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Are breaking waves, bores, surges and jumps the same flow?

01 Feb 2017-Environmental Fluid Mechanics (Springer Netherlands)-Vol. 17, Iss: 1, pp 47-77
TL;DR: In this paper, a review of the different analogies proposed in the literature and to discuss current practices is presented, and a discussion is developed an aimed at improving the use of possible breaking proxies.
Abstract: The flow structure in the aerated region of the roller generated by breaking waves remains a great challenge to study, with large quantities of entrained air and turbulence interactions making it very difficult to investigate in details. A number of analogies were proposed between breaking waves in deep or shallow water, tidal bores and hydraulic jumps. Many numerical models used to simulate waves in the surf zone do not implicitly simulate the breaking process of the waves, but are required to parameterise the wave-breaking effects, thus relying on experimental data. Analogies are also assumed to quantify the roller dynamics and the energy dissipation. The scope of this paper is to review the different analogies proposed in the literature and to discuss current practices. A thorough survey is offered and a discussion is developed an aimed at improving the use of possible breaking proxies. The most recent data are revisited and scrutinised for the use of most advanced numerical models to educe the surf zone hydrodynamics. In particular, the roller dynamics and geometrical characteristics are discussed. An open discussion is proposed to explore the actual practices and propose perspectives based on the most appropriate analogy, namely the tidal bore.

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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LUBIN, P., and CHANSON, H. (2017). "Are breaking waves, bores, surges and jumps the same flow?" Environmental
Fluid Mechanics, Vol. 17, No. 1, pp. 47-77, (DOI: 10.1007/s10652-016-9475-y) (ISSN 1567-7419 [Print] 1573-1510
[Online]).
1
Are breaking waves, bores, surges and jumps the same flow?
by
Pierre LUBIN (
1
) (
3
) and Hubert CHANSON (
2
)
(
1
) Université de Bordeaux, I2M, CNRS UMR 5295, 16 avenue Pey-Berland, 33607 Pessac, France
(
2
) The University of Queensland, School of Civil Engineering, Brisbane QLD 4072, Australia
(
3
) Corresponding author, Email: p.lubin@i2m.u-bordeaux1.fr
Abstract
The flow structure in the aerated region of the roller generated by breaking waves remains a great challenge to study,
with large quantities of entrained air and turbulence interactions making it very difficult to investigate in details. A
number of analogies were proposed between breaking waves in deep or shallow water, tidal bores and hydraulic jumps.
Many numerical models used to simulate waves in the surf zone do not implicitly simulate the breaking process of the
waves, but are required to parameterise the wave-breaking effects, thus relying on experimental data. Analogies are
also assumed to quantify the roller dynamics and the energy dissipation. The scope of this paper is to review the
different analogies proposed in the literature and to discuss current practices. A thorough survey is offered and a
discussion is developed an aimed at improving the use of possible breaking proxies. The most recent data are revisited
and scrutinised for the use of most advanced numerical models to educe the surf zone hydrodynamics. In particular, the
roller dynamics and geometrical characteristics are discussed. An open discussion is proposed to explore the actual
practices and propose perspectives based on the most appropriate analogy, namely the tidal bore.
Keywords: Breaking waves, Breaking bores, Hydraulic jumps, Air bubble entrainment, Flow singularity, Tidal bores.
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 major visible feature during wave breaking is the large quantities of air entrained in the form of
bubble clouds and whitecaps, generally coined surface foam (Figures 1 and 2). The generation of bubble clouds has
been shown to induce energy dissipation and turbulent mixing, to contribute to heat exchange and enhance gas transfer
(Hwung et al., 1992; Wanninkhof et al., 2009). Bubble clouds have been shown to influence climate and intensification
of tropical cyclones (Véron, 2015), and cause the ocean ambient noise (Prosperetti, 1988). The breakup and evolution
of entrained air into numerous bubbles is a source of acoustic noise, which is important for naval hydrodynamics. The
hydrodynamic performance of ships is influenced by the wake modified by the air entrainment, and the sound generated
by the bubble clouds render the ships subject to detection. In hydraulic engineering, large spillways are often protected
from cavitation damage by controlling aeration (Russell and Sheehan, 1974; Falvey 1990).
Many numerical models (e.g. Boussinesq equations) used to study waves in the surf zone do not implicitly simulate the
breaking process of the waves (Christensen et al., 2002). The wave-breaking effects have to be parameterised by
incorporating additional terms in the mass and momentum equations (e.g. Musumeci et al. 2005; Cienfuegos et al.,
2010; Bjørkavåg and Kalisch, 2011; Tissier et al., 2012, Kazolea et., 2014). The challenge is to take the breaking
process into account to ensure an accurate description of the surf zone, including the wave height decay and the setup
development. The main consideration is to dissipate energy when wave breaking is likely to occur. Svendsen (1984a,
1984b) proposed the roller concept, in the form of a volume of water carried shoreward with the wave. Local roller
thickness and mean front slope of the breaker were used to quantify part of the local momentum deficit. But the vertical
surface roller of the breaking wave is only considered to play an important part in the momentum and energy
conservation. However, the energy flux and dissipation during wave breaking remain difficult to quantify. Most recent
modelling attempts are still struggling with the lack of physical knowledge of the finest details of the breaking
processes, which makes the task of parameterising breaking effects very difficult since no universal scaling laws for
physical variables have been proposed so far. Physical parameters, such as the height and length of the roller, have to
be quantified and criteria have to be defined with critical bounded values to estimate where the waves break and stop
breaking. Thus models still need calibration and further improvements (Brocchini, 2013).
The turbulent flow dynamics in bubble clouds is a very challenging numerical problem. Esmaeeli and Tryggvason
(1996) studied direct numerical simulations of buoyant bubbles in a two-dimensional periodic domain. They simulated
144 and 324 bubbles, showing that the work done by the buoyant bubbles increased the energy of flow structures much
larger than the bubbles. But 3D direct modeling of air bubble entrainment and evolution at the scale of the surf zone is
computationally unaffordable. Another way of tackling dispersed two-phase flows is using a continuum-mechanical

