W. Kendall Melville
University of California, San Diego
Scripps Institution of Oceanography
La Jolla, CA 92093-0213
Tel.:858 534 0478
Fax: 858 534 7132
The aims of the proposed work are to measure the influence of surface wave breaking on imaging across the surface and develop measurements and models of breaking statistics as input to the interpretation and modeling of oceanic radiance measurements.
Image transmission across breaking surfaces will be measured in both the laboratory and the field. Field measurements of breaking and breaking statistics will be used to quantify the degradation and recovery of image fidelity by surface and subsurface processes associated with breaking, including surface turbulence and bubble entrainment. The PI will collaborate with other PIs in the use of breaking measurements and models to interpret measurements and develop models of oceanic radiance.
The transmission of light across the ocean surface, whether downwelling or upwelling, depends strongly on refraction across the air-sea interface. Models of refractive effects depend on the structure of the surface; ideally, the surface displacement and all its spatial and temporal derivatives. However, measuring the surface and its derivatives at all relevant scales is technically not possible at present as the spatial scales range from millimeters to kilometers, and the temporal scales from milliseconds to hours. The task is simplified if the temporal and spatial scales can be related through the dispersion relationship for linear surface waves, , where s is the radian frequency, and is the magnitude of the wavenumber vector; but this only works if the wave slope, (linear waves), whereas more generally. The most important departures from the linear assumption occur in the neighborhood of breaking waves of all scales, from long large gravity waves, to the much smaller, but just as steep, gravity-capillary waves. In the context of ocean optics, the fact that breaking occurs near the crests of the larger waves gives combinations of large surface displacements and large slopes, which can lead to significant departures from the simplest horizontal planar-surface assumption that leads to a simple Snellís cone. Breaking also leads to surface turbulence, which does not have a dispersion relationship, and therefore no explicit deterministic relationship between the length and time
scales of the surface. At the larger scales, breaking also leads to significant air entrainment and the attenuation and scattering of light by bubbles. For all these reasons, a better understanding of the occurrence (statistics) and scales of breaking in the context of light transmission across the ocean surface, will lead to improved forward and inverse models of the oceanic radiance distribution.
For imaging through the surface, one of the primary questions concerns the characterization of the fraction of time during which the turbulence and bubbles due to breaking will make any imaging impractical. This requires a statistical description of the probability of breaking over different length and time scales; the characterization of the time scales between breaking at a point; the distance between breaking events at a particular time; and the time scale for the disturbance (turbulence and bubble clouds) to decay to acceptable levels for imaging.
In a seminal paper, Phillips (1985) introduced,, the average length of breaking fronts traveling with velocities in the range . The first moment of the corresponding scalar distribution, , gives the area per unit area of ocean surface per unit time swept out by breakers traveling in the same speed range. Therefore, gives the area per unit area per unit time swept out by all breakers. If we assume that imaging is impractical during active breaking at a point, this gives a lower estimate of the probability of breaking interfering with imaging during any time interval. Using simple arguments, based on Froude scaling (that the length and time scales are related through the dispersion relationship) it may be shown that the whitecap coverage, the fraction of surface covered by breaking waves, is proportional to the second moment, . Similar arguments applied to the depth to which breaking mixes the surface water (and also the small optically-significant bubbles) result in the volume of fluid mixed down by breaking per unit area per unit time being proportional to the third moment, . Thus measurements of breaking are fundamental to a determination of the effects of breaking on the transmission of light through the ocean surface and the ability to image through the surface.
Jahne B. & Riemer K.S. Two-dimensional wave number spectra of small-scale water surface waves. J. Geophys. Res., 95, C7, 11531-46, 1990.
Melville, W.K. The role of surface wave breaking in air-sea interaction. Annu. Rev. Fluid Mech., 28, 279-321, 1996.
Phillips, O.M. Spectral and statistical properties of the equilibrium range in wind-generated gravity waves. J. Fluid Mech.,156, 505-31, 1985.
Rapp, R.J. & Melville, W.K. Laboratory measurements of deep-water breaking waves. Proc. Roy. Soc. Lond. A331, 735-800, 1990.