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.