Aeration due to breaking waves. Part II: Fluxes

Measurements have recently been obtained of bubble concentrations at a coastal shelf-sea site. A simple model of the generation of persistent bubble clouds by wind waves as they break, and of the subsequent evolution of the clouds, is here developed that harnesses these measurements. Estimates are derived of the frequency of wave breaking, the volume of air entrained on cessation of breaking, and the rate of transfer of carbon dioxide between bubbles and water in the clouds. Bubble clouds are generated at an estimated rate, 50chi(2)(g/lambda(5))(1/2), per unit sea surface area, where x is the dominant wave slope, or ratio of significant wave height H-s to energetically dominant wavelength l, and g is the acceleration due to gravity. Cloud generation contributes a term, 500 x 4, to the active whitecap fraction. Entrainment distributes bubbles over a volume of equivalent hemispherical radius, 2H(s). The large-scale turbulence surviving breaking is insufficient to sustain bubbles - by opposing their buoyancy - to the largest size held stable while rising by surface tension. The bubble size distribution on cessation of breaking is instead predicted to fall off rapidly for bubbles in excess of a radius, a(m) = 7 x 10(-3)(v(2)lambda(3)/g)(1/6), where v is the kinematic viscosity of seawater. At a (10 m) wind speed of 10 m s(-1) at the site, the volume of air entrained per unit area of sea surface - the upward displacement of the surface by bubbles - is estimated to be a factor of 3 times a(m) on cessation of breaking. The transfer of carbon dioxide following breaking within the clouds is insignificant.