The Connection between Bubble Size Spectra and Energy Dissipation Rates in the Upper Ocean

Abstract

Abstract A formula for the maximum size of a bubble for which surface tension forces can prevent bubble breakup by inertial forces, combined with the observed sizes of air bubbles in breaking waves, implies an energy dissipation rate. One dataset from the surf zone gives a dissipation rate of the order of 0.1 W kg−1, but the large number of small bubbles, and the bubble size spectrum generally, are puzzling. A simple dimensional cascade argument suggests that injected air beneath a breaking wave is rapidly broken up by turbulence, producing an initial size spectrum proportional to (radius)−10/3 before modification by dissolution and rising under buoyancy. This spectral slope is comparable with data from the surf zone. The cascade argument does, however, predict that for a constant dissipation rate there is a rapid accumulation of a large number of bubbles at the scale at which surface tension prevents further breakup; it is possible that the observed size spectrum reflects the range of turbulent energy di...