7.2 Phase-ensemble averaged turbulence characteristics
7.2.1 Turbulence intensity
The horizontal turbulence intensity, u′, represents deviations of the measured instantaneous value, ui, from the mean valuehui, defined by the root-mean-square of velocity given by :
√u′2=u′r.m.s= v u u t1
N
N−1
X
i=0
(ui− hui)2 (7.1)
A similar equation is used for the vertical turbulence intensityw′. In the remainder of the work reported here, the primed variables (u′, w′) will be used to represent the root-mean-square values of the horizontal and vertical turbulent fluctuations, respectively.
Figures 7.1 and 7.2 show contour plots of the spatial variation of the horizontal and vertical turbulence intensities, respectively, for the flow at station 12a. The colour code shows the magnitude and direction of the turbulence intensity component. The direction for the horizontal and vertical turbulence intensity components are the same as that defined previously for the mean horizontal and vertical velocity com- ponents. Each contour map shows the spatial distribution of the turbulent intensities at the different wave phases. These results show that turbulent intensities have peak values of 70 cm/s for the horizontal and 40 cm/s for the vertical. Both figures show that turbulence intensities which are initially present in almost the entire water column, gradually decrease with progress of the phase. A high horizontal turbulence intensity region appears between elevation z =- 5 cm and the free surface as observed at phases, 0.00, 0.05, 0.10 and 0.15 of Figure 7.1. These results are in agreement with results ofDe Serio
&Mossa [68], who also observed that higher turbulence is localized near the surface rather than near the bottom. Consistent with results byLiiv [2], it is observed from the turbulence contours that as the wave propagates towards the shore in the surf zone, the horizontal and vertical turbulences generated near the surface due to breaking waves diffuse to the bottom of the bed where some of it is dissipated as heat by friction with the bed. Figure 7.2 shows that high vertical turbulence intensity is near the free surface and diffuses deeper into flow than the horizontal. The turbulence results obtained here are also consistent with the observation that high turbulent intensity occurs in the crest region as reported by previous researchers (e.g.,Govender et al. [42]; Kimmoun & Branger [43]; Huang et al.[44]; Huang et al.[88];Okayasu et al. [182]).
In order to compare the horizontal and vertical turbulence intensities of the flow, the variation of these components with depth are plotted on the same axis for each phase, as shown in Figure 7.3. During the early phases of the flow, vertical and horizontal turbulence intensities below elevationz= -5 cm are almost of the same order. From elevation z = -5 cm going towards the crest, horizontal turbulence intensity increases sharply to peak values of nearly 70 cm/s. The magnitude of the peak horizontal turbulence intensity decreases as the flow progress in phase. When the crest has passed the horizontal intensity reduces to about double the vertical as observed at phases 0.20 and 0.25. During the early phases, both horizontal and vertical turbulence intensities were found to rise linearly from the bed reaching about 20 cm/s near the elevationz/h = -0.5 cm. Thereafter it rises sharply to peak values of about 70 cm/s for the horizontal and about 40 cm/s for the vertical. Outside the aerated region, maximum horizontal turbulence intensity is of the order of 20 cm/s. Chang &Liu [41] obtained turbulence intensity of the order of 11 cm/s in the trough section for a wave height of 14.5 cm and deep water wavelength of 121 cm. These results are also in good agreement with results obtained byLennon &Hill [120].
In order to show the phase evolution of turbulence intensities of the flow, separate plots of the variation of horizontal and vertical turbulence intensities with depth are presented for all six phases on the same axis as shown in Figure 7.4 and Figure 7.5, respectively. It is evident from the preceding figures that turbulence is generated near the free surface and gradually decays by diffusing to the flume bed as flow progresses.Pedersen et al.[183], pointed out that in breaking waves, most of the production of turbulence takes place near the surface and part of the turbulence spreads downward while it gradually dissipates into heat. These results are also in agreement with observations by Ting & Kirby [30], who showed
−255 −250 −245 −240 −235 −230 −225 −220
−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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−5 0 5 10
Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.10
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−5 0 5 10
Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.15
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−5 0 5 10
Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.20
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−10
−5 0 5 10
Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.25
(cm/s)
0 10 20 30 40 50 60 70 80
Figure 7.1: Contour plots showing the phase evolution of the horizontal turbulence intensity, u′ for the six phases under consideration.
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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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−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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−10
−5 0 5 10
Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.20
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−10
−5 0 5 10
Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
t/T = 0.25
(cm/s)
0 10 20 30 40 50
Figure 7.2: Contour plots showing the phase evolution of the vertical turbulence intensity,w′for the six phases under consid- eration.
0 5 10 15 20
−15
−10
−5 0 5 10 15
Elevation, z, relative to SWL (cm)
Turbulence intensity (cm/s) t/T = 0.00
bed position vertical, w’ horizontal, u’
0 50 100
−15
−10
−5 0 5 10 15
Elevation, z, relative to SWL (cm)
Turbulence intensity (cm/s) t/T = 0.05
bed position vertical, w’ horizontal, u’
0 20 40 60 80
−15
−10
−5 0 5 10 15
Elevation, z, relative to SWL (cm)
Turbulence intensity (cm/s) t/T = 0.10
bed position vertical, w’ horizontal, u’
0 20 40 60
−15
−10
−5 0 5 10 15
Elevation, z, relative to SWL (cm)
Turbulence intensity (cm/s) t/T = 0.15
bed position vertical, w’ horizontal, u’
0 20 40 60
−15
−10
−5 0 5 10 15
Elevation, z, relative to SWL (cm)
Turbulence intensity (cm/s) t/T = 0.20
bed position vertical, w’ horizontal, u’
0 20 40 60
−15
−10
−5 0 5 10 15
Elevation, z, relative to SWL (cm)
Turbulence intensity (cm/s) t/T = 0.25
bed position vertical, w’ horizontal, u’
Figure 7.3: Profile of turbulence intensity as a function of depth measured at the center of the panel (atx= -238 cm) at each phase : horizontal component (u′) - (black) and vertical component-(w′)-(blue).
that turbulence intensity is higher under the wave front, showing a peak, and then decays rapidly after the wave crest passes. As previous researchers (e.g. Longo et al. [65]; Peregrine [184]; Christensen et al.[185]) noted, turbulence in the surf zone is primarily generated in the crest region of breaking waves and secondarily generated in the bottom layer.