LUBIN, P., and CHANSON, H. (2017). "Are breaking waves, bores, surges and jumps the same flow?" Environmental
Fluid Mechanics, Vol. 17, No. 1, pp. 47-77, (DOI: 10.1007/s10652-016-9475-y) (ISSN 1567-7419 [Print] 1573-1510
[Online]).
2
approach (Drew, 1983). Two-fluid models are used to model the polydisperse two-fluid bubbly flow based on mixture
theory (Carrica et al. 1999; Moraga et al., 2008, Shi et al., 2010; Ma et al. 2011; Derakhti & Kirby, 2014). A first
attempt to use a continuum type model for studying bubbly flow under surface breaking waves was made by Shi et al.
(2010). They proposed a physically-based numerical model for prediction of air bubble population in a surf zone-scale
domain. The air entrainment was formulated by connecting the shear production at air–water interface and the bubble
number density with the bubble size spectra as observed by Deane and Stokes (2002). The model was initially fed with
the entrained bubbles and used to simulate the evolution of the bubble plumes. This approach requires much less spatial
and temporal resolution than needed to capture detailed air entrainment process in DNS simulations. The model results
revealed that bubbles larger than 1 mm provide a major contribution to void fraction, while smaller bubbles contribute
significantly to the cumulative interfacial area of the bubble cloud but do not contribute much to the total volume of air.
Discrepancies between observations and model behaviour were nevertheless reported. Based on the works of Ma et al.
(2011), Derakhti and Kirby (2014) used an Eulerian–Eulerian polydisperse two-fluid model in an LES framework.
Detailed overviews on methods and models for CFD of multiphase flows can be found in textbooks (Drew and
Passman, 1999; Crowe et al. 2011). More information about turbulence modelling in the framework of multiphase
flows is given by Labourasse et al. (2007) and Bombardelli (2012). Smoothed-particle hydrodynamics (SPH) is also a
mesh-free method which can be used to describe accurately the 3D surf zone hydrodynamics, as recently shown by
Farahani and Dalrymple (2014) who investigated some novel coherent turbulent vortical structures under broken
solitary waves. The state-of-the-art is detailed by Gomez-Gesteira et al. (2010) and Violeau and Rogers (2016), who
detailed a number of examples in which SPH simulations have been successfully used in fluid flow research and
hydraulic engineering.
Numerical models still rely on experimental data. Detailed information on the temporal and spatial variations of the
void fraction fields beneath breaking waves is required. 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. Models for air-entrainment are critically dependent upon accurate estimates of the surface area
affected by wave breaking. Controlled laboratory experiments and accurate measurements of void fraction and bubble
size distributions beneath plunging and spilling breakers are still very challenging. When a wave breaks, the tip forms a
liquid jet which impinges on the front face of the wave and creates an air cavity which breaks into bubbles. The
characterisation of the bubble sizes resulting from the cavity collapse has to be measured and the trajectories of these
entrained bubbles are also critical information. The initial stages of the breaking of a wave generated a large amount of
bubbles production and to the distribution at greater depths. The bubble clouds will then form, grow and decay during
the propagation of the turbulent air/water mixing region forming the bore, the temporal variations of all bubble cloud
dimensions reflecting this evolution. The large volumes of air in bubbles rapidly evolve into a distribution of bubble
sizes which interacts with liquid turbulence and organised motions.
The motion of bubbles relative to the liquid causes velocity fluctuations in the water column and increases the energy
of liquid motion at the scales comparable with the bubble diameter (Derakhti and Kirby, 2014). Bubble plume
kinematics and dynamics, and the structure of the turbulent bubbly flow under breaking waves constitute critical
information to be taken into account for an accurate description of the wave breaking process (Melville 1996). While
the former can be studied experimentally, the liquid–bubble interactions, i.e. the effects of dispersed bubbles on
organised and turbulent motions, are still poorly understood.
When looking at a bore, whereas it has been generated by a stationary hydraulic jump, a surface wave breaking on the
ocean or in the surf zone, or a tidal bore propagating upstream a river, the question is: are we looking at the same flow?
Is there only one bore structure, or are there variations depen
ding on the initial conditions leading to its occurrence and
behaviour? To what extent can we compare the bores and use the quantities through similarity? It is the aim of this
contribution to contribute to the transfer of knowledge from detailed measurements realised in hydraulic jumps and
tidal bores, to the wave breaking investigation. 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. The next part reports on the state-of-the-art
of the studies focusing on the void fraction and velocity analysis under breaking waves, tidal bores and hydraulic
jumps. Based on this survey, we attempt to identify and assess the quantities which can be considered for possible
analogies. The most recent data are revisited and scrutinised for the use of most advanced numerical models to educe
the surf zone hydrodynamics, highly influenced by the wave breaking process. An open discussion is proposed to
explore the actual practises and propose perspectives based on the most appropriate analogy, namely the tidal bore.
2. KNOWLDEGE GAPS FOR THE MODELLING OF THE SURF ZONE
HYDRODYNAMICS
2.2 Current state of practice in numerical modelling and limitations
Most numerical models only consider macro-scale roller properties. The roller formation and propagation have been

