8th IAHR ISHS 2020 Santiago, Chile, May 12th to 15th 2020 DOI: 10.14264/uql.2020.584

Air-water flow properties in breaking bores and stationary hydraulic jumps with the same Froude number - Analogies and dissimilarities

D. Wüthrich1, R. Shi1 and H. Chanson1

1School of Civil Engineering The University of Queensland

Brisbane, Australia E-mail: d.wuthrich@uq.edu.au

ABSTRACT A breaking bore in a translating system of reference is mathematically comparable with a stationary hydraulic jump, whose dissipative nature is used in hydraulic structures to limit damage during floods. Although visually similar, analogies and dissimilarities between hydraulic jumps and bores have been discussed for decades. Recent developments in the investigation of unsteady flows allowed for a direct comparison between stationary and non-stationary flow motions. In this context, the present study provides a preliminary comparative analysis between a hydraulic jump and a breaking bore with the same Froude, Reynolds and Morton numbers in terms of roller toe characteristics and air-water flow properties. The results showed overall a good agreement between the two phenomena, with some differences associated with the non-stationary nature of breaking bores. The comparison between time-averaged void fractions in the hydraulic jump and instantaneous ensemble-averaged void fractions in breaking bore revealed similar patterns, in agreement with existing albeit limited literature. A quantification of analogies and dissimilarities is relevant to the energy dissipation processes, useful to practical engineers and researchers to optimise the design of hydraulic structures.

Keywords: Hydraulic Jump, Breaking bore, Void fraction, Roller characteristics, Energy dissipation

1. INTRODUCTION

A hydraulic jumps is the result of a discontinuity between supercritical and subcritical flows, associated with high energy dissipation (Bélanger 1841, Bakhmeteff 1932). These flows are used in hydraulic structures to optimise and localise the dissipation of residual kinetic energy. Stationary hydraulic jumps were investigated in the past both experimentally and numerically, providing a solid and comprehensive database of its main features, both in terms of flow characteristics and air-water flow properties. A hydraulic jump in translation is also known as a positive surge, compression wave or bore (Favre 1935, Stoker 1957, Chanson 2011). These unsteady flows may be observed during dam-break waves, rejection/acceptance load surges in hydropower channels and in water supply channels following gate operation (Tricker 1965, Henderson 1966, Montes 1998).

Despite different generation mechanisms, the analogies and dissimilarities between stationary hydraulic jump and bore in translation have been discussed in literature for decades (Rouse 1938, Jaeger 1956, Jones 1964, Montes 1979). In a system of reference in translation with the bore front, the positive surge corresponds to a stationary hydraulic jump (Henderson 1966, Montes 1998, Chanson 2004a). Mathematically similar, but physically different, the main properties of both hydraulic jumps and breaking bores are tightly linked to the inflow Froude number Fr1, defined as a function of the upstream flow conditions relative to the jump toe:

Hydraulic jump (stationary flow) Breaking bore (non-stationary flow) 1

11

Fr Vg d

111

FrV U

g d

(1)

where g is the gravitational constant (g = 9.8 m/s2), U the bore front celerity (positive in the upstream direction), V1 and d1 the upstream velocity and water depths, respectively, as shown in Figure 1. A preliminary comparison between breaking bores with Fr1 = 1.5-2.1 and a hydraulic jumps with Fr1 = 3.8 was developed by Wang et al. (2017), showing a number of similar roller features. In this context, the purpose of the current study is to present a direct comparison between a hydraulic jump and a breaking bore with the same Froude number Fr1 = 2.4, Reynolds number Re = ρꞏV1ꞏd1/μ = 1.86×105 and Morton number in terms of roller characteristics and air-water flow properties.

(a) Non-stationary bore (b) Stationary hydraulic jump

Figure 1. Definition sketch of the main parameters in: (a) non-stationary breaking bore and (b) stationary hydraulic jump, as well as the instrumentation set-up.

