6.3 Velocity flow fields under plunging waves
6.3.2 Mean ensemble-averaged velocity fields
Figure 6.5: Partial phase ensemble average velocity flow fields for phases : Tt= 0.00, 0.05 and 0.10. The results have every alternate row and column of vectors omitted for clarity of the velocity fields. Each vector is an average of at least 60 instantaneous vectors.
Figure 6.6: Partial phase ensemble average velocity flow fields for phases : Tt= 0.15, 0.20 and 0.25. The results have every alternate row and column of vectors omitted for clarity of the velocity fields. Each vector is an average of at least 60 instantaneous vectors.
Figure 6.7: Vertical profiles of phase ensemble-averaged velocity flow fields measured at station 12a as flow progressed.
in Table 4.1. This means that the resolution of the measurements are different at each station. This is why the legends showing 100 cm/s arrow vectors in these plots have different lengths. There is a general decrease in the fluid velocity towards the shore.
Figure 6.8: Vertical profiles of phase ensemble-averaged velocity fields under the crest phases, at different cross-shore positions along the flume at the five measurement stations. The position of the SWL is shown in each plot.
Although the spatially dense velocity vector field measurements afford a whole map of the flow, it is instructive to look at filled contour plots of mean flow which present the whole spatial map of the flow field. Figure 6.9 shows colour contour plots of the mean horizontal velocity component for the six phases
under consideration. DCIV cross correlation analysis was performed by moving the interrogation window is steps of 8 pixels both vertically and horizontally. Therefore the jags/jumps observed on the average free surface and bed slope of these and all other contours that follow represent jumps of 8 pixels which correspond to≈5 mm. As mentioned byKimmoun &Branger [43], owing to PIV interrogation window size resolution, it was not possible to measure velocities exactly at wave crest, and edges, but at half interrogation window size i.e. 1.0 cm below the wave crest and1.0 cm away from the edges. The colour bar represents the magnitude and direction of the velocity vector, with red pointing in the positivex- direction and blue in the negativex-direction, respectively. Thus for the horizontal velocity component, negative values represent seaward flow, while positive indicate onshore flow.
The vector and contour plots show some prominent features. The horizontal velocity profiles feature a relatively broader region of shoreward liquid surface current driven by the shoreward wave propagation and breaking, and a narrower seaward undertow region that serves to ensure volume conservation and hence no change in the time-averaged shore position. Before the crest arrives, water in the flume (at phase 0.00) is moving seaward (to the left). When the crest eventually arrives, there is strong mixing that creates a shear boundary layer between the shore bound crest and the bottom sea- bound undertow (phases 0.05−0.15). Eventually there is flow reversal that culminates in the bulk of the flume water moving shore-ward. From phase 0.15 onwards, it is observed that the flow is completely reversed and all water is flowing towards the shore with peak velocities exceeding 200 cm/s, which gradually decreases with increasing phase or passage of the crest. The fluid with fast longitudinal mean velocity moves between elevation z = -5 cm and the free surface (phases 0.05,0.10 and 0.15) while the fluid with low velocity is confined to below the elevationz= -5 cm. Peak horizontal velocities are observed to dwell on the front face of the crest and decrease in intensity as the crest passes. Experimental and RANS results of the phase-ensemble averaged results byRivillas-Ospina et al. [160], for plunging waves withH = 10 cm andT = 1.5 s and breaking on a 1:5 slope, show peak phase-averaged horizontal velocities of over 150 cm/s. Our results are also in good agreement with the results obtained byPedrozo-Acuna et al.[178] for a similar plunging breaker type. When the fast moving crest fluid meets the trough water moving in the opposite direction, it is observed that the bottom surface of the fast moving crest gets deformed because of friction at the shear boundary layer. The development of the shear layer is evident from the regions of high velocity vectors. This shear layer grows in thickness with distance from the leading edge of the breaking region and significant downstream flow appears at the free surface upstream of the wave crest.
A similar trend was observed byCoakley &Duncan [179]. Figure 6.10 shows contour plots of the mean horizontal velocity component at later phases in the flow, that include the trough part of the wave. This shows decreasing peak shoreward horizontal velocity at selected phases later in the flow, which eventually reverses direction as flow progresses.