LUBIN, P., and CHANSON, H. (2017). "Are breaking waves, bores, surges and jumps the same flow?" Environmental
Fluid Mechanics, Vol. 17, No. 1, pp. 47-77, (DOI: 10.1007/s10652-016-9475-y) (ISSN 1567-7419 [Print] 1573-1510
[Online]).
3
shown to be a highly unsteady process, with air entrainment and turbulence generation. The most advanced models,
which are generally used to simulate non-linear wave transformations in coastal areas, are based either on the Non-
linear Shallow Water equations (NSW), the Boussinesq-type equations (BT), or some form of hybrid model. Extensive
developments and break-through progress have been made recently for a large variety of coastal engineering
applications (e.g. Tissier, 2012; Bacigaluppi et al., 2014; Brocchini, 2013; Kazolea, 2014). A key feature, the breaking
process, is however not explicitly simulated and missing in these models. Several approaches and parametrisations have
thus been proposed to introduce wave breaking in NSW and BT models.. Any such approach requires the quantification
of energy dissipation, dynamically activated when wave breaking is likely to occur. Some physically based criteria have
to be able to activate or deactivate these extra terms and simple expressions are generally favoured. Simple quantities
include geometrical aspects of the roller, including heights, lengths and angles, easily extracted from any visual
observations in laboratory and in the field, All these quantities cannot be estimated from a single experiment. 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 Fr characteristic of wave breaking, of when it occurs and stops (with Fr varying with water
depth). Currently, an accepted value for the transition between non breaking and breaking waves has been
identified in Froude number range between 1.3 and 1.6 (Okamoto and Basco, 2006). 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 h
r
, derived from momentum considerations (see Appendix II);
3. the roller length L
r
, determined empirically. A common parameterisation is L
r
= 2.91h
r
(Haller and Catalan,
2009), although the re-analysis of large-scale experiments suggests L
r
/h
r
1 to 8 (Figure 5). In Figure 5,
steady breaker, stationary hydraulic jump and tidal bore data are compared;
4. the mean front slope angle ɸ (Schäffer et al., 1993), typically between to 30° for the termination and
initiation of the breaking event respectively;
5. the roller celerity (or celerity of the breaking wave);
6. the energy dissipation in the roller region;
7. the bubble size distributions, often improperly estimated based upon Hinze's (1955) model developed in the
case of a single droplet under non-coalescecing conditions (!).
To estimate most of these quantities, flow analogies have been considered, but some limitations are clearly identified
and some modifications, based on new experimental data analysis, are proposed in the following sections.
2.2 Flow analogies or not?
A number of analogies were proposed between breaking waves, bores and jumps (Appendix I). Appendix I lists a
number of early seminal references and Figure 1 presents definition sketches. The steady breaker configuration was
proposed as a simplification of the spilling breaker (Banner and Phillips 1974, Banner and Melville 1976). Important
results were obtained (Duncan 1981, Banner and Peregrine 1993, Cointe and Tulin 1994, Lin and Rockwell 1995,
Dabiri and Gharib 1997), but there is still on-going argument about the validity of this analogy (Kiger & Duncan 2012).
Further links were developed between breaking waves and steady flow configurations. These encompassed
comparisons between plunging breakers and plunging jets (Cipriano and Blanchard 1981, Hubbard et al. 1987,
Chanson and Cumming 1994, Oguz et al. 1995, Chanson et al. 2002,2006, Salter et al. 2014), between spilling breakers
and stationary hydraulic jumps (Longuet-Higgins 1973, Peregrine and Svendsen 1978, Madsen 1981, Brocchini et al.
2001a,b), and between spilling breakers and translating hydraulic jumps (also called positive surges or tidal bores)
(Longuet-Higgins 1973, Peregrine and Svendsen 1978, Brocchini and Peregrine 2001b). In parallel, there have been
numerous discussions about the similarities and differences between stationary and translating hydraulic jumps (e.g.
Darcy and Bazin 1865, Stoker 1957, Tricker 1965, Lighthill 1978), although the open channel hydraulic literature
develops the same integral approach for both types (Henderson 1966, Lighthill 1978, Chanson 2004, 2012).
To date, the mechanistic connections between these flows are not well understood and have not always been successful.
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. What is better
characterised however, is the volume of air trapped by the initial contact of the jet with the wave face, which has been
numerically simulated, and its shape has been successfully modelled, at least for a limited set of conditions (e.g. Lubin
and Glockner 2015). However, 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.
Furthermore, wave breaking is a combination of transient processes which evolve within the breaking duration making
adequate physical understanding a challenging proposition. Overall, In studying any turbulent flow it is very helpful if
it can be shown to be similar to other well known flows(Peregrine and Svendsen,1978). Below, a number of seminal
flow configurations are explored and the relevance of flow comparisons is discussed.