2. EXPERIMENTAL SET UP AND SIGNAL PROCESSING

All experimental tests were performed at the University of Queensland, in Brisbane, Australia. Both a hydraulic jump and a breaking bore with a Froude number of Fr1 = 2.4 and a Reynolds number Re = 1.86ꞏ105 were reproduced, using air and water as the two fluids. The hydraulic jump was induced in a horizontal rectangular channel with a length of 3.2 m, a width of 0.5 m and a depth of 0.4 m. Water was initially discharged into an upstream head tank equipped with flow straighteners and a rounded undershoot gate (Ø = 0.3 m), inducing a horizontal and contraction-less impinging flow in the downstream channel. The latter was built with a smooth HDPE bed and glass sidewalls. The position of the roller toe was constrained at xtoe = 1.30 m through an adjustable vertical overflow gate located at the downstream end of the channel. The same experimental facility was used by Wang (2014). Experiments on breaking bores were conducted in a 19 m long, 0.7 m wide and 0.5 m deep tilting channel. The slope of the channel was set to 1.25%, inducing a steady flow with the properties presented in Table 1. The breaking bore was generated through the sudden closure of a Tainter gate located at the downstream end of the channel (Leng and Chanson 2019a,b). The bore propagated upstream with a front celerity U, herein defined positive in the upstream direction. All measurements were conducted at a distance x = 8.5 m from the channel inlet, ensuring that the breaking bore was fully developed. For both the hydraulic jump and the bore, x represents the direction of the flow, while y and z are the transverse and vertical coordinates, respectively (Figure 1). The physical properties of the hydraulic jump and the breaking bore generated in the present study are detailed in Table 1. Flow conditions were chosen to have the same relative inflow conditions (V1,jump = V1,bore + U), thus guaranteeing the same Froude and Reynolds numbers. For both set-ups, the water discharge was controlled by flowmeters guaranteeing a precision of 1-2%. For all tests, Ultra-High Speed video movies were recorded by means of a Phantom (v2011) camera with a maximum acquisition frequency of 22,700 frames per second (fps) in full HD (1280×800 pixels). Side-view movies were recorded using a lens ZeissTM Planar T* 85mm f1.4 located at a distance of 1.5 m from the sidewall. For the top view videos, the camera was equipped with a lens NikkorTM AF 50 mm f1.4 located about 1.3 m above the channel bottom. Both lenses had a negligible level of distortion. Lighting conditions were optimised using an array of Light Emitting Diodes (LEDs). The longitudinal profile of the travelling bore was captured at x = 8.5 m from the channel inlet using an Acoustic Displacement Meter (ADM) type Microsonic™ Mic+25/IU/TC, calibrated in situ and sampled with a frequency of 200 Hz, an accuracy of 1% and a spatial resolution of 0.1 mm. Air-water measurements were recorded with double-tip phase-detection conductivity probes (Ø = 0.25 mm). For the stationary hydraulic jump, one double-tip probe was located at the channel centreline and measurements were taken at (x-xtoe)/d1 = 0.60, 1.19, 2.38, 3.57, 4.76, being sampled with an acquisition frequency of 20 kHz for a duration of 45s (Toombes 2002, Wang 2014). For the unsteady measurements in breaking bores, an array of two conductivity probes located at x = 8.5 m was used, with a reference probe and a measurement probe installed at

y/W = 0.57 and y/W = 0.50, respectively (Figure 1). The reference probe had two tips with Δx = 0 mm and Δy = 1.8 mm, located a constant elevation of zref/d1 = 1.06 (Figure 1). The measurement probe had Δx = 5.1 mm and Δy = 1.8 mm, and was located at elevations (z-zref)/d1 ranging between -0.24 to 1.78 (Figure 1). Note that ADM tests were performed without the conductivity probe to avoid interactions between instruments. Herein, the reference probe was used as a time reference, following the approach of Chanson (2004b, 2005) and Leng and Chanson (2019a).

Table 1. Flow characteristics of hydraulic jumps and breaking bores

d1 [m] d2 [m] W [m] U [m/s] V1 [m/s] Q [m3/s] Re Fr1 Hydraulic Jump 0.084 0.245 0.50 0.000 2.211 0.092 1.86×105 2.4 Breaking bore 0.084 0.245 0.70 0.504 1.707 0.101 1.86×105 2.4 Note: Fr1 = Froude number in Eq.(1); d1 = upstream water depth; d2 = conjugate depth; W = channel width; U = front celerity; v1 = upstream flow velocity; Q = discharge; Re = Reynolds number [Re = ρ(U+V1)d1/μ]

Table 2. Ultra-High-Speed videos recorded for both tidal bore and hydraulic jump.

