# On the Clouds of Bubbles Formed by Breaking Wind-Waves in Deep Water, and their Role in Air -- Sea Gas Transfer

S. A. Thorpe

## Abstract

Clouds of small bubbles generated by wind waves breaking and producing whitecaps in deep water have been observed below the surface by using an inverted echo sounder. The bubbles are diffused down to several metres below the surface by turbulence against their natural tendency to rise. Measurements have been made at two sites, one in fresh water at Loch Ness and the other in the sea near Oban, northwest Scotland. Sonagraph records show bubble clouds of two distinct types, columnar clouds' which appear in unstable or convective conditions when the air temperature is less than the surface water temperature, and billow clouds' which appear in stable conditions when the air temperature exceeds that of the water. Clouds penetrate deeper as the wind speed increases, and deeper in convective conditions than in stable conditions at the same wind speed. The response to a change in wind speed occurs in a period of only a few minutes. Measurements of the acoustic scattering cross section per unit volume, M$_{v}$, of the bubbles have been made at several depths. The distributions of M$_{v}$ at constant depth are close to logarithmic normal. The time-averaged value of M$_{v}$, $\overline{M}_{v}$, decreases exponentially with depth over scales of 40-85 cm (winds up to 12 m s$^{-1}$),, the scale increasing as the wind increases. Values of $\overline{M}_{v}$ at the same depth and at the same wind speed are greater in the sea than in the fresh-water loch, even at smaller fetches. Estimates have been made of the least mean vertical speed at which bubbles must be advected for them to reach the observed depths. Several centimetres per second are needed, the speeds increasing with wind. Results depend on the conditions at the surfaces of the bubbles, that is whether they are covered by a surface active-film. The presence of oxygen (or gases other than nitrogen) in the gas composing the bubbles appears not to be important in determining their general behaviour. The presence of turbulence in the water also appears unlikely to affect the gas diffusion rates from individual bubbles at wind speeds up to 16 m s$^{-1}$, except perhaps very close to the surface. The vertical variation of $\overline{M}_{v}$, and the trend with increasing wind speed is moderately well predicted by a `cell model' taken to represent turbulent motions in the water. Analytical and numerical models in which the tendency of bubbles to rise is balanced by turbulent diffusion, and the effects of solubility of the gas within the bubbles are accounted for, are in reasonable agreement with the observations. An eddy diffusion coefficient is taken (in neutral conditions) to be equal to that in the atmospheric boundary layer over a rigid surface, linearly proportional to depth and friction velocity. The effects of stable or unstable conditions, and those of varying the saturation level in the water, are briefly examined. Estimates are also made, by using the observed values of $\overline{M}_{v}$ supported by the analytical results, of the gas flux from the bubbles. Most of the flux occurs in the upper 2m of the water column. This flux is compared with existing measurement of the net gas flux across the air-water interface. It is concluded that in Loch Ness the component of the flux via the bubbles is small at wind speeds up to 12 m s$^{-1}$ but that at sea the contribution is significant at wind speeds of 12 m s$^{-1}$ (at least when the water is close to being saturated) and that at higher wind speeds the bubble contribution may dominate in the processes of air-water gas transfer.

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