LUBIN, P., and CHANSON, H. (2017). "Are breaking waves, bores, surges and jumps the same flow?" Environmental
Fluid Mechanics, Vol. 17, No. 1, pp. 47-77, (DOI: 10.1007/s10652-016-9475-y) (ISSN 1567-7419 [Print] 1573-1510
[Online]).
4
3. VOID FRACTION KINEMATICS
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. He highlighted
the importance to study quantitatively the air entrainment process for a detailed comprehension of the surf zone
physics. Vagle and Farmer (1992) and recently Anguelova and Huq (2012) reviewed the different techniques used to
quantify the void fraction under breaking waves. Both works concluded that combined techniques were the best
approach. Indeed, the higher the concentrations of bubbles within bubble clouds, the more difficult it is to count and
measure individual bubbles.
Some studies have been conducted in field while others have been completed in physical wave tanks. 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. Monahan (1993)
proposed the terms Alpha-plume (high void fraction, short lifespan), Beta-plume, and Gamma-plume (low void
fraction, long lifespan) to describe the evolution of a bubble cloud, from its formation to its disappearance (e. g.
dissolution, degassing and advection). Most field studies confirmed that the Alpha-plumes consist of high void
fractions (10% or more) with large bubble sizes (radii ranging from tens of micrometers to millimeters). At the other
end of the process, the Gamma-plume were observed to be very low void fraction between 10
-5
to 10
-8
and containing
bubbles with radii on the order of O(10-100)m. The lifetime of a whole bubble cloud may be about a hundred of
seconds. The bubble clouds are also generally confined to the first few meters of the water column. For example,
Lamarre & Melville (1992) compared field and laboratory void fraction measurements obtained with an impedance
probe, and showed large void fraction values at shallow locations while lower void fraction values were found deeper.
Deane (1997) used acoustic and optical measurements of individual breaking waves in the surf zone, off La Jolla
Shores beach, California. Total void fractions of 0.3–0.4 were measured, consisting of bubbles with radius greater than
1 mm. Stokes and Dean (1999) observed that the time scale for the generation of clouds of submillimetric bubbles was
on the order of about 90 ms. Dahl & Jessup (1995) found comparable quantities in deep-ocean studies. 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). Interestingly Gemmrich (2010) found
higher turbulence levels within the wave crest region of the breaking waves, suggesting that the bubble fragmentation
process is mainly driven by turbulence. Most studies reported that void fraction changes significantly during the
lifetime of the bubble cloud, from high void fractions in the first seconds of the breaking event to residual void
fractions persisting for long times. Most field studies consisted in wind-waves breaking observations, with only few
events giving data susceptible to be accurately analysed.
A lot of studies investigated the hydrodynamics in the surf zone, especially the general mechanisms involved during the
breaking process (Peregrine, 1983), the generation of turbulence (Battjes, 1988), and sediment transport. When waves
break, the flow suddenly exhibits a violent transition from irrotational to rotational motion over the entire water
column. Two main types of breaker types have been studied: (1) the spilling breakers, where white foam, consisting of
a turbulent air/water mixture, appears at the wave crest and spills down the front face of the propagating wave; and (2)
the plunging breakers, where the front face of the steepening wave overturns and impacts the forward face of the wave.
These two breaker types have been shown to have similar initial motions, but with different length scales (Basco,
1985). When approaching a beach, the waves change form due to the decrease in water depth. The forward face of the
wave steepens and the wave becomes asymmetric. Once the front face becomes almost vertical, a jet of liquid is
projected from the crest of the wave. The tongue of water thrown from the crest develops and free falls down forward
into a characteristic overturning motion, and eventually hits the water at the plunge point. Depending on the position of
the plunge point, different breaker types can be observed. If the plunge point is located very near to the crest of the
wave, the resulting splash is directed down the wave leading to a spilling breaker. 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 plunging jet
encloses an air pocket when it finally hits the wave face at the plunge point. The jet re-enters the water after impact,
forcing up a second jet, called splash-up. 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. The overturning process, subsequent overturning
motion and plunging jet impact were described, resulting in the identification and tracking of breaker vortices
trajectories. Some information about the evolution (size, shape and position) of the bubble plumes were also detailed.
The jet-splash cycles, occurring several times in a single breaker, have been shown to be responsible for the generation
of a sequence of large-scale vortices with a horizontal axis of rotation, some of these eddies have been shown to be co-
rotating vortices and some counter-rotating vortices depending on the splash-up mechanism (Miller, 1976; Bonmarin,

