The unsteady response of a water free surface to a localized pressure source moving at constant speed U in the range 0.95c min U 1.02c min , where c min is the minimum phase speed of linear gravity-capillary waves in deep water, is investigated through experiments and numerical simulations. This unsteady response state, which consists of a V-shaped pattern behind the source and features periodic shedding of pairs of depressions from the tips of the V, was first observed qualitatively by Diorio et al. (Phys. Rev. Let., 103, 214502, 2009) and called state III. In the present investigation, cinematic shadowgraph and refraction-based techniques are utilized to measure the temporal evolution of the free surface deformation pattern downstream of the source as it moves along a towing tank, while numerical simulations of the model equation described by Cho et al. (J. Fluid Mech., 672, 288-306, 2011) are used to extend the experimental results over longer times than are possible in the experiments. From the experiments, it is found that the speed-amplitude characteristics and the shape of the depressions are nearly the same as those of the freely propagating gravity-capillary lumps of inviscid potential theory. The decay rate of the depressions is measured from their height-time characteristics, which are well fitted by an exponential decay law with an order one decay constant. It is found that the shedding period of the depression pairs decreases with increasing source strength and speed. As the source speed approaches c min , this period tends to about 1 s for all source magnitudes. At the low-speed boundary of state III, a new response with unsteady asymmetric shedding of depressions is found. This response is also predicted by the model equation.

The air entrainment due to the turbulence in a free surface boundary layer shear flow created by a horizontally moving vertical surface-piercing wall is studied through experiments and direct numerical simulations.In the experiments, a laboratory-scale device was built that utilizes a surface-piercing stainless steel belt that travels in a loop around two vertical rollers, with one length of the belt between the rollers acting as a horizontally-moving flat wall. The belt is accelerated suddenly from rest until reaching constant speed in order to create a temporally-evolving boundary layer analogous to the spatially-evolving boundary layer that would exist along a surface-piercing towed flat plate. To complement the experiments, Direct Numerical Simulations (DNS) of the two-phase boundary layer problem were carried out with the domain including a streamwise belt section simulated with periodic boundary conditions. Cinematic Laser-Induced Fluorescence (LIF) measurements of water surface profiles in two vertical planes oriented parallel to the belt surface (wall-parallel profiles) are presented and compared to previous measurements of profiles in a vertical plane oriented normal to the belt surface (wall-normal profiles). Additionally, photographic observations of air entrainment and measurements of air bubble size distributions and motions are reported herein. The bubble entrainment mechanisms are studied in detail through the results obtained by the DNS simulations. Free surface features resembling breaking waves and traveling parallel to the belt are observed in the wallparallel LIF movies. These free surface features travel up to 3 times faster than the free surface features moving away from the belt in the wall-normal LIF movies. These breaking events are thought to be one of the mechanisms by which the air is entrained into the underlying flow. The bubble size distribution is found to have a characteristic break in slope, similar to the Hinze scale previously observed in breaking waves (Deane and Stokes, 2002). The number of bubbles, their velocity, and size are re-ported versus depth from the experimental data. These results are qualitatively similar to results obtained by the simulations. Finally, several entrainment mechanisms are found in the simulations and their prevalence in the free surface boundary layer is assessed.

Wave breaking plays a critical role in air-sea interaction processes in both the open ocean and the surf zone. The energy transferred from the atmosphere to the ocean through wind-wave generation is ultimately dissipated by wave breaking. Therefore, quantifying the energy dissipation due to wave breaking is directly relevant to wave prediction models used for operational sea-state forecasting and the impact of waves on coastal regions. At high-wind speeds, bubbles generated by large scale breaking waves are the primary mechanism for gas transfer and dominate the energy dissipation due to breaking (Lamarre & Melville, 1991). Bubbles generated by breaking waves also contribute to marine aerosol formation through spray droplets produced when foam bubbles burst at the surface (Erinin et al., 2019; Veron, 2015, and references therein). Foam generated by wave breaking has increased reflectivity of solar radiation that can affect the earth's albedo (Evans et al., 2010; Gordon & Jacobs, 1977) and the enhanced microwave emissivity of foam impacts space-borne radiometer measurements of wind speed. In short, wave breaking is an important mechanism for fluxes of momentum, gas, and heat across the air-water interface and for global ocean remote sensing applications. Here we focus on breaking waves that produce visible foam.

In this experimental study, we investigate the interaction of gravity-capillary solitary waves generated by two surface pressure sources moving side by side at constant speed. The nonlinear response of a water surface to a single source moving at a speed just below the minimum phase speed of linear gravity-capillary waves in deep water (c min ≈ 23 cm s −1 ) consists of periodic generation of pairs of three-dimensional solitary waves (or lumps) in a V-shaped pattern downstream of the source. In the reference frame of the laboratory, these unsteady lumps propagate in a direction oblique to the motion of the source. In the present experiments, the strengths of the two sources are adjusted to produce nearly identical responses and the free surface deformations are visualized using photographybased techniques. The first lumps generated by the two sources move in intersecting directions that make a half angle of approximately 15 • and collide in the center-plane between the sources. A steep depression is formed during the collision, but this depression quickly decreases in amplitude while radiating small-amplitude radial waves. After the collision, a quasi-stable pattern is formed with several rows of localized depressions that are qualitatively similar to lumps but exhibit periodic amplitude oscillations, similar to a breather. The shape of the wave pattern and the period of oscillations depend strongly on the distance between the sources. †

Air entrainment due to turbulence in a free-surface boundary layer shear flow created by a horizontally moving vertical surface-piercing wall is studied through experiments and direct numerical simulations (DNS). In the experiments, the moving wall is created by a laboratory-scale device composed of a surface-piercing stainless steel belt that travels in a loop around two vertical rollers; one length of the belt between the rollers simulates the moving wall. The belt accelerates suddenly from rest until reaching constant speed and creates a temporally evolving boundary layer analogous to the spatially evolving boundary layer that would exist along a surface-piercing towed flat plate. We report cinematic laser-induced fluorescence measurements of water surface profile histories, cinematic observations and measurements of air entrainment events, and air bubble size distributions and motions. To complement the experiments, DNS of the temporally evolving turbulent boundary layer were conducted, considering both the air and water phases. Because of cost considerations, only a portion of the belt was simulated at a lower Reynolds number, keeping the Froude number, however, at the same levels as in the experiments. The results of the experiments and DNS are found to be in qualitative agreement and are used synergistically to explore the physics of the air entrainment process; quantitative agreement is not to be expected given the differences in setup and Reynolds numbers. In the experiments and DNS, the free-surface motion is found to consist of a region near the belt with fast-moving uncorrelated large-amplitude ripples and an outer region of small-amplitude propagating waves. Entrainment events similar to plunging breaking waves are found in the experiments, and these and other entrainment mechanisms are examined in detail in the DNS. The spatial distributions of bubble numbers and velocities are reported along with their diameter distributions.