On the Role of the Explosive Interaction of Three Surface Waves at the Initial Stage of Spray Generation in Strong Winds

Abstract

This work is devoted to a theoretical study of the hydrodynamic instability of the water–air interface. The development of this instability may result in “bag-breakup” fragmentation, which is one of the main sources of droplets in hurricane winds. A hypothesis according to which the initial water surface elevations subjected to fragmentation are formed by the hydrodynamic instability of disturbances of the wind drift current in the water is proposed. The weakly nonlinear stage of instability in the form of a resonant three-wave interaction is considered. It is found that the nonlinear resonant interaction of a triad of wind drift perturbations, one wave of which is directed along the flow and two other waves are directed at an angle to the flow, leads to an explosive increase in amplitudes. As part of the piecewise continuous model of the drift current profile, the characteristic time and spatial scales of disturbances are found and it is shown that their characteristic dependences on the air friction velocity agree with previously obtained experimental data.