LUBIN, P., and CHANSON, H. (2017). "Are breaking waves, bores, surges and jumps the same flow?" Environmental
Fluid Mechanics, Vol. 17, No. 1, pp. 47-77, (DOI: 10.1007/s10652-016-9475-y) (ISSN 1567-7419 [Print] 1573-1510
[Online]).
5
1989). Nadaoka et al. (1989) detailed the flow field under a turbulent bore propagating towards the shoreline, resulting
from a spilling breaking wave. Large-scale horizontal eddies are present in the bore front, while behind the wave crest
the flow structure changes rapidly into obliquely downward stretched three-dimensional (3D) eddies, so-called
‘obliquely descending eddies’. Lin and Hwung (1992), Govender et al. (2002) and Kimmoun and Branger (2007) also
described the large motions of aerated regions under plunging breaking waves, with splash-ups and vortical structures.
Miller (1976) measured the average bubble concentration in plunging and spilling breakers and indicated a larger
bubble density presence in plunging breakers (about 31% in the late stage compared to 19% for spilling breakers); these
results were in agreement with earlier descriptions from Miller (1972). Lamarre and Melville (1991) concluded that a
large portion of the mechanical energy of the wave was lost in entraining the bubble clouds. 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. They later confirmed that air entrainment was closely related with the
energy dissipation of the breaking wave (Lamarre and Melville, 1994). Several other works provided more
comprehensive laboratory measurements of the void fraction in breaking waves, detailing the vertical and horizontal
distributions of void fraction. Cox and Shin (2003) measured the void fraction in the aerated region at a point using a
capacitance probe, and observed peak ensemble-averaged void fractions in the range of 15–20%. Surprisingly, they
measured higher void fractions under the spilling breakers than under the plunging breakers. The temporal variation of
void fraction, above and below the still water level, was analysed using three breaker types (spilling, spilling/plunging
and plunging). The temporal variation of void fraction above the still water normalized by the wave period and average
void fraction appears to be remarkably self-similar (independently of the breaker type). Hwung et al. (1992) found a
deeper penetration of air bubbles under plunging breaking waves and higher void fractions (18%), compared to the
spilling breaking waves (12%). Similarly Hoque and Aoki (2005), using a conductivity probe, measured maximum
void fractions of 20% and 16% beneath plunging and spilling breakers, respectively. Mori et al. (2007, 2008) obtained
void fractions of 19% beneath spilling breaking waves and 24% beneath plunging breaking waves, using dual-tip
resistivity void probe. Interestingly they also studied scale effects according to Froude similarity and using two
different scaled experiments. Void fractions were affected by the geometric scale, with larger quantities being found in
the larger experiment, while the bubble size spectra proved to be nearly independent. Kimmoun and Branger (2007)
estimated the evolution of void fractions using particle image velocimetry images and velocity measurements. They
reported large void fractions of up to 88% in the first splash-up location, decreasing slowly when the breaking wave
propagates towards the shore, with values between 20 and 30%. Much lower void fractions were found in other studies.
Kalvoda et al. (2003) investigated the geometric and kinematic characteristics of large air bubbles clouds produced by
spilling breaking wind waves. They observed that the lifetime of the bubble cloud was about 1.4 times the wave period,
with bubbles diameters in the range of 1.0–10 mm. They found a void fraction of about 0.4%. Leifer et al. (2006)
reported void fractions between 0.2% and 2.3% beneath breaking wind waves, using a video system to characterise the
bubble clouds. Blenkinsopp and Chaplin (2007) studied plunging, spilling/plunging and spilling breaking waves. They
calculated integral properties of the bubble clouds and splash-ups, such as areas and volumes of air entrained,
trajectories of centroids and energy dissipation, and showed remarkable similarity between plunging and spilling
breakers. Their data indicated that the evolution of the bubble clouds was subjected to scale effect. Rojas and Loewen
(2010) detailed the void fraction evolution in spilling and breaking breakers. They observed that beneath plunging
breaking breakers, the mean void fraction ranged between 1.2 to 37%, while beneath spilling breaking waves, the mean
void fraction ranged between 17 to 29%. They found that “an energetic spilling breaker may entrain approximately the
same volume of air as a steeper, larger-amplitude plunging breaker”. 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. Beneath the plunging breaker, the celerity of the air cavity
was about 70% of the phase speed. This has to be compared to the celerity of the bubble cloud entrained by the
propagating splash-up which has been measured to be about 90% of the phase speed. Blenkinsopp and Chaplin (2007)
and Rojas and Loewen (2010) found that the volume of air entrained by the splash-up, observed during a plunging
breaking event, was greater than the volume of air entrained by the initial plunging jet (about 60% more). More
recently Anguelova and Huq (2012) used an imaging technique to quantify the phase dependent void fraction, and
measured values reaching 80–99% at the wave crest phase and decreasing to 20-30% at the trough phase. Lim et al.
(2015) confirmed these results in the case of a plunging breaker. They showed that the distribution of the turbulent
intensities matched the vorticity and void fraction fields. Nevertheless, some differences could be observed in the
experimental results for the peak values of void fraction, indicating a strong temporal and spatial variability in the
unsteady breaking waves (Lim et al., 2015). The difference in the locations of the measurements and the method used
to generate the breaking could also be responsible for the discrepancies. Some authors indicated that the mean void
fraction could be modelled by a linear function of time followed by an exponential decay. Hoque and Aoki (2005)
found that the void fraction distribution followed the analytical solution of an advection equation. This is not surprising
as there is a general consensus about in void fractions contours in the breaking waves, shapes and general kinematics of
the aerated regions. However, some differences can also be noted. Lamarre and Melville (1991) found that that the
temporal variation of the normalized void fraction in deep water breakers could be fitted by a power law t
-2.3
, while

