Radiated Sound from Oceanic Breaking Waves

This was my PhD research, conducted under co-supervisors Dr. R. Lynn Kirlin and Dr. David M. Farmer at the University of Victoria, BC, Canada.


An acoustic array was deployed in the nearsurface layer in Saanich Inlet, B.C., to image breaking waves using only the naturally occurring acoustical radiation from the breaking region over the band [160 Hz, 2000 Hz]. The 15-element array was configured as a horizontal cross with an 8 m aperture, bottom-moored, and positioned nominally 3 m beneath the surface.

Due to sensor sparseness, the array PSF at any particular frequency was badly contaminated by grating lobes. A novel broadband scheme was devised to combine information at multiple independent frequencies to yield unambiguous images with resolution of about 0.2 m at the sea surface.

The broadband scheme assumed space-time separability in the source mutual spectral density. This is only considered valid for breaking waves above about 400 Hz. Nonstationarity and time-bandwidth constraints yielded at most six independent frequency bands within the system passband.

A parametric image analysis showed that the images align closely with the wind and can be observed moving downwind with a speed about two-thirds the phase speed of the dominant component of the wind waves.

Absolute power levels were found to be consistent with previously published results. The absolute power levels were parameterized by $S_0 e^{20+\lambda(f)}$ where $S_0$ = 1 $\mu$Pa$^2$/Hz and $\lambda(f)$ is well-described by a simple first order relation $\lambda = b_0 + b_1 \ln f$, where $b_0$ varied depending on the size of the wave but $b_1$ appeared to be a more universal constant estimated at $-4.55 \pm 0.47$.

The source mechanism for frequencies below about 400 Hz was modeled two ways: (1) as a point source (which would follow if an acoustically compact "collective oscillation" region had formed), and (2) as due to off-peak spectral contributions from bubbles resonant at 400 Hz. Neither model achieved a satisfactory fit to the observed data. This seems to imply that the mechanism below about 400 Hz was acoustically extended and radiating as energetically as any resonant bubbles.


  • Broadband Acoustical Superresolution Imaging of Breaking Ocean Waves , University of Victoria, BC, Canada, 1997. Here's the electronic version.
  • Andrew, Farmer and Kirlin, "Broadband Acoustical Imaging of Breaking Ocean Waves", 133rd Meeting of the Acoustical Society of America, State College, PA, June 1997.
  • Andrew, "Radiated Autospectra over [160 Hz, 2000 Hz] of Individual Breaking Ocean Waves", Acoustics Week in Canada 99, Victoria, BC, November 1999 (Also in the Canadian Journal of Acoustics Need the reference!). You can download the MSWord document, or the postscript version of page 1 or page 2. (I couldn't successfully merge the two pages. Sorry.)
  • Andrew and Kirlin, "A Maximum-Likelihood Imager for a Class of Separable Extended Space-Time Objects", IEEE Signal Processing, May 2000. (Or something like that).
  • Andrew, Farmer and Kirlin, "Broadband Acoustical Imaging of Breaking Ocean Waves", submitted to the J. Acoust. Soc. Am.