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 tilt of such platforms due to the waves using data from Lagrangian floats built at the Applied Physics Laboratory (APL/UW) and carrying a Nortek Signature 1000 Current Profiler with an AHRS (Attitude and Heading Reference System). We analyze carefully chosen data segments where the wave-induced tilts are finite but small and the float does not rotate significantly, in a two-dimensional, depth-downwave coordinate system assuming 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 is confirmed by swinging the AHRS on pendulums in the laboratory. The same tests disturbingly indicate that the tilts produced by the AHRS can have large errors for tilts larger than a few degrees. The tilt is predicted to an accuracy of about 10\% from the wave properties by a 3-parameter linear dynamical 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.