Citations
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01 Apr 1983
TL;DR: In this article, a theoretical model for wave heights and set-up in a surf zone is developed for wave flux, radiation stress, and energy dissipation, and the transitions immediately after breaking are analyzed and shown to be in accordance with the above mentioned ideas.
Abstract: A theoretical model is developed for wave heights and set-up in a surf zone. In the time averaged equations of energy and momentum the energy flux, radiation stress and energy dissipation are determined by simple approximations which include the surface roller in the breaker. Comparison with measurements shows good agreement. Also the transitions immediately after breaking are analysed and shown to be in accordance with the above mentioned ideas and results.

354 citations

Journal ArticleDOI
TL;DR: In this paper, a scaling law for energy dissipation in the inner surf zone was proposed, which achieves satisfactory results at both the time-averaged and wave-by-wave scales.
Abstract: The spatial and temporal variation of energy dissipation rates in breaking waves controls the mean circulation of the surf zone. As this circulation plays an important role in the morphodynamics of beaches, it is vital to develop better understanding of the energy dissipation processes in breaking and broken waves. In this paper, we present the first direct field measurements of roller geometry extracted from a LiDAR data set of broken waves to obtain new insights into wave energy dissipation in the inner surf zone. We use a roller model to show that most existing roller area formulations in the literature lead to considerable overestimation of the wave energy dissipation, which is found to be close to, but smaller than, the energy dissipation in a hydraulic jump of the same height. The role of the roller density is also investigated, and we propose that it should be incorporated into modified roller area formulations until better knowledge of the roller area and its link with the mean roller density is acquired. Finally, using previously published results from deepwater wave breaking studies, we propose a scaling law for energy dissipation in the inner surf zone, which achieves satisfactory results at both the time‐averaged and wave‐by‐wave scales.

34 citations

Journal ArticleDOI
TL;DR: In this article, the propagation features of the dry-front are investigated using an analytical boundary-layer type model (Whitham/Dressler/Chanson model) constructed matching an (outer) inviscid dynamic wave to an (inner) viscous diffusive wave.
Abstract: Dam-break flood waves are associated with major environmental disasters provoked by the sudden release of water stored in reservoirs. Ritter found in 1892 an analytical solution to the wave structure of an ideal fluid released during an instantaneous dam failure, propagating over initially dry horizontal terrain. This solution, though ideal, hence frictionless, is widely used to test numerical solutions of the Shallow Water Equations (SWE), and as educational tool in courses of fluid mechanics, given that it is a peculiar case of the Riemann problem. However, the real wave structure observed experimentally differs in a major portion of the wave profile, including the positive and negative fronts. Given the importance of an accurate prediction of the dam break wave, the positive and negative wave portions originating from the breaking of a dam with initially dry land on the tailwater reach are revisited in this work. First, the propagation features of the dry-front are investigated using an analytical boundary-layer type model (Whitham/Dressler/Chanson model) constructed matching an (outer) inviscid dynamic wave to an (inner) viscous diffusive wave. The analytical solution is evaluated using an accurate numerical solution of the SWE produced using the MUSCL-Hancock finite-volume method, which is tested independently obtaining the solution based on the discontinuous Galerkin finite-element method. The propagation features of the negative wave are poorly reproduced by the SWE during the initial stages of dam break flows, and, thus, are then investigated using the Serre–Green–Naghdi equations for weakly-dispersive fully non-linear water waves, which are solved using a finite volume-finite difference scheme.

30 citations

Journal ArticleDOI
TL;DR: A review of physical and numerical modelling of air-water flows is developed, providing some fundamentals towards a consistent modelling of such flows to graduate and Ph.D. level students as well as young researchers in environmental sciences and engineering with pre-requisite knowledge in basic fluid mechanics.
Abstract: In free-surface turbulent flows, large amount of air may be entrapped and advected in the water current. The resulting air-water flows are frequently observed in natural water systems, where they are also relevant to water quality, ecological sustainability and integrated assessment within such systems. Herein, a review of physical and numerical modelling of air-water flows is developed, providing some fundamentals towards a consistent modelling of such flows to graduate and Ph.D. level students as well as young researchers in environmental sciences and engineering, with pre-requisite knowledge in basic fluid mechanics. After some theoretical and metrology considerations, the main criteria for the design of physical models and the current literature on the numerical studies are discussed. Two case-studies, the hydraulic jump and the dropshaft, are used to show the application of such criteria and methods. Overall, the paper presents current knowledges/challenges on physical and numerical modelling of self-aerated free-surface flows.

