<p>The recent experimental study [1], [2] identify &#8216;&#8216;bag breakup&#8217;&#8217; fragmentation as the dominant mechanism by which spume droplets are generated at hurricane wind speeds. These droplets can significantly affect the exchanging processes in the air-ocean boundary layer. In order to estimate spray-mediated heat, momentum and mass fluxes we need not only reliable experimental data, but a theoretical model of this process. The &#8220;bag-breakup&#8221; fragmentation is a strongly non-linear process, and we focus only on its first stage which includes the small-scale elevation of the water surface.</p><p>Our model of the bag&#8217;s initiation is based on a weak nonlinear interaction of a longitudinal surface wave and two oblique waves propagating at equal and opposite angles to the flow as it was done in [3], [4]. All of these waves have the same critical layer where cross velocities of oblique waves become infinite making inviscid analysis invalid. So we took into account viscous effects. As a result, it has been established that for a piecewise continuous velocity profile explosive growth of wave amplitudes is possible at the wind speeds exceeding the critical one.</p><p>The present model let us find the dependency of &#8220;bag&#8217;s&#8221; transverse size on the wind speed and estimate its lifetime.</p><p>&#160;</p><p>&#160;Acknowledgements</p><p>This work was supported by the RSF project 19-17-00209 and the RFBR projects 19-05-00249, 19-35-90053, 18-05-00265.</p><p>References:</p><ol><li>Troitskaya, Y. et al. Bag-breakup fragmentation as the dominant mechanism of sea-spray production in high winds. Sci. Rep. 7, 1614 (2017).</li>
<li>Troitskaya, Y. et al. The &#8220;Bag Breakup&#8221; Spume Droplet Generation Mechanism at High Winds. Part I: Spray Generation Function. J. Phys. Oceanogr., 48, 2167&#8211;2188 (2018).</li>
<li>A. Craik. Non-linear resonant instability in boundary layers// Journal of Fluid Mechanics. 50, 393-413 (1971).</li>
<li>A. Craik. Resonant gravity-wave interactions in a shear flow// Journal of Fluid Mechanics. 34, 531-549 (1968).</li>
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