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A new type of vortical structures under breaking waves

As described in the previous sections, depending on the type of breaker, different types of structures are observed under the breaking waves.

Thanks to the initial condition of an unstable sine wave already used previously (Lubin et al., 2006), the generation of a filament vortex could be observed. It can be clearly deduced from Table 3 that the vortex filaments are found only beneath plunging breaking waves.

We have observed that the generation of vortex filaments is an extremely rapid process (Lubin and Glockner, 2013; Lubin and Glockner, 2015). When the water jet collides with the front of the wave, we witness the tumultuous impact of a body of water. At the moment of the impact of the jet, a line of craters is created upstream of the point of impact, from where the splash-up develops. Craters do not penetrate deeply, but are deformed under pressure increasing between the mass of water of the impacting jet and the front face of the wave. The impacting jet splits into two parts, as we have already described (Lubin et al., 2006), creating a line of discontinuity. The craters are then stretched along this line, and rotate.

The rotating structures are then clearly identified as soon as the jet enters the front face of the wave. Vortex filaments are located at the exact boundary between the impacting jet water and the water of the front face of the wave, along the discontinuity line. The structures at the beginning of the surf are disorganized, while during the development phase of the splash-up a more regular organization can be observed with coherent structures.

To identify and visualize the vortex filaments, we use the criterion Q (which is the second invariant of the gradient tensor) which will enable us to analyze the evolution of structures in space over time (Jeong and Hussain, 1995). It can be seen that aerobic vortex structures coincide with the coherent structures identified by the Q criterion. We can see that the vortices are regularly spaced and seem regularly organized. These fine structures look like

Table 3: Vortex filaments observed as a function of the breaker type. WP: weak plunging; PL: plunging breaker.

d/L

H/L

Breaker type

Vortex occurrence

0.10

0.08

PL

Yes

0.10

PL

Yes

0.12

PL

Yes

0.13

0.09

PL

Yes

0.11

PL

Yes

0.13

PL

Yes

0.17

0.10

WP

No

0.12

PL

Yes

0.14

PL

Yes

0.20

0.11

WP

No

0.13

PL

Yes

0.15

PL

Yes

ribs, connecting the splash-up and the air tube formed during the overturning motion of the wave. The air entrainment coincides with the structures identified by the Q criterion, while it seems sucked into the vortex core. Figure 2 shows the spiral movement of the water, confirming the presence of these vortex filaments under the breaking waves. It can also be observed that the spiraling structures are areas of low pressure. Once the vortex is formed, the air is entrained and the pressure at the heart of the vortices is weaker than that of the surrounding water. The spiral motion of the filament shell is illustrated in Figure 2, the current lines wrapping around structures. Figure 2 confirms the observation that vortices do not have a preferential direction of rotation.

Discussion and future work

Previous works dedicated to the exact same configuration (Lubin et ah, 2006), where the vortex filaments have never been observed, used a sequential version of the numerical tool. The simulations were then limited in mesh grid resolution in order to have an affordable computation time. However, the computational time usually took more than several weeks. In order to discuss this point, a mesh grid sensitivity investigation was proposed, considering four mesh grid densities (Lubin and Glockner, 2015). This numerical study confirmed that the vortex filaments could not be simulated using a coarse mesh grid density. As it could be expected, much less detail could be seen for the air entrainment, and no vortex filaments were detected. Then, the finest mesh grid density allowed a better description of the aeration inside the vortex filaments. The structures could also be better identified and aeration could be observed to last longer in the core of the filaments, due to a more accurate ffee-surface description. One of the most interesting results was to conclude that the coarse grid was sufficient to describe the largest eddies in the flow and account for the correct decay rate of the total energy of the wave (Lubin and Glockner, 2015).

Callaghan et al., 2016 indicated that estimating individual breaking wave energy dissipation in the field remains a fundamental problem. At the same time, it remains a very challenging issue. Thus, laboratory experiments and numerical simulations are still mandatory to fill the gaps in our knowledge.

To date, there are a very limited number of studies on air entrainment induced by breaking waves. Recent studies on air entrainment induced by breaking waves detailed the

Sketch of the colliding jet with the flow separation

Figure 1: Sketch of the colliding jet with the flow separation: downstream the plunge point, the main tube of air is entrapped, while the splash-up is growing upstream. The arrows represent the opposing flows meeting and separating, creating a line of discontinuity. Taken from (Lubin and Glockner, 2015).

