The Motion and Tilts of Subsurface Floats due to Surface Waves

Subsurface and nearly neutrally-buoyant floats can be stable, well-behaved platforms for measuring ocean dynamics in the near-surface wave zone. Here, we measure and model the wave-induced tilt of one such platform. We use data from Lagrangian floats built at the Applied Physics Laboratory (APL/UW) and carrying a Nortek Signature1000 Acoustic Doppler Current Profiler with an AHRS (Attitude and Heading Reference System). We analyze carefully chosen data segments where the wave-induced tilts are measurable yet small and the float does not rotate significantly. We adopt a two-dimensional, depth-downwave coordinate system and assume small tilts and linear surface wave dynamics. By combining the constraints due to geometry, a wave-following float, and wave dynamics, we link measurements of both linear and angular acceleration to measure the tilts to an accuracy of a few tenths of a degree and simultaneously show that the data is consistent with the analysis assumptions. This analysis is further vetted by swinging the AHRS on pendulums in the laboratory. The same tests disturbingly indicate that the AHRS attitude readings can have large errors for tilts larger than a few degrees. The wave-induced tilt of the floats is predicted to an accuracy of about 10\% from the wave properties by a 3-parameter linear semi-empirical model calibrated with field data. The waves force tilt through their horizontal acceleration and through their strain exerting torques on the float. These floats are a somewhat underdamped oscillator (Quality Factor=3, resonance at 3 second period) and will exhibit a decaying oscillation of a few cycles when perturbed.