Aeration Due to Breaking Waves. Part I: Bubble Populations

Abstract

The population of bubbles produced by breaking waves in (10 m) winds of up to 12 m s?1 is analyzed using calibrated images from a vertical pencil-beam sonar system placed on the seabed near the Dutch coast. The structure in the images is parameterized, and the volumetric bubble backscatter is inverted to yield bubble concentrations. Data were obtained at three acoustic frequencies, with inversion effected by prescribing a bubble spectrum with two free variables, leaving a redundant measurement to test the robustness of the model. Median concentrations may in this way be obtained up to the sea surface. Measurements are multiply regressed on wind and dominant-wave variables. Bubbles penetrate to a depth of about a factor of 6??1 times the significant wave height Hs, where ? is the wave age, or ratio of dominant-wave phase speed to wind speed. The measured mean bubble radius decreases weakly with depth, unless waves are gently sloping, at about 5% m?1. At 0.4 m, the mean radius ranges from 30 to 80 ?m and is typically about two-thirds of the radius contributing most to void fraction. The total, depth-integrated surface area of the bubbles and their upward displacement of the sea surface, or ?void displacement,? increase as wind speed to the powers 7 ± 1 and 8 ± 1, respectively, dependences ascribed to the preferential breaking of short, steep wind waves. It is estimated, on extrapolating trends, that the total bubble surface area on average is equal to that of the sea surface above them, and the mean void displacement is equal to the mean bubble radius, at a wind speed of about 15 m s?1.