The Small-Scale Instability of the Air–Water Interface Responsible for the Bag-Breakup Fragmentation

Abstract

Abstract The “bag breakup” fragmentation is the dominant mechanism for spume droplet production in high winds, which substantially affects the ocean–atmosphere exchange processes. The amount of droplets ejected from the surface, as well as their typical sizes, is prescribed by the surface wind velocity and fetch. The corresponding empirical correlations were obtained only for the limited parameters of the laboratory environment. The applicability range can be extended through the construction of a theoretical model that describes the initiation of the bag-breakup fragmentation, estimates the fragmenting liquid volume prescribing the droplet sizes, and determines the dependence on the wind parameters. This paper presents such a model. First, we conducted linear stability analysis of small-scale disturbances at the water surface under a high wind; this showed that the small-scale ripples (about 1 cm) propagating against the wind in the surface wind drift following the reference frame grew fast due to the Kelvin–Helmholtz instability, when the wind friction velocity exceeded the threshold of about 1 m s−1. Given the weak dispersion, the nonlinear stage of evolution was addressed using the Riemann simple wave equation modified to describe the increasing disturbances. The analytical solution for the equation suggested the scaling of the volume of liquid undergoing the bag-breakup fragmentation and its dependence on in agreement with the laboratory data. Using the scaling, we calculated the statistics of the bag-breakup fragmentation based on the lognormal size distribution of the fragmenting objects. Significance Statement The “bag breakup” fragmentation is the dominant mechanism for generating spray in hurricane winds. The parameters of spray droplets substantially affect the exchange processes between the ocean and the atmosphere and, thereby, the development of sea storms. The rapid process of spray generation can only be studied in laboratory environments using sophisticated experimental techniques. To apply the laboratory data to field conditions, we need a theoretical model that describes the threshold for fragmentation initiation, the fragmenting liquid volume, which scales the size and number of spray droplets, their dependence on wind parameters, etc. In the present work, we suggest a simple analytical model of the bag-breakup initiation, verify it in the laboratory experiment, and suggest the statistical description of the fragmentation events.