Figure 6.11 shows colour contour plots of the mean vertical velocity component of the flow for the phases under study. Contrary to fluid with high horizontal velocity residing near the crest, fluid with high vertical velocity is observed under the crest. These plots also reveal that as the crest comes into view, there is a strong upward flow as seen at Tt = 0.05. This upward flow is caused by the interaction of two opposing motions - the high velocity, shore bound crest fluid and the sea bound trough fluid. This strong
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−10
−5 0 5 10
Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.00
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−10
−5 0 5 10
Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.05
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Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.10
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Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.15
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Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.20
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Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.25
(cm/s)
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Figure 6.9: Contour plots of the evolution of mean horizontal velocity component,huiwith wave phase. The colour bar represents the magnitude and direction of the velocity vector, with red pointing in the positivex-direction, while blue points in the negative x-direction.
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Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.30
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Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.35
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Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.45
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Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.65
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Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.80
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Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.95
(cm/s)
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Figure 6.10: Contour plots of the evolution of mean horizontal velocity component,huiat other selected phases later in the flow : Tt = 0.30, 0.35, 0.45, 0.65, 0.80 and 0.95.
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Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.00
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−10
−5 0 5 10
Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.05
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−10
−5 0 5 10
Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.10
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−10
−5 0 5 10
Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.15
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Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.20
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Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.25
(cm/s)
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Figure 6.11:Contour plots of the evolution of meanvertical velocitycomponent,hwiwith wave phase. The colour bar represents the magnitude and direction of the velocity vector, with red pointing in the positivez-direction, while blue points in the negative z-direction.
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Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.30
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Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.35
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Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.45
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Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.65
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Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.80
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Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.95
(cm/s)
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Figure 6.12: Contour plots of the evolution of mean vertical velocity component,hwiat other selected phases later in the flow.
The phase numbers corresponding to these plots are shown near the top right corner.
upward moving jet causes the wave to rise as the water has nowhere else to go and further break up. This upward moving flow may be responsible for lifting up sediments from the bottom as the crest passes.
As flow progress, it is observed another strong vertical flow whose center is located about 30 cm behind the first, emerging at phase Tt = 0.10 and moving along the direction of the flow, while at the same time diffusing towards the flume bed. The effect of these two strong vertically upward flows creates a saddle point located between two peaks observed at some phases. The two peak upward velocity centers eventually diffuse below the trough and continue to move downstream and finally disappear from the flow. Patches of blue, representing downward fluid motion observed on either side of the strong upward fluid motions are responsible for mixing. Both horizontal and vertical velocity components of the flow are observed to weaken gradually as flow progresses.
Figure 6.12 shows contour plots of the mean vertical velocity component at other later phases as flow pro- gresses. These show that as the flow progresses, fluid pockets with high vertical velocity are slowed down as they homogeneously mix with the return current moving sea-ward. At depths below the wave trough vertical mean velocity decays to zero near the bottom. Peak phase-ensemble averaged vertical velocities of about 40 cm/s are observed. These results are in good agreement with results byRivillas-Ospina et al.[160] who obtained peak, experimental and RANS phase-ensemble averaged vertical velocities of the order∼60 cm/s for waves withH = 10 cm andT = 1.5 s, breaking on a 1:5 slope.
Mean velocity profiles of both horizontal and vertical velocity components along the vertical direction of the shear are presented in Figure 6.13. These profiles were extracted from the center of each contour plot for each phase. i.e. atx= -238 cm. High horizontal velocities are observed at phases 0.10,0.15 and 0.20. Vertical velocities are more or less uniform with minor variation across the depth. Results of the vertical profile ofhuiare similar to those given byCowen et al.[60] for a plunging wave, although theirs were obtained for a weakly plunging breaker with a water depth of only up to about 6.0 cm.
Figure 6.14 shows the phase evolution of the vertical profile of normalized horizontal velocity, hui/c, measured atx= -238 cm for all the six phases. Abovez/h= -0.5 cm, the velocity is observed to decrease with increasing phase. Comparing the magnitudes of the maximum velocities between the normalized uprush and normalized downwash shown in Figure 6.14 it is observed that the normalized downwash is 50 and uprush is up to four times greater.Sou and Yeh [12] gave a similar phase dependent vertical profile of horizontal velocity averaged across the field of view of the camera, but observed that the magnitude of the uprush and downwash velocities are similar (22 cm/s) in the surf zone. The difference could be due to the fact thatSou &Yeh[12] used a water depth of only 4 cm, whereas a water depth of more than 25 cm in the surf zone was used in this study.