22 citations

Journal ArticleDOI
TL;DR: In this paper, a weakly compressible smoothed particle (WCSPH) model, coupled with a two-equation model for turbulent stresses, has been employed for this scope.
Abstract: The present paper, places emphasis on the vorticity induced by wave breaking, which greatly contributes to sediments pick up and suspension as well as to air–water exchange at the wave interface, thus deserving a thorough study. A weakly-compressible smoothed particle (WCSPH) model, coupled with a two-equation model for turbulent stresses, has been employed for this scope. A careful calibration of the SPH’s numerical parameters has been first performed, based on experiments carried out in a sloped wave channel, specifically using wave elevation and velocity data. Once proved the reliable performance of the model, the characteristics of vorticity induced just prior and post breaking for both the cases of a spilling and a plunging wave have been numerically studied. The main and detailed results indicate that for both the types of breakers there is a cause-effect relation observed between the stream wise flow deceleration and the vorticity generation.

20 citations

References
More filters
Journal Article
01 Jun 1978
TL;DR: In this paper, the authors evaluated the applicability of the standard κ-ϵ equations and other turbulence models with respect to their applicability in swirling, recirculating flows.
Abstract: The standard κ-ϵ equations and other turbulence models are evaluated with respect to their applicability in swirling, recirculating flows. The turbulence models are formulated on the basis of two separate viewpoints. The first perspective assumes that an isotropic eddy viscosity and the modified Boussinesq hypothesis adequately describe the stress distributions, and that the source of predictive error is a consequence of the modeled terms in the κ-ϵ equations. Both stabilizing and destabilizing Richardson number corrections are incorporated to investigate this line of reasoning. A second viewpoint proposes that the eddy viscosity approach is inherently inadequate and that a redistribution of the stress magnitudes is necessary. Investigation of higher-order closure is pursued on the level of an algebraic stress closure. Various turbulence model predictions are compared with experimental data from a variety of isothermal, confined studies. Supportive swirl comparisons are also performed for a laminar flow case, as well as reacting flow cases. Parallel predictions or contributions from other sources are also consulted where appropriate. Predictive accuracy was found to be a partial function of inlet boundary conditions and numerical diffusion. Despite prediction sensitivity to inlet conditions and numerics, the data comparisons delineate the relative advantages and disadvantages of the various modifications. Possible research avenues in the area of computational modeling of strongly swirling, recirculating flows are reviewed and discussed.

5,396 citations

BookDOI
26 Aug 2011
TL;DR: In this article, the authors present a test case for a single-phase flow Turbulence Modulation by Particles (SPM) model using the Brownian Motion model.
Abstract: Introduction Industrial Applications Energy Conversion and Propulsion Fire Suppression and Control Summary Properties of Dispersed Phase Flows Concept of a Continuum Density and Volume Fraction Particle or Droplet Spacing Response Times Stokes Number Dilute versus Dense Flows Phase Coupling Properties of an Equilibrium Mixture Summary Exercises Size Distribution Discrete Size Distributions Continuous Size Distributions Statistical Parameters Frequently Used Size Distributions Summary Exercises Particle-Fluid Interaction Single-Particle Equations Mass Coupling Linearmomentumcoupling Energy Coupling Summary Exercises Particle-Particle Interaction Particle-Particle Interaction Particle-Wall Interaction Summary Exercises Continuous Phase Equations Averaging Procedures Volume Averaging Property Flux Through a Particle Cloud Volume-Averaged Conservation Equations Equation Summary Summary Exercises Turbulence Review of Turbulence in Single-Phase Flow Turbulence Modulation by Particles Review of Modulation Models Basic Test Case for Turbulence Models Volume-Averaged Turbulence Models Application to Experimental Results Summary Exercises Droplet-Particle Cloud Equations Discrete Element Method (DEM) Discrete Parcel Method (DPM) Two-Fluid Model PDF Models Summary Numerical Modeling Complete Numerical Simulation DNS Models LES Models VANS Numerical Models Summary Experimental Methods Sampling Integral Methods Local Measurement Techniques Summary Exercises Appendix A: Single-Particle Equations Appendix B: Volume Averaging Appendix C: Volume-Averaged Equations Appendix D: Turbulence Equations 425 Appendix E: Brownian Motion References Nomenclature Index

2,821 citations


"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]....

    [...]