Position Nb. of videos

Acquisition frequency [fps]

Resolution [pixels]

Frames per video

Lens aperture/ exposure time

Hydraulic Jump

Top View 25 22,000 1280×800 49,654 2.0 / 44 μs Side View 1 22,000 1280×800 40,000 1.4 / 45 μs

Breaking bore

Top View 25 22,000 1280×800 30,757 2.0 / 40 μs Side View 8 22,000 1280×800 5,011 1.4 / 45 μs

2.1. Image processing

An edge detection technique was developed to track the air-water boundaries in both the hydraulic jump and breaking bore. The algorithm included four main steps: (1) the lens distortion was checked from the raw video images; (2) new images were generated by subtracting the Gaussian smoothed image from the raw images, removing the background information and preserving the sharp edges of the images; (3) the spatial gradients of the new images were filtered using the median filtering technique to remove salt-and-pepper noise; (4) the upper and lower boundaries of the air-water flow region were extracted, based upon the increase in image gradients. Figure 2a presents a typical example of the detected air-water boundaries for the side view of the hydraulic jump. For the top view videos (Figure 2b), the procedure was similar but, for step (4), only the upper boundary was detected. The accuracy was directly dependent upon the pixel size (⁓ 0.4-0.6 mm) and an average over 25 consecutive frames was performed to maximise the precision. The same edge detection technique was previously developed by Wüthrich et al. (2020) for breaking bores.

(a) Hydraulic jump (b) Breaking bore

Figure 2. Detected air-water boundaries for (a) side view of the hydraulic jump; (b) top view of a transient bore. Image exposure time: 45 μs (hydraulic jump), 40 μs (breaking bore).

V1

U

W = 0.7 m

2.2. Signal processing in air-water flows

Inside the air-water flow, the needle-shaped sensors were able to simultaneously detect the air or water phase based on the different values of the electrical resistance (Crowe et al. 1998). Signal processing was different for stationary and non-stationary flows. For stationary hydraulic jumps, long duration measurements (45s) were conducted and a single threshold technique was used, set at 50% of the voltage difference between air and water (Chanson 2002, Toombes 2002, Chanson and Carosi 2007). This assigned an instantaneous void fraction value of 1 for air and 0 for water. The time-averaged void fraction C was defined as the average time spent in air relative to the total duration of the signal. For breaking bores, because of the non-stationary nature of the flow, long-duration measurements would be physically meaningless. Thus, a larger number of repetitions and an ensemble analysis was conducted in terms of ensemble-averaged properties (Leng and Chanson 2019a,b). A detailed sensitivity analysis over 2,000 tests showed that a minimum of 100 repetitions was necessary in order to obtain accurate void fraction data (not shown herein). Raw data were post-processed using a linear threshold technique between 10% and 90% of the voltage difference between air and water. This led to an instantaneous void fraction signal ranging between 0 for water and 1 for air. All data were synchronised based upon the bore arrival time at the reference probe, i.e. first air-to-water detection. The instantaneous void fraction data were then ensemble-averaged over all tests. This process led to a void fraction profile in the temporal domain at each elevation. At all vertical elevations the link between spatial and temporal domains was achieved through the bore front celerity U measured at x = 8.5 m :

x U t (2)