Figures 7.6 and 7.7 show phase dependence of both horizontal and vertical turbulence intensity compo- nents near the trough level at three separate elevations from the flume bed. These results show that for the elevation in the trough, the variation of both horizontal and vertical turbulence components with phase is almost similar, with the horizontal being higher than the vertical at almost all phases. Both
0 10 20 30 40 50 60 70 80
−1
−0.8
−0.6
−0.4
−0.2 0 0.2 0.4 0.6 0.8 1
z/h
Horizontal turbulence intensity, (cm/s)
bed position phase = 0.00 phase = 0.05 phase = 0.10 phase = 0.15 phase = 0.20 phase = 0.25
Figure 7.4: Evolution of the vertical profile ofu′atx= -238 cm for the six phases as flow progresses.
0 5 10 15 20 25 30 35 40 45 50
−1
−0.8
−0.6
−0.4
−0.2 0 0.2 0.4 0.6 0.8 1
z/h
Vertical turbulence intensity (cm/s)
bed position phase = 0.00 phase = 0.05 phase = 0.10 phase = 0.15 phase = 0.20 phase = 0.25
Figure 7.5: Evolution of the vertical profile ofw′atx= -238 cm for the six phases as flow progresses.
turbulence components are observed to increase up to peak values at phase 0.15. After phase 0.20, there is a general decrease of both horizontal and vertical turbulence intensities at all elevations as flow progresses.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0 10 20 30 40 50 60
Phase t/T
u’, (cm/s)
z = −8.0 cm z = −3.0 cm z = +2.0 cm
Figure 7.6: Phase variation of horizontal turbulence intensity,u′at different elevations from the flume bed : (blue) - near the bed,x= -8 cm ; (black)- between trough and crest,x= -3 cm, and (red)- near crest,x= +2 cm.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0
5 10 15 20 25 30 35 40
Phase t/T
w’, (cm/s)
z = −8.0 cm z = −3.0 cm z = +2.0 cm
Figure 7.7: Phase variation of vertical turbulence intensity,w′at different elevations from the flume bed : (blue) - near the bed, x= -8 cm ; (black)- between trough and crest,x= -3cm, and (red)- near crest,x= +2 cm.
Figures 7.8 shows a comparison of the variation of turbulence intensity components with phase, for points at elevationz= -3 cm, for all the twenty phases. High horizontal and vertical turbulence intensities are observed during the early phases of the flow (t/T = 0.00 - 0.30). These are the phases of interest in this study. During the early phases of the flow, the horizontal component is higher than the vertical.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0 5 10 15 20 25 30 35 40 45
Phase t/T
Turbulence intensity (cm/s)
u’
w’
Figure 7.8: Phase variation of turbulence intensity components at elevationz= -3 cm.
Figure 7.9 shows the phase dependence of the ratio of the horizontal intensity to the vertical, wu′′. Whilst there are some variations of this ratio with phase for elevations abovez = -3 cm, there is an almost uniform variation of around 1.5 for all phases at elevationz = -8 cm. A much bigger variation in the ratio wu′′ is largest at elevation z = -3.0 cm. Once again the missing data points at some phases imply that the wave profile for those phases was well below that point, so the turbulence intensity components do not exist.
In order to map the structure of turbulence in the plunging breaker, a simple index is considered which links the vertical and the horizontal turbulence components. Figure 7.10 shows the variation with depth of the ratiow′2/u′2 measured at x= -238 cm at each phase of the flow. In this plot, the elevation was limited to z/h= -0.2 cm (just below the SWL) so that comparisons could be made with the results of
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Phase t/T
u’/ w’
z = −8.0 cm z = −3.0 cm z = +2.0 cm
Figure 7.9: Phase dependence of the ratio of horizontal to vertical turbulence intensity components uw′′, at points : (blue)- near the bed (x, z) = (-238, -8) cm ; (black)- between trough and crest (x, z) = (-238, -3) cm and (red)- near crest (x, z) = (-238, +2) cm.
0 0.2 0.4 0.6 0.8 1
−1.1
−1
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
w’2/u’2
z/h
phase = 0.00 phase = 0.05 phase = 0.10 phase = 0.15 phase = 0.20 phase = 0.25
De Serio−Moosa sect 47 De Serio−Moosa sect 48
Figure 7.10: Variation with depth of the ratio of horizontal to vertical turbulence intensities,w′2/u′2measured atx= -238 cm at each phase of the flow. Also included for comparisons are plunging wave results byDe Serio&Mossa[68].
De Serio&Mossa [68]. Below the trough level, the ratiow′2/u′2has peak values of up to 0.8 for phases most phases.The graph shows there is a reasonably good agreement between results from the represent experiment and those ofDe Serio & Mossa [68] for the elevations considered, particularly during the early phases of the flow.