A note on the theoretical comparison of wave staffs and wave rider buoys in steep gravity waves

Abstract The sea surface displacements measured by a wave staff, fixed in horizontal position, and a wave rider buoy, which moves with the water particles, are compared. Second-order theory shows that, to this approximation, the second harmonic in the surface displacement is not measured by the wave rider. Here a simple approximation to maximum amplitude gravity waves is considered; then a freely floating wave rider gives an approximately sinusoidal record at a lower frequency than the wave, while a tethered wave rider gives results depending on the mooring system. The horizontal motion of a tethered buoy still affects the measurements, particularly of the second and higher harmonics.