3. FLOW PATTERNS

The flow visualisation showed that the air entrainment mechanisms and the air-water flow patterns of a breaking bore with Fr1 > 1.5 had a similar behaviour to those of a hydraulic jump with low Froude numbers (Wang et al. 2017). Herein, for the same Froude number Fr1 = 2.4, both the hydraulic jump and breaking bore presented a discontinuity in free surface, resulting in a sudden increase in flow depth. The roller toe was characterised by a large amount of air-entrainment associated with strong fluctuations of the free-surface (Figure 3). The interactions between the incoming flow and the roller incorporated large air cavities, subsequently broken into smaller bubbles and advected downstream before rising to the free-surface through a buoyancy driven flow. Both the jump and bore showed the presence of predominant Kelvin–Helmholtz instabilities, with the development of a turbulent shear layer. On the upper part of the roller, both surge and jump induced some recirculation, characterised by large vortices, responsible for the free-surface fluctuations with generation of foamy structures. The length of the roller was visually estimated to Lr/d1 ⁓ 8 for the hydraulic jump and to Lr/d1 ⁓ 6 for transient bores, thus suggesting that the bore had a slightly shorter length. For both the jump and bore, the conjugate depths on the downstream side of the roller was in close agreement with the values predicted by the momentum equation for a horizontal, rectangular channel (Bélanger 1841, Henderson 1966, Chanson 2004a).

4. RESULTS

4.1. Roller profile (side view)

The geometrical properties of the air-water flow region in hydraulic jumps and breaking bores may be used to yield entrainment ratios and dimensions of large-scale turbulence structures (Dimotakis 1986; Hoyt and Sellin 1989). Herein, the upper and lower boundaries of air-water flow region in the hydraulic jump were detected using the image processing technique detailed in Section 2.1. The upper boundary defined the free-surface profile, whereas the lower boundary represented the depth of the air-water mixture and the extension of its turbulent structures. Figure 4 presents the ensemble-averaged values of the air-water flow boundaries based upon 40,000 frames for the stationary hydraulic jump and 5,000 frames for the transient bore (Table 2). Overall, results indicated an increase in free-surface elevation with increasing longitudinal distance. For the hydraulic jump, a smooth lower boundary was observed, with a convex behaviour. Data were compared with a breaking bore with the same Froude number, in which the ensemble-averaged upper and lower boundaries were obtained using the same edge detection technique. Overall, the comparison showed a good agreement in terms of magnitude and longitudinal trends. The lower boundary in breaking bore exhibited a relatively larger scatter, because of the smaller number of images used in the ensemble-averaging process (Table 2). The free-surface profile measured

using acoustic displacement meters (ADMs) in the breaking bore is presented in Figure 4 for completeness, showing a reasonable agreement with the edge-detection method and the free-surface data in the hydraulic jump.

(a) breaking bore (b) hydraulic jump

Figure 3. Flow patterns of: (a) breaking bore and (b) hydraulic jump for Fr1 = 2.4 and Re = 1.86ꞏ105. Image exposure time: 45 μs.

Figure 4. Ensemble-averaged upper and lower boundaries of the air-water region in a hydraulic jump and a tidal bore with Fr1 = 2.4. Data obtained using the image processing technique is compared with ADM measurements.

Note: HJ = Hydraulic Jump and TB = Tidal Bore.

Figure 5. Fluctuations of the upper and lower boundaries of the air-water region in a hydraulic jump and a

breaking bore with Fr1 = 2.4. Note: HJ = Hydraulic Jump and TB = Tidal Bore.

(x-xtoe)/d1

z/d1

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.00.0

0.5

1.0

1.5

2.0

2.5

3.0

HJ upper boundaryHJ lower boundaryTB upper boundaryTB lower boundaryTB ADM

(x-xtoe)/d1

(d75

-d25

)/d1

0 1 2 3 4 5 60.0

0.2

0.4

0.6

0.8

1.0HJ upper boundaryHJ lower boundaryTB upper boundaryTB lower boundary

U

V1 V1

The fluctuations of both upper and lower boundaries were defined as the difference between the third and first quartile of the dataset (d75-d25). Streamwise behaviours of the fluctuations are presented in Figure 5, showing a constantly increasing behaviour in the upper boundary for both the hydraulic jump and the bore. For the lower boundary, the fluctuations in the hydraulic jump seemed to approach a constant value, whereas for bores a higher fluctuating behaviour was observed, due to the lower availability of video data. Nevertheless, the overall results (Figures 4 and 5) revealed similar air-water boundary characteristics for both stationary and non-stationary rollers, confirming a similar physical process between the hydraulic jump and breaking bore, for these flow conditions.

