Are breaking waves, bores, surges and jumps the same flow?
Summary (4 min read)
1. INTRODUCTION
- Surface wave breaking, occurring in the open ocean or the coastal zone, is a complex and challenging two-phase flow phenomenon which plays an important role in numerous processes, including air–sea transfer of gas, momentum and energy, and in a number of technical applications such as acoustic underwater communications and optical properties of the water column.
- The large volumes of air in bubbles rapidly evolve into a distribution of bubble sizes which interacts with liquid turbulence and organised motions.
- The first part of the article is dedicated to the identification of the knowledge gaps encountered when attempting to simulate numerically the hydrodynamics of breaking waves and a review of the various analogies which have been proposed in the literature.
- An open discussion is proposed to explore the actual practises and propose perspectives based on the most appropriate analogy, namely the tidal bore.
2.2 Current state of practice in numerical modelling and limitations
- Most numerical models only consider macro-scale roller properties.
- Several approaches and parametrisations have thus been proposed to introduce wave breaking in NSW and BT models..
- Instead a composite set of data and practices have been elaborated though time by looking at various analogue flows, and some variations have been proposed in order to fill the gaps.
- Practically, most numerical models need to evaluate: 1. a Froude number.
- This is based upon the analogy with non-breaking undular hydraulic jump and bore (Favre, 1935; Treske, 1994; Chanson and Montes, 1995, Lennon and Hill 2006, Chanson and Koch 2008); 2. the roller height hr, derived from momentum considerations ; 3. the roller length Lr, determined empirically.
2.2 Flow analogies or not?
- A number of analogies were proposed between breaking waves, bores and jumps .
- Wave-plunging jet conditions appear to produce a qualitatively different type of impact, with almost no penetration into the oncoming flow and a pronounced splash that cascades multiple times down the face of the wave.
- The processes that follow the initial contact are only known qualitatively for the majority of the breaking conditions, and thus still require further study in order to acquire improved physical understanding.
3.1 Breaking waves
- Fûhrboter (1970) discussed the correlation between the turbulence generated in the surf zone and the amount of air entrained during the breaking of the waves, as well as the sudden reduction of wave height and energy.
- Thorpe (1982) studied wind-waves breaking and speculated that wind speed, salinity, and temperature were major factors, possibly responsible for existing discrepancies that arised when comparing data from different sources.
- Gemmrich and Farmer (1999) measured void fraction values (e.g. 10-2 at 0.25 m below the free-surface), associated with low penetrating breaking events (spilling breakers), while they speculated that higher values of void fractions found deeper would be associated with more energetic violent events (plunging breakers).
- Otherwise, if the jet is ejected farther towards the lower part of the face of the steepening wave, the wave becomes a plunging breaker.
- The early works of Miller (1976), Basco (1985), Jansen (1986) and Bonmarin (1989) were dedicated to qualitative description of the dynamics of the breaking process, the air entrainment and the evolution of the large-scale geometric properties of bubble plumes.
3.2 Tidal bores
- Undular tidal bores are observed for Froude numbers less than 1.3 to 1.4, and breaking tidal bores with a marked roller are seen for Froude numbers large than 1.4 to 1.6 (Koch and Chanson 2008, Chanson 2010a).
- Velocity measurements in breaking tidal bores were performed using particle image velocimetry and acoustic Doppler velocimetry with most data obtained in the clear-water column below the aerated roller region and for Froude numbers less than 2.5 (Hornung et al.
- Their data showed a substantial number of bubbles with millimetre sizes: i.e., between 1 and 5 mm, with larger bubbles detected at higher vertical elevations in a more intermittent manner.
- That is, the celerity of the roller toe fluctuated rapidly with both time and transverse distance, although in a quasi-two-dimensional manner on average (Leng and Chanson 2015b).
3.3 Hydraulic jumps
- A hydraulic jump is the sudden and rapid transition from a supercritical to subcritical flow, characterised by the development of large-scale turbulence, surface waves and spray, energy dissipation and air entrainment .
- The breaking jump is a turbulent shear flow (Rouse et al.
- Figure 3 presents some typical air-water flow measurements in hydraulic jumps with breaking roller.
- Both equations (1) and (2) are compared with experimental data in Figure 3B, with solid lines and dashed lines respectively.
4. DISCUSSION
- Based on the previous section, the authors propose a discussion on limitations, disagreements and obstacles which have to be overcome to improve the knowledge of the turbulent air-water dynamics encountered in breaking waves and bores.
- The authors focus on the flow aeration and bubble sizes distribution in the water column, water salinity and the definition of the Froude number.
4.1 Flow aeration and bubble sizes
- Very few detailed studies on air entrainment induced by breaking waves exist (section 3.1).
- Some studies were centred on deep-water breaking waves while others focused on depth-limited conditions, some breaking waves were mechanically generated, others were wind-waves.
- In both spilling and plunging waves, the propagation of the roller to the shore line is associated with higher levels of turbulence (Govender et al., 2002).
- Bubbles can be observed to split under several breakup mechanisms, including turbulent induced breakup, shear-driven breakup resonant oscillation and tip-streaming (Clift 1978, Taylor 1934, Chanson 2009).
- The bubble radius distributions showed a preponderance of small bubble sizes relative to the mean: the mode was between 0 and 0.5 mm, although the mean radius was about 1.5 to 2.3 mm (Table 1).