Evolution of the coherent vortical structures underneath the plunging breaking wave at t

Figure 2: Evolution of the coherent vortical structures underneath the plunging breaking wave at t = 0.17 s (left column) and t = 0.24 s (right column), for H/L = 0.13 and d/L = 0.13 (Ll configuration). Taken from (Lubin and Glockner, 2015). The coherent vortex filaments are educed using the Q-criterion (Hunt et ah, 1988). The vortex envelopes are visualised with the positive Q = 1 isosurfaces (in green), (a): the free-surface is identified with the isocontour of the phase function (in blue), showing the air entrainment; (b): pressure isocontour (p = 0.7 N.m~2, with the reference p = 0 located at the free-surface) illustrating the low pressure inside the vortex filaments; (c): streamlines showing spiralling flow around and inside the fine elongated vortex filaments; (d): the colour scale on the isosurfaces of Q = 1 refers to the local value of the spanwise velocity. Regions associated with positive spanwise velocity are in red, negative in blue.

relation between underwater bubbles generation, turbulence production and energy dissipation. Plunging waves tend to carry large amounts of air at greater depths than other types of breaker type. The dynamics of a bubble under unsteady perturbations are affected by the balance between forces acting on the bubble; the residence time of the bubble in the turbulent flow field also needs to be taken into account (Chanson and Lee, 1997; Chanson et ah, 2002). A large number of bubbles are generated and broken in the shear zones, where velocity gradients play a great role in the breakup process. This aspect of the flow remains a technical challenge for both the numerical models and experimental techniques. Our current understanding indicates that some research effort needs to be done to elucidate the physics of the unsteady motion of a breaking roller (Lubin and Chanson, 2017). Practically, there is still a need to evaluate:

  • • a Froude number (Fr) characteristic of wave breaking
  • • the roller height
  • • the roller length
  • • the roller celerity
  • • the mean front slope angle of the roller
  • • the energy dissipation in the roller region
  • • the bubble size distributions.

The Hinze scale is classically admitted to determine the size of the smallest bubbles affected by turbulence (Hinze, 1949; Hinze, 1955; Hinze, 1975). (Ho-.Toon et ah, 2007) and (Bvoungjoon et ah, 2016) studied experimentally the relation between air entrainment, vortical structures and energy dissipation, highlighting the difficulty to perform measurements in highly aerated areas. Using particle image velocimetry (PIV) and bubble image velocimetry (B1V) techniques, they carefully detailed the air entrainment at every stage of splash-ups and vortical structures generation during the breaking event. Void fraction has proved to be an important quantity to consider, as well as bubble size distribution (Callaghan et al., 2016). (Wang et ah, 2016) and (Deike et ah, 2016) numerically investigated 3D breaking waves and subsequent air entrainment. These works proved the great progress made by numerical tools, but also reported the great costs in terms of computational times required by such simulations. They also showed that a major parameter for accurate numerical simulations is the choice of the mesh size, which will determine the size of the smallest resolved structures of the flow. Usually, the experimental findings indicated the targeted length scales which are to be resolved.

Moreover, the bubble cloud physics has been shown to be also affected by other parameters like surfactant, temperature or salinity (Callaghan et ah, 2014; Callaghan et ah, 2017; Anguelova and Huq, 2018), which are out of reach for present Navier-Stokes numerical simulations. Consequently, more detailed numerical simulations and experiments are needed to investigate and understand the details of the flow. The metrology is clearly an issue to get accurate and reliable physical measurements in this rapidly-varied aerated turbulent flow. Moreover, in the breaking process even without wind, the role of air is crucial. Recent numerical studies showed that an important part of breaking dissipation and turbulence generation comes from the air entrainment and the presence of vortices above the free surface (Iafrati et ah, 2013).

It has been discussed that instabilities (Rayleigh-Taylor and Kelvin-Helmholtz) can be possibly observed at different stages of the wave breaking event (Lubin et ah, 2019): plunging jet ejection at the wave crest, plunging jet growth and disintegration in droplets, plunging jet impact and splash-up occurrence. This, in turn, leads to droplets and bubbles generation. Understanding which physical parameters control the instabilities will allow to understand and predict many aspects of wave breaking. Taking surface tension into account in future simulations is thus required to go further into the analysis of plausible instability mechanisms. The challenge is to deduce a physically based model as time advances during a single breaking event. (Deike et ah, 2017) indeed showed that modelling air entrainment induced by a single wave breaker (Deike et ah, 2016) was a necessary step towards an averaged estimation of the amount of air entrained by breaking waves in the open ocean.

The aim of this chapter was to present the first study of these coherent eddy structures. 3D wave breaking processes, including wind and current, are thus still poorly understood, yet essential in a number of open ocean and nearshore processes. Therefore, the understanding of the complete physical processes induced by breaking waves and the subsequent flow structure is still lacking in its finest details. (Zhou et al„ 2017) investigated the interaction between wave-breaking induced turbulent coherent structures and suspended sediment transport, indicating that the understanding of the whole 3D flow structures in the surf zone (including turbulent eddies, aeration, currents and turbulence near the bed) is clearly needed to be able to evaluate the erosion budget for beaches. But studying the characteristics of a propagating breaking roller is still a major challenge (Leug and Chanson, 2019).

 
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