4.2. Roller perimeter properties (top view)

The edge detection algorithm was used to compute the instantaneous (transverse) roller toe perimeter X(x,y,t) for both breaking bore and hydraulic jump. For both, the roller toe perimeter had a shape that rapidly evolved in space and time, with wavelike shapes in the transverse direction (Leng and Chanson 2015). An example of detected roller perimeter of breaking bore is shown in Figure 2b. The shape of the roller toe suggested the presence of transverse wave patterns with dimensionless wave length lw/W between 2/3 and 2 (Zhang et al. 2013), while the ensemble-median values revealed a transverse straight line (Zhang et al. 2013, Wang and Murzyn 2017). Herein, the instantaneous median position of the roller toe perimeter, computed across the whole channel width, Xm(x,t) was plotted as a function of time in Figure 6, where the vertical axis represents the streamwise direction positive downstream. One may notice the different nature between the bore, characterised by a translating behaviour, and the jump, with a roller toe position localised in space within x = xtoe ±d1 (Figure 6b). Results for the hydraulic jump also showed that the ensemble- median position of Xm (black line in Figure 6b) had a fairly constant behaviour in time. For the moving bore, the grey areas in Figure 6 represent intervals during which the roller toe perimeter data was incomplete within the measurement window. For the breaking bore, video data presented in Figure 6a compared well with the bore front celerity measured with the ADM sensors (Wüthrich et al. 2020).

(a) Breaking bore (b) Hydraulic jump

Figure 6. Temporal position of the instantaneous transverse median value of the roller toe perimeter Xm for: (a) hydraulic jump and (b) breaking bore. Note that grey areas represent intervals during which the roller toe

perimeter was incomplete within the measurement window.

For both jump and bore, the fluctuations of the roller toe perimeter (X’) relative to its instantaneous transverse median value (Xm) were isolated as X’ = X - Xm (Figure 2b). The Probability Distribution Functions (PDF) for all 25 repetitions are presented in Figure 7. A shape similar to the Gaussian bell function was observed, suggesting a high level of randomness in the process. Results for the hydraulic jump and breaking bore showed a similar behaviour in terms of fluctuations of the roller toe, highlighting some similarity between the two physical processes. This is confirmed quantitatively in terms of the difference between the third and first quartiles (X-Xm)75 - (X-Xm)25 providing an insight into turbulent inner length scales, leading to values of 0.043 m for the bore and 0.045 m for the jump. A further characterisation of the roller toe perimeter is the indentation coefficient IC defined as the ratio of the toe perimeter to the channel width, i.e. W = 0.5 m for the hydraulic jump and W = 0.7 m for the bore. Results are presented in Figure 8, showing higher values of the indentation coefficient associated with the

t(g/d1)0.5

X m /

d 1

0 2 4 6 8 10 120

1

2

3

4

5

6

Test 1-25Ensemble MedianADM

t(g/d1)0.5

X m /

d 1

0 3 6 9 12 15 18 21 24-3

-2

-1

0

1

2

3Test 1-25Ensemble Median

hydraulic jump ( CI = 1.99) in comparison to the breaking bore ( CI = 1.76). The funding suggested a more fragmented roller toe perimeter, hence turbulent behaviour, in stationary hydraulic jumps compared to breaking bores, for identical Froude, Reynolds and Morton numbers.

Figure 7. PDF of the fluctuations of the roller toe perimeter (X’) to its instantaneous transverse median value (Xm) for: (a) breaking bore and (b) hydraulic jump for Fr1 = 2.4. Data include measurements at all transverse

locations.

Figure 8. PDF of indentation coefficient IC of a breaking bore and hydraulic jump for Fr1 = 2.4.

4.3. Void fraction

For stationary flows, long duration measurements allowed to compute the time-averaged void fraction C(x,y,z). This approach provided a detailed characterisation of the temporal behaviour of the air-water properties at each measurement location. For non-stationary bores, the temporal variability required a large number of repetitions, for an estimate of the ensemble-averaged instantaneous void fraction values C(t,y,z). Because of the non-stationary nature of the moving bore, this second approach led to a more detailed spatial characterisation of the instantaneous void fraction along the whole roller length, with the signal being continuously measured in the streamwise direction. Both the time-averaged void fraction C(x,y,z) for the hydraulic jump and the instantaneous ensemble-averaged void fraction C(t,y,z) for the breaking bore characterised the amount of air in the roller, allowing for a comparison between the two flows.

