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Abstract An experimental investigation of droplet generation by a plunging breaking wave is presented. In this work, simultaneous measurements of the wave crest profile evolution and of droplets ranging in radius down to 50 μm for a mechanically generated plunging breaker during many repeated breaking events in freshwater are performed. We find three distinct time zones of droplet production, first when the jet impacts the free surface upstream of the wave crest, second when the large air bubbles entrapped by the plunging jet impact reach the free surface and burst, and third when smaller bubbles burst upon reaching the free surface later in the breaking process. These subprocesses account for 22%, 44%, and 34%, respectively, of the average of 653 droplets produced per breaking event. The probability distributions of the ranges of large and small droplet radii are well represented by power law functions that intersect at a radius of 418 μm. 

Spray formed by a myriad of secondary droplets generated by the impact of raindrops on a deep-water pool is studied with a laboratory rain facility. Experiments are performed with two rain rates and raindrops fall on the water surface at a nearly constant velocity. The secondary droplets at various heights above the pool's water surface are recorded with a cinematic digital in-line holographic technique that consists of a high-speed camera, a pulsed Nd:YLF laser and associated optics. The experimental results show that in the heat-map scatter plots of radius versus velocity near the water surface of the pool, the droplets are distributed into three regions, corresponding to distinct physical mechanisms of droplet generation. It is found that the diameter distribution of the droplets in the rain field changes with height above the pool's water surfaces. Both numerical simulation and experimental data reveal that the liquid water content, due to the presence of secondary droplets, in the atmospheric surface layer decreases exponentially with increasing height. 

The effects of surfactants on a mechanically generated plunging breaker are studied experimentally in a laboratory wave tank. Waves are generated using a dispersively focused wave packet with a characteristic wavelength of$$\lambda _0 = 1.18$$m. Experiments are performed with two sets of surfactant solutions. In the first set, increasing amounts of the soluble surfactant Triton X-100 are mixed into the tank water, while in the second set filtered tap water is left undisturbed in the tank for wait times ranging from 15 min to 21 h. Increasing Triton X-100 concentrations and longer wait times lead to surfactant-induced changes in the dynamic properties of the free surface in the tank. It is found that low surface concentrations of surfactants can dramatically change the wave breaking process by changing the shape of the jet and breaking up the entrained air cavity at the time of jet impact. Direct numerical simulations (DNS) of plunging breakers with constant surface tension are used to show that there is significant compression of the free surface near the plunging jet tip and dilatation elsewhere. To explore the effect of this compression/dilatation, the surface tension isotherm is measured in all experimental cases. The effects of surfactants on the plunging jet are shown to be primarily controlled by the surface tension gradient ($$\Delta \mathcal {E}$$) while the ambient surface tension of the undisturbed wave tank ($$\sigma _0$$) plays a secondary role. 

An experimental study of the dynamics and droplet production in three mechanically generated plunging breaking waves is presented in this two-part paper. In the present paper (Part 2), in-line cinematic holography is used to measure the positions, diameters ($$d\geq 100\ \mathrm {\mu }{\rm m}$$), times and velocities of droplets generated by the three plunging breaking waves studied in Part 1 (Erininet al.,J. Fluid Mech., vol. 967, 2023, A35) as the droplets move up across a horizontal measurement plane located just above the wave crests. It is found that there are four major mechanisms for droplet production: closure of the indentation between the top surface of the plunging jet and the splash that it creates, the bursting of large bubbles that were entrapped under the plunging jet at impact, splashing and bubble bursting in the turbulent zone on the front face of the wave and the bursting of small bubbles that reach the water surface at the crest of the non-breaking wave following the breaker. The droplet diameter distributions for the entire droplet set for each breaker are fitted with power-law functions in separate small- and large-diameter regions. The droplet diameter where these power-law functions cross increases monotonically from 820 to 1480$$\mathrm {\mu }{\rm m}$$from the weak to the strong breaker, respectively. The droplet diameter and velocity characteristics and the number of the droplets generated by the four mechanisms are found to vary significantly and the processes that create these differences are discussed. 

An experimental study of the dynamics and droplet production in three mechanically generated plunging breaking waves is presented in this two-part paper. In the present paper (Part 1), the dynamics of the three breakers are studied through measurements of the evolution of their free surface profiles during 10 repeated breaking events for each wave. The waves are created from dispersively focused wave packets generated with three wave maker motions that differ primarily by small changes in their overall amplitude. Breaker profiles are measured with a cinematic laser-induced fluorescence technique covering a streamwise region of approximately one breaker wavelength and over a time of 3.4 breaker periods. The aligned profile data is used to create spatio-temporal maps of the ensemble average surface height and the standard deviation of both the local normal distance and the local arc length relative to the instantaneous mean profile. It is found that the mean and standard deviation maps contain strongly correlated localized features and indicate that the transition from laminar to turbulent flow is a highly repeatable process. Regions of high standard deviation include the splash created by the plunging jet impact and subsequent splash impacts at the front of the breaking region as well as the site where the air pocket entrained under the plunging jet at the moment of jet tip impact comes to the surface and pops. In Part 2 (Erininet al., J. Fluid Mech., vol. 967, 2023, A36), these features are used to interpret various features of the distributions of droplet number, diameter and velocity. 

In this article, the terrain classifications of polarimetric synthetic aperture radar (PolSAR) images are studied. A novel semi-supervised method based on improved Tri-training combined with a neighborhood minimum spanning tree (NMST) is proposed. Several strategies are included in the method: 1) a high-dimensional vector of polarimetric features that are obtained from the coherency matrix and diverse target decompositions is constructed; 2) this vector is divided into three subvectors and each subvector consists of one-third of the polarimetric features, randomly selected. The three subvectors are used to separately train the three different base classifiers in the Tri-training algorithm to increase the diversity of classification; and 3) a help-training sample selection with the improved NMST that uses both the coherency matrix and the spatial information is adopted to select highly reliable unlabeled samples to increase the training sets. Thus, the proposed method can effectively take advantage of unlabeled samples to improve the classification. Experimental results show that with a small number of labeled samples, the proposed method achieves a much better performance than existing classification methods.