Partitioning the $$\hbox {CO}_2$$ Flux Mediated by Droplets Released from Breaking Waves

Abstract

The $$\hbox {CO}_2$$ flux from spume droplets occurs in two steps. First, the initial droplet–air gas concentration gradient $$\nabla C$$ is immediately removed with no change in the droplet solubility. Then, the solubility changes with droplet temperature T and radius r evolution, but the flux maintains the condition $$\nabla C=0$$ . The gas content of a droplet can be determined by $$\nabla C=0$$ since the parameters T and r are known. Therefore, the net gas influx of a droplet depends on the values of T and r in its return to the sea. In the second step, the droplet temperature T evolves to an equilibrium temperature $$T_{eq}$$ , and the radius r is then reduced by evaporation at constant $$T_{eq}$$ . For the droplet spectrum, a cut-off radius $$r_{cut}$$ is used to separate short-lived ( $$r> r_{cut}$$ , returning to the sea before $$T=T_{eq}$$ ) and long-lived $$r\le r_{cut}$$ conditions. The net influx is split into three contributions: the first ( $$S_{2S}$$ ) is mediated by short-lived mechanisms, and the second and the third by long-lived ( $$S_{2L}$$ ) mechanisms that are further separated into temperature-varying ( $$S_{2L}^T$$ ) and radius-varying ( $$S_{2L}^R$$ ) stages. The results show that, in the cases with large air–sea temperature differences, the first stage $$S_{2S}$$ dominates the net gas input, but its importance decreases as the value of $$r_{cut}$$ increases. The temperature-varying stage $$S_{2L}^T$$ is dominant in cases with both large values of $$r_{cut}$$ and large temperature differences, while the radius-varying stage $$S_{2L}^R$$ increases as either the temperature difference decreases or as the value of $$r_{cut}$$ increases.