X - Xm [m]

PDF

-0.15 -0.1 -0.05 0 0.05 0.1 0.150.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09BREAKING BORE

X - Xm [m]

PDF

-0.15 -0.1 -0.05 0 0.05 0.1 0.150.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09HYDRAULIC JUMP

Indentation coefficient IC

PDF

1.4 1.6 1.8 2.0 2.2 2.4 2.50.00

0.02

0.04

0.06

0.08

0.10

0.12Breaking boreHydraulic jump

Time-averaged void fractions in stationary hydraulic jumps are a function of the longitudinal distance behind the roller toe (x-xtoe)/d1. Vertical profiles commonly present distributions characterised by a lower shear layer and an upper recirculating region (Resch and Leutheusser 1972, Chanson 1995, Chanson and Brattberg 2000, Murzyn et al. 2005, Wang 2014). For fully developed strong jumps (Fr1 > 3.1), a prominent peak is observed in the lower shear region, whereas for lower Froude numbers (Fr1 = 2.4), such a local peak in void fraction was only observed close to the roller toe, i.e. (x-xtoe)/d1 < 2.3, as shown in Figure 9. In the upper recirculating region, the void fraction monotonically increased until the value of C = 1 was asymptotically reached. For the breaking bore, vertical profiles of the instantaneous ensemble-averaged void fraction were obtained combining multiple repetitions at different elevations. Profiles at selected times after the arrival of the bore are presented in Figure 9 (empty symbols). In Figure 9, the comparison between jump and bore data may be based upon Equation (2). Detailed results showed that, in the first part Immediately behind the roller toe, instantaneous void fractions presented some exponential profiles for Uꞏt/d1 < 0.9 (Figure 9, upper left quadrant). This behaviour is consistent with results previous presented by Chanson (2004b) in dam break waves over a stepped invert and by Leng and Chanson (2019b) in a breaking bore. Further downstream, similarly to the hydraulic jump, typical S-shaped profiles were recognised, with void fraction values reaching C = 1 in the upper region. The comparison between time-averaged profiles for the hydraulic jumps and instantaneous ensemble-averaged void fractions for the breaking bores showed a relatively good agreement (Figure 9). The synchronisation between the jump and bore was achieved through Eq. (2), at selected times tꞏU= x-xtoe. Differences were observed in the recirculating region, possibly suggesting a slightly different process associated with the non-stationary nature of breaking bores. Furthermore, breaking bores did not exhibit a local peak in void fraction, typically observed in the shear layer of hydraulic jumps (Gualtieri and Chanson 2007, Wang 2014). More, breaking bores had lower values of Z90 as compared to the hydraulic jump, where Z90 is the flow depth at which C = 90%. This is in agreement with results derived from image processing, previously presented in Figure 4. Nevertheless, the authors acknowledge a difference in spatial resolution in the vertical direction between the hydraulic jump and the bore, which might explain some differences between the two phenomena.

Figure 9. Comparison between void fraction profiles of hydraulic jump and braking bore with the same Froude

number Fr1 = 2.4.

(x-xtoe)/d1 + C , Ut/d1 + C

z/d1

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.00.5

1.0

1.5

2.0

2.5

3.0

0.5

1

1.5

2

2.5

3

Hydraulic Jump - (x-xtoe)/d1 = 0.60Hydraulic Jump - (x-xtoe)/d1 = 1.19Hydraulic Jump - (x-xtoe)/d1 = 2.38Hydraulic Jump - (x-xtoe)/d1 = 3.57Hydraulic Jump - (x-xtoe)/d1 = 4.76Hydraulic Jump - z = Z90

Bore - Ut/d1 = 0.60Bore - Ut/d1 = 1.19Bore - Ut/d1 = 2.38Bore - Ut/d1 = 3.57Bore - Ut/d1 = 4.76Bore - z = Z90

Ut/d1 + C

z/d1

0.0 0.4 0.8 1.2 1.6 2.00.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2Ut/d1 = 0.006Ut/d1 = 0.090Ut/d1 = 0.150Ut/d1 = 0.290Ut/d1 = 0.630Ut/d1 = 0.900

