate the free and bound waves and confirm this finding. It was found that free wave amplitudes decay with depth in exact accordance with the linear theory, while bound wave amplitudes decay much faster than the linear wave and Stokes theories predict. This difference and the unknown law of bound waves’ attenuation can lead to the inference of inaccurate orbital velocities from free surface elevations.

Keywords

• nonlinear waves
• orbital velocity
• damping of wave motion at depth
• free and bound waves
• waves at intermediate depth
• laboratory and numerical experiments