A vorticity-based model for gas transfer under breaking waves : Special topic on : Ocean-atmosphere interactions

TLDR: In this paper, the renewal rate is proportional to the vorticity of the waves at the water surface, and it is shown that the transfer velocity increases with increasing wave height for waves of the same frequency.

Abstract: This paper presents a new renewal model for gas transfer under the influence of breaking waves. It is proposed that the renewal rate is proportional to the vorticity of the waves at the water surface. Constants were evaluated from experimental data obtained in a wave flume at the Laboratory of Harbour Works Athens. Experiments on oxygenation due to breaking waves on a uniformly sloping beach and on a rubble mound breakwater of the S-type were performed. The water was chemically deoxygenated and dissolved oxygen (D.O.) concentration was followed over time in characteristic locations. Experimental data showed that the transfer velocity increased with increasing wave height for waves of the same frequency. Experiments with waves of the same wave height but increasing wave frequency showed also an increase in transfer velocity. The one-dimensional transport equation was used for the determination of the transfer coefficients. Preliminary analysis of the data indicated that the transfer coefficients varied almost linearly with the vertical wave velocity at the water surface. A rather good linear correlation was obtained for the breaking wave data, with a much higher slope as compared to the case of non-breaking waves. Further, an additional positive influence of the wave steepness on the dimensionless transfer coefficient was shown. However, in both of these correlations there was a distinct difference between sets with different wave frequencies. For the vorticity-based model presented in the paper no such difference appears between different sets of data. Two equations, with high correlation coefficients, are obtained, one for the breaking waves on the sloping beach and one for the breaking waves on the breakwater. The breakwater data give lower transfer velocities as compared to the sloping beach data for the same wave characteristics.