BORE FRONT

5. CONCLUSION

Hydraulic jumps are commonly used in hydraulic structures to dissipate the residual energy of the flow. Dam-break waves, floods and the sudden operation of hydropower plans can generate breaking bores propagating in rivers and channels. In a reference system in translation with the bore front, a breaking bore is commonly associated to a hydraulic jump. Analogies and dissimilarities have been discussed in literature for years without a clear consensus. In this context, the present study presents the first experimental comparison of a hydraulic jump and a breaking bore with identical Froude and Reynolds numbers (Fr = 2.4, Re = 1.86ꞏ105), as well as identical Morton number. Both hydrodynamic processes presented a discontinuity in the form of a breaking roller, responsible for a large amount of energy dissipation. Visual observations showed that both rollers had similar air entrainment characteristics with the development of a shear layer, intense recirculation and large surface fluctuations. Image processing with ultra-high speed videos from the side view showed close similarities between the two phenomena in terms of free-surface profiles, shear layer boundaries and fluctuations. Top view analyses of the roller toe perimeter revealed some differences in terms of the position of the instantaneous transverse median, associated with the transient nature of the breaking bore. However, both hydraulic jump and bore had fluctuations with a random behaviour, well described by a Gaussian distribution. The roller toe perimeter was more indented for the hydraulic jump, thus suggesting a slightly more turbulent process as compared to the breaking bore. The stationary nature of the hydraulic jump allowed to capture the time-averaged void fraction, whereas the moving bore required a large number of repetitions providing instantaneous ensemble-averaged values of the void fraction. Bores exhibited an exponential profile in the vicinity of the roller toe, subsequently followed by S-shaped profiles, consistent with the literature. The comparison in void fraction between the hydraulic jump and the bore at specific times and locations showed some relatively similar behaviour. However, the bores did not exhibit a local maximum in void fraction in the shear layer region. While further analysis is needed, this preliminary comparison in terms of roller characteristics and air-water flow properties pointed out both similarities and differences between the two flows, favouring the understanding of the inner-energy dissipation process.

6. ACKNOWLEDGMENTS

The authors acknowledge the technical assistance of Jason Van Der Gevel and Stewart Matthews (The University of Queensland). The financial support of the Swiss National Science Foundation (grant P2ELP2_181794) and of the University of Queensland, School of Civil Engineering is acknowledged.

7. REFERENCES

Bakhmeteff, B.A. (1932) Hydraulics of Open Channels, McGraw-Hill, New York, USA.

Bélanger, J. B. (1841). Notes sur l’Hydraulique [Notes on hydraulic engineering], Ecole Royale des Ponts et Chaussées, Paris, 223 (in French).

Chanson, H. (1995). Air Entrainment in Two-dimensional Turbulent Shear Flows with Partially Developed Inflow Conditions. International Journal of Multiphase Flow, 21(6), 1107-1121.

Chanson, H. (2002). Air-Water Flow Measurements with Intrusive, Phase-Detection Probes: Can We Improve Their Interpretation? Journal of Hydraulic Engineering, 128(3), 252-255.

Chanson, H. (2004a). The Hydraulics of Open Channel Flow: An Introduction. Butterworth-Heinemann, Oxford, UK, 630 pages

Chanson, H. (2004b). Unsteady air–water flow measurements in sudden open channel flows. Experiments in Fluids, 37, 899-909.

Chanson, H. (2005). Air-Water and Momentum Exchanges in Unsteady Surging Waters: an Experimental Study. Experimental Thermal and Fluid Science, 30(1), 37-47.

Chanson, H. (2011). Tidal Bores, Aegir, Eagre, Mascaret, Pororoca: Theory and Observations. World Scientific, Singapore, 220 pages

Chanson, H. and Brattberg, T. (2000). Experimental Study of the Air-Water Shear Flow in a Hydraulic Jump. International Journal of Multiphase Flow, 26(4), 583-607.

Chanson, H. and Carosi, G. (2007). Advanced Post-Processing and Correlation Analyses in High-Velocity Air-Water Flows. Environmental Fluid Mechanics, 7(6), 495-508.