Figure 6.15 shows the evolution of vertical profiles of the normalized vertical velocity component,hwi/c, measured at x=-238 cm as flow progresses. Below an elevation of z/h = -0.5 cm, the magnitude of the peak normalized vertical velocity for most of the phases is about 10 while above this elevation it is around 30 near the crest. Abovez/h= -0.5 cm, the velocity is observed to decrease with increasing phase. Figure 6.16 shows a plot of the phase ensemble averaged velocity flow field for the entire wave measured at a fixed point corresponding to middle of each image. This plot was generated by extracting
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Elevation, z, relative to SWL (cm)
Velocity (cm/s) t/T = 0.00
bed position
vertical horizontal
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Elevation, z, relative to SWL (cm)
Velocity (cm/s) t/T = 0.05
bed position vertical horizontal
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Elevation, z, relative to SWL (cm)
Velocity (cm/s) t/T = 0.10
bed position vertical horizontal
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Elevation, z, relative to SWL (cm)
Velocity (cm/s) t/T = 0.15
bed position vertical horizontal
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Elevation, z, relative to SWL (cm)
Velocity (cm/s) t/T = 0.20
bed position vertical horizontal
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Elevation, z, relative to SWL (cm)
Velocity (cm/s) t/T = 0.25
bed position vertical horizontal
Figure 6.13: Variation of phase-ensemble averaged horizontal velocity as a function of depth, measured at the center of the images (atx= -238 cm) for each phase : horizontal component,hui,-(blue) and vertical component,hwi, -(black).
a vertical column of vectors atx= -238 cm from each phase ensemble velocity flow field and stacking them side by side, and then rearranging the phases so that the crest lies in the middle. Phases of interest
t
T = 0.0, 0.05, 0.10, 0.15, 0.20, 0.25 now lie at new phase positions : 0.55, 0.50, 0.45, 0.40, 0.35 and 0.30 respectively. It is only here that new phase labels are used, however, the original phase labels will be used in rest of the discussions coming up in later chapters. A scale vector is provided to give indication of magnitudes of the velocity vectors. The vertical profile of the horizontal velocity can be noted from this figure. The dotted line is an estimated profile for one full wavelength. The front face of the wave is steeper and relatively flat behind the crest. Velocities fields near the bottom decrease due to boundary
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−1
−0.5 0 0.5 1
z/h
<u>/c
bed position phase = 0.00
phase = 0.05 phase = 0.10 phase = 0.15 phase = 0.20 phase = 0.25
Figure 6.14: Evolution of the profile of normalized horizontal velocity,hui/c, as a function of normalized depthz/h, measured at atx=-238 cm as flow progresses. Local water depth,h= 0.12 m andc=p
(gh) = 1.08 m/s.
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−1
−0.5 0 0.5 1
z/h
<w>/c
bed position phase = 0.00
phase = 0.05 phase = 0.10 phase = 0.15 phase = 0.20 phase = 0.25
Figure 6.15: Evolution of the profile of normalized vertical velocity,hwi/c, as a function of normalized depthz/h, measured at x=-238 cm as flow progresses. Local water depth,h= 0.12 m andc=p
(gh) = 1.08 m/s.
layer effects. These velocity field results are consistent with the results obtained byGovender et al.[42]
for plunging waves.
Figure 6.17 shows the phase dependence of phase averaged velocity components with elevation at three elevationsz= -8 cm, -3 cm and +2 cm for both horizontal (a) and vertical (b) components. Both graphs show that at an elevation ofz=+2 cm (near the crest), there is missing data at some phases for both horizontal and vertical velocity components. This is due to the fact that for these phases the wave profiles lie below the elevation being considered. Horizontal velocity is observed to increase with elevation above the bed for all the phases. For the vertical ( Figure 6.17 (b)), the only significant feature occurs when the crest arrives, at which point strong vertical velocity components are observed at phase 0.40. At this phase, water near the bed (black line) is moving in the negativezdirection with velocities up to -5 cm/s while at an elevationz= +2 cm (red graph) peak vertical velocities exceed 20 cm/s. Figure 6.18 shows the phase dependence of the ratio of horizontal to vertical velocity components at several elevations in the flow. At elevationz = -3.0 cm, this ratio is around zero for most phases. Large fluctuations are observed for elevations towards the crest,z=+2 cm.
Figure 6.16:Profile of phase-ensemble averaged velocity fields for all 20 phases measured atx= -238 cm as a function of depth.
The phases have been shifted so that the wave crest lies in the middle. In this plot, the phases of interestTt = 0.0, 0.05, 0.10, 0.15, 0.20, 0.25 now lie at 0.55, 0.50, 0.45, 0.40, 0.35 and 0.30 respectively.