Book
01 Jan 1966
TL;DR: The importance of basic principles is recognized in this article in two ways : first, by devoting the opening chapters to a fairly leisurely discussion of introductory principles, including a recapitulation of the underlying arguments derived from the parent subject of fluid mechanics; and second, by takingnevery opportunity in the later chapters to refer back to this earlier material in order to clarify particular applications as they arise.
Abstract: PrefaceAlthough this book was originally conceived as a text for use by the civilnengineering student in advanced courses either in his senior year or at graduatenlevel, it is also designed to have some appeal to the practicing engineer.Open channel flow, like any topic of engineering interest, is defined andnclassified partly by its possession of certain characteristic applications andnpartly by the principles that are invoked to deal with them. This particularnsubject is so rich in the variety and interest of its practical problems that anyntextbook on the subject is in danger of becoming a mere catalogue of applicationsnand routine techniques devised for dealing with them. But it has to benremembered that mastery of this subject, as of any other, demands a grasp ofbasic principles no less than a facility in routine operations. The practicing nengineer is reminded of this fact whenever he turns from the familiar numericsnof backwater curves and flood-routing procedures to some unusual transitionnproblem whose solution requires a good grasp of fundamentals.The importance of basic principles is recognized in this text in two ways :nfirst, by devoting the opening chapters to a fairly leisurely discussion of introductorynprinciples, including a recapitulation of the underlying argumentsnderived from the parent subject of fluid mechanics; and second, by takingnevery opportunity in the later chapters to refer back to this earlier materialnin order to clarify particular applications as they arise. It is hoped that thenpracticing engineer, as well as the student, will find this kind of treatmentnhelpful, and a compensation for the fact that not every application is pursuednthrough every possible variant that occurs in practice. Further compensationnwill, it is also hoped, be found in the fairly complete system of references andnin the unusually large number of applied topics dealt with.This insistence on the importance of principles does not imply that theynshould be given a status and significance independent of the applications theynpossess. The engineer invokes principles in order to deal with problems thatnarise in practice, and when dealing with these general principles he stillnremains in touch with the physical events which have prompted the need to generalize. This notion has dictated the structure of many chapters in thisnbook, particularly Chapters 2 and 3. In each of these, a typical basic problemnis discussed first; the theory is then developed to solve this problem, and isnfinally generalized to cover other problems as well. n n n n

2,297 citations

Journal ArticleDOI
TL;DR: The physical and chemical condition of emulsions of two fluids which do not mix has been the subject of many studies, but very little seems to be known about the mechanics of the stirring processes which are used in making them.
Abstract: The physical and chemical condition of emulsions of two fluids which do not mix has been the subject of many studies, but very little seems to be known about the mechanics of the stirring processes which are used in making them. The conditions which govern the breaking up of a jet of one fluid projected into another have been studied by Rayleigh and others, but most of these studies have been concerned with the effect of surface tension or dynamical forces in making a cylindrical thread unstable so that it breaks into drops. The mode of formation of the cylindrical thread has not been discussed. As a rule in experimental work it has been formed by projecting one liquid into the other under pressure through a hole. It seems that studies of this kind which neglect the disruptive effect of the viscous drag of one fluid on the other, though interesting in themselves, tell us very little about the manner in which two liquids can be stirred together to form an emulsion. When one liquid is at rest in another liquid of the same density it assumes the form of a spherical drop. Any movement of the out er fluid (apart from pure rotation or translation) will distort the drop owing to the dynamical and viscous forces which then act on its surface. Surface tension, however, will tend to keep the drop spherical. When the drop is very small, or the liquid very viscous, the stresses due to inertia will be small compared with those due to viscosity.

2,250 citations


"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]....

    [...]

Journal ArticleDOI
J. O. Hinze1
TL;DR: In this paper, Taylor's experiments on the breakup of a drop in simple types of viscous flow, (b) breakup of an air stream, and (c) emulsification in a turbulent flow are studied.
Abstract: The splitting of globules is an important phenomenon during the final stages of disintegration processes. Three basic types of deformation of globules and six types of flow patterns causing them are distinguished. The forces controlling deformation and breakup comprise two dimensionless groups: a Weber group NWe and a viscosity group NVi. Breakup occurs when NWe exceeds a critical value (NWe)crit. Three cases are studied in greater detail: (a) Taylor's experiments on the breakup of a drop in simple types of viscous flow, (b) breakup of a drop in an air stream, (c) emulsification in a turbulent flow. It is shown that (NWe)crit depends on the type of deformation and on the flow pattern around the globule. For case (a) (NWe)crit shows a minimum value ∼ 0.5 at a certain value of (NVi) and seems to increase indefinitely with either decreasing or increasing ratio between the viscosites of the two phases. For case (b) (NWe)crit varies between 13 and ∞, depending on NVi and on the way in which the relative air velocity varies with time, the lowest value refers to the true shock case and Nvi→0. For case (c) (NWe)crit, which determines the maximum drop size in the emulsion, amounts to ∼1, and the corresponding values of NVi appear to be small. A formula is derived for the maximum drop size.

2,196 citations


"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 (!)....

    [...]

  • ...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....

    [...]

  • ...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 (!)....

    [...]

Frequently Asked Questions (9)
Q1. What are the contributions in this paper?

The flow structure in the aerated region of the roller generated by breaking waves remains a great challenge to study, with large quantities of entrained air and turbulence interactions making it very difficult to investigate in details. The scope of this paper is to review the different analogies proposed in the literature and to discuss current practices. In particular, the roller dynamics and geometrical characteristics are discussed. 

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. 

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. 

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. 

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. 

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. 

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 

The temporal variation of void fraction, above and below the still water level, was analysed using three breaker types (spilling, spilling/plunging and plunging). 

The wave-breaking effects have to be parameterised by incorporating additional terms in the mass and momentum equations (e.g. Musumeci et al.