Crowe, C., Sommerfield, M. and Tsuji, Y. (1998). Multiphase Flows with Droplets and Particles. CRC Press, Boca Raton, USA, 471 pages.

Dimotakis, P. E. (1986). Two-dimensional shear-layer entrainment. AIAA Journal, 24(11), 1791–1796.

Favre, H. (1935). Etude Théorique et Expérimentale des Ondes de Translation dans les Canaux Découverts. [Theoretical and Experimental Study of Travelling Surges in Open Channels.] Dunod, Paris, France (in French).

Gualtieri C, Chanson H (2007) Experimental analysis of Froude number effect on air entrainment in hydraulic jumps. Environmental Fluid Mechanics, 7(3), 217–238.

Henderson, F.M. (1966). Open Channel Flow. MacMillan Company, New York, USA.

Hoyt, J.W. and Sellin, R.H.J. (1989). Hydraulic Jump as ‘Mixing layer.’ Journal of Hydraulic Engineering, 115(12), 1607-1614.

Jaeger, C. (1956). Engineering Fluid Mechanics. Blackie & Son, Glasgow, UK, 529 pages.

Jones, L.E. (1964). Some observations on the Undular Jump. Journal of the Hydraulics Division-ASCE, 90(HY3), 69-82.

Leng, X., and Chanson, H. (2015). Breaking Bore: Physical Observations of Roller Characteristics. Mechanics Research Communications, Vol. 65, pp. 24-29 (DOI: 10.1016/j.mechrescom.2015.02.008).

Leng, X. and Chanson, H. (2019a). Air-Water Interaction and Characteristics in Breaking Bores. International Journal of Multiphase Flow, 120, 103101.

Leng, X. and Chanson, H. (2019b). Two-phase Flow Measurements of an Unsteady Breaking Bore. Experiments in Fluids, 60(42).

Montes, J. S. (1979). Undular Hydraulic Jump. Journal of the Hydraulics Division-ASCE, 105(9), 1208-1211.

Montes, J.S. (1998). Hydraulics of Open Channel Flow. ASCE Press, New-York, USA, 697 pages.

Murzyn, F., Mouaze, D. and Chaplin, J. R. (2005). Optical fibre probe measurements of bubbly flow in hydraulic jumps. International Journal of Multiphase Flow, 31(1), 141-154.

Resch, F.J. and Leutheusser H.J. (1972). Le Ressaut Hydraulique: mesure de turbulence dans la Région diphasique. [The Hydraulic Jump: turbulence measurements in the two-phase flow region]. La Houille Blanche, 4, 279-293.

Rouse, H. (1938). Fluid Mechanics for Hydraulic Engineers. McGraw-Hill Publ., New York, USA, 422 pages.

Stoker, J.J. (1957). Water Waves. The Mathematical Theory with Applications, Interscience Publ. Inc., New York.

Toombes, L. (2002). Experimental Study of Air-Water Flow Properties on Low-Gradient Stepped Cascades. PhD Thesis, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 272 pages.

Tricker, R.A.R. (1965). Bores, Breakers, Waves and Wakes. American Elsevier Publ. Co., New York, USA.

Wang, H. (2014). Turbulence and Air Entrainment in Hydraulic Jumps. Ph.D. thesis, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 341 pages & Digital appendices.

Wang, H. and Murzyn, F. (2017). Experimental assessment of characteristic turbulent scales in two-phase flow of hydraulic jump: from bottom to free surface. Environmental Fluid Mechanics, 17, 7-25.

Wang, H., Leng, X. and Chanson, H. (2017). Bores and Hydraulic Jumps. Environmental and Geophysical Applications. Engineering and Computational Mechanics, Proceedings of the Institution of Civil Engineers, 170(EM1), 25-42.

Wüthrich, D., Shi, R. and Chanson, H. (2020). Physical Study on the 3-dimension characteristics and free-surface properties of a breaking roller n bores and surges. Experimental Thermal and Fluid Science, 112, 109980.

Zhang, G., Wang, H. and Chanson, H. (2013). Turbulence and Aeration in Hydraulic Jumps: Free-Surface Fluctuation and Integral Turbulent Scale Measurements. Environmental Fluid Mechanics, 13(2), 189-204.