MULTIFRACTAL REPRESENTATION OF BREAKING WAVES ON THE OCEAN SURFACE

It is established for the first time that the spatial distribution of breaking waves on the ocean surface is a multifractal process. This re sult is based on an analysis of airborne visible and near-infrared ima gery of the ocean surface under a limited range of wind speed and fetc h. A detailed study of the optical spectra of the images and the cumul ative probability structure of the prevalent background shows that the lower-intensity reflective areas follow a Rayleigh probability distri bution. By contrast, the higher-intensity pixels associated with the s cattered light from foam and breaking waves demonstrate scaling charac teristics in both the optical spectra and the cumulative probability d istributions. It is demonstrated that the degree to which the whitecap s are singularities on a dark background is described by a Lipschitz e xponent alpha, which uniquely tags each breaking wave. This identifica tion process, called ''fractal'' or ''singularity filtering'', leads t o a critical condition alpha(c) = 1 tentatively associated with the cr ossover from active entraining whitecaps to passively dissipating foam . The multifractal representation associated with the degree of singul arity is simply a restatement that the imagery is composed of a contin uum of sets, where each set consists of those breaking waves at a part icular phase in their existence. The fractal spectrum of the image abo ve a threshold is shown to be representable by a fractal generator. Ph ysically, the fractal generator models the energy exchange in a breaki ng wave field as a flux of energy input from the atmosphere to the wav e field cascaded over scales of the order of a kilometer to meters. If the energy flux is further parameterized in terms of the receiving ar ea, an assumption similar to closure techniques used in classical turb ulence models, the empirical results symmetrically span Phillips's bas ic arguments for the energy flux terms controlling a wind-driven sea.