A physically-informed sea spray generation model for splashing waves

Abstract

Large sea spray drops - of up to 2mm in diameter - constitute one of the most uncertain factors controlling the intensification of hurricanes and severe storms because their generation mechanisms are not understood. Wave splashing produces among the largest spray drops, but observational data regarding these drops is difficult to obtain and hence cannot inform current modelling efforts. In this study, we instead propose a sea spray generation function (SSGF) for ocean wave splashing by assembling a model from first principles. First, we introduce the transverse collision of two cylindrical liquid rims as the basic mechanism for drop production. We characterize the resulting drop production in terms of three competing processes: ligament production and merging, drop generation by end-pinching, and gravity which arrests the mechanism. Second, we formulate a theoretical model which explains the drop size distributions produced by the colliding rims and test it against existing experimental and numerical data. Finally, the model can be developed into a full SSGF by incorporating sea state information with relatively few tuning parameters. The model is flexible and can be extended by including related effects such as finite droplet lifetime and secondary breakup. Altogether, our model suggests that wave splashing can efficiently produce numerous secondary droplets, challenging prior assumptions that it is an inefficient generation mechanism for sea spray.

Figures (3)

• Figure 1: (a): Morphological evolution of a deep-water plunging breaker, with secondary splashing shown in the two frames at the bottom right Mostert2021. The wave travels from top left to bottom right in each frame. (b): Side views of a typical rim splashing process. (c): Experiment from Ref. erinin2023plunging showing the generation of secondary splash drops. (d,e): Sketches showing the configurations of secondary wave splashing and rim collision, adapted from Refs. erinin2023plungingtang2024fragmentation.
• Figure 2: (a): Sketch showing all timescales present in the current rim splashing configuration. (b): The evolution of the fragment size distribution of rim splashing over time. Coloured crosses and circles indicate rim splashing with $Bo = 125$ and 0, respectively. The threshold for grid convergence, $r = 4\Delta_{11}$, has been marked in all subsequent plots presenting fragment size distributions. (c): Splash drop size distributions at $t/\tau_{\rm cap} = 0.227$ for different $We$ (scattered points), in comparison with the prediction of \ref{['for:size-dist-model']} (solid lines).
• Figure 3: (a): Predicted SSGFs without (grey solid line) and with (black solid line) secondary bag breakup for splash drops, with contributions from bag film and rim drops shown for the latter. (b): Comparison of our SSGFs with those reviewed by Veron Veron2015 (coloured dotted lines) and recently proposed by Troitskaya et al.Troitskaya2018 (black dotted lines). Sources for previous SSGF models reviewed by Veron Veron2015 are listed below. Green: Ref. fairall1994effect; dark purple: Ref. andreas1992sea; light purple: Ref. fairall2009investigation; orange: Ref. andreas1998new; yellow and dark brown: Ref. pattison1999production; dark blue: Ref. smith1993marine; light blue: Ref. mueller2009sea.