4.2 Water solution: freshwater, saltwater or seawater?
- A number of studies tested the influence of salinity on the air bubble entrainment, although there is no agreement between most published results.
- A majority of such studies tested experimentally saltwater solutions, typically by gradually adding salt to freshwater: i.e., synthetic seawater (Cartmill and Su 1993, Loewen et al.
- An overall conclusion was that large amount of air bubbles were entrained in all solutions, and the majority of bubbles in the aerated flow region had radii on the order of a millimetre .
- It must be stressed however that the rare data were obtained with different geometric scales.
4.3 Froude number and definition
- The definition of the Froude number is of paramount importance, because it is used to detect the breaking event onset and termination during the evolution of the waves in the surf zone.
- An improvement in the quest has been the use of a Relative Trough Froude Number (RTFN, Okamoto and Basco, 2006), based on the analogy with a moving hydraulic jump in a one-dimensional open channel flow.
- The roller length Lr increases monotonically with increasing Froude number, as illustrated in Figure 6A.
5. HOW CAN BETTER FLOW ANALOGIES HELP?
- This study clearly shows that more work needs to be done to elucidate the physics of the unsteady motion of a breaking roller.
- The rapid transition, called the roller, is characterised by spray and splashing with a highly fluctuating free-surface, together with highly-aerated turbulent flow structures within, and a large amount of energy dissipation takes place (Bakhmeteff 1932).
- A breaking bore with a quasi-two-dimensional roller is observed for Froude numbers greater than 1.4 to 1.6 (Koch and Chanson 2008, Leng and Chanson 2015b), although localised form of breaking might appear for Froude numbers above 1.3 to 1.4, including shock waves upstream of and limited breaking at the first wave crest (Treske 1994, Chanson 2010a).
- The roller length and height have been found to be fairly similar between hydraulic jumps and tidal bores (Fig. 6), even comparing laboratory and field studies, thus free of scale effects.
- The definition of the Froude number, as given for tidal bores in Table 2, should then be useful for breaking waves studies.
6. CONCLUSIONS
- The authors analysed and discussed the different analogies proposed in the literature to model the breaking process of the waves in the surf zone.
- Even the most up-to-date and accurate numerical models are still limited by empirical aspects.
- So a better knowledge of the temporal and spatial evolution of the aerated region under breaking waves is crucial.
- Two features are reported to be of great importance in all experimental studies: the bubble size distribution and the bubble cloud void fraction, the latter being highly dependent on the accurate quantification of the number of bubbles.
- A number of issues remain and definitive conclusions cannot be drawn.
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"Are breaking waves, bores, surges a..." refers methods in this paper
...Detailed overviews on methods and models for CFD of multiphase flows can be found in textbooks [61, 72]....
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"Are breaking waves, bores, surges a..." refers background in this paper
...Bubbles can be observed to split under several breakup mechanisms, including turbulent induced breakup, shear-driven breakup resonant oscillation and tip-streaming [35, 57, 169]....
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"Are breaking waves, bores, surges a..." refers methods in this paper
...The bubble size distributions, often improperly estimated based upon Hinze’s [89] model developed in the case of a single droplet under non-coalescing conditions (!)....
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...Some practice, such as the use of the Hinze’s [89] scale, are also believed to be misleading, as the theory was originally developed under assumptions not valid in the case of breaking waves....
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...The bubble size distributions, often improperly estimated based upon Hinze’s [89] model developed in the case of a single droplet under non-coalescing conditions (!)....
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Frequently Asked Questions (9)
Q2. What is the advanced model used to simulate nonlinear wave transformations in coastal areas?
The most advanced models, which are generally used to simulate non-linear wave transformations in coastal areas, are based either on the Nonlinear Shallow Water equations (NSW), the Boussinesq-type equations (BT), or some form of hybrid model.
Q3. What is the importance of the void fraction and interfacial velocity data?
Instantaneous void fraction and interfacial velocity data are critically needed to calibrate and improve numerical models of the two-phase flow generated beneath plunging and spilling breaking waves.
Q4. How did they find the celerity of the bubble cloud?
They identified and tracked successive bubble clouds, detailed the void fractions at each step of the breaking events, and found that, beneath the spilling breaker, the celerity of the bubble cloud compared with the phase speed.
Q5. What is the definition of a surface wave breaking?
Surface wave breaking, occurring in the open ocean or the coastal zone, is a complex and challenging two-phase flow phenomenon which plays an important role in numerous processes, including air–sea transfer of gas, momentum and energy, and in a number of technical applications such as acoustic underwater communications and optical properties of the water column.
Q6. How many void fractions were observed in a wave?
High values of void fractions (up to 100 %) were found next to the free-surface, and void fractions of at least 20% were observed for up to half a wave period after the breaking occurrence.
Q7. What is the advection-diffusion equation for interfacial ?
In the upper free-surface region above, the void fraction increases monotonically with increasing distance from the bed from a local minimum up to unity, following an analytical solution of the advection-diffusion equation for interfacial aeration/de-aeration: x Zz D xV 2 1erf1 2 1=C 50 t 1 (2)where
Q8. What type of breaker was used to measure the void fraction above and below the still water?
The temporal variation of void fraction, above and below the still water level, was analysed using three breaker types (spilling, spilling/plunging and plunging).
Q9. How do you parameterise the effects of the wave breaking?
The wave-breaking effects have to be parameterised by incorporating additional terms in the mass and momentum equations (e.g. Musumeci et al.