8.2 Spatial distribution of vorticity
8.2.2 Mean flow vorticity
−60 −40 −20 0 20 40 60 80 100 120 140 160
−15
−10
−5 0 5 10 15
Elevation, z, relative to SWL (cm)
Instantaneous vorticity, (s−1)
bed position phase = 0.00 phase = 0.05 phase = 0.10 phase = 0.15 phase = 0.20 phase = 0.25
Figure 8.3: Profiles of instantaneous vorticityωy as a function of depth, measured atx= -238 cm as flow progresses.
the intensity is observed to increase. This may again be caused by increased resolution used towards the shore, which enables the identification of small but equally intense vorticity patches in the flow. Both negative and positive vorticity of magnitude up to 100s−1 can be observed impinging the flume bed as flow progresses. Such high vorticity fluid elements are responsible for lifting sediments from the bed and transporting them. Statistics on the number of high vorticity patches impinging the bottom and their magnitudes can be determined and is vital information in sediment transport studies.
−300 −295 −290 −285 −280 −275 −270
−10
−5 0 5 10
Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
Win11b x = −286 cm
−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)
Win12a x = −238 cm
−210 −205 −200 −195 −190 −185 −180
−10
−8
−6
−4
−2 0 2 4 6 8 10
Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
Win12b x = −193 cm
−160 −155 −150 −145 −140
−8
−6
−4
−2 0 2 4 6 8
Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
Win13a x = −147 cm
−110 −108 −106 −104 −102 −100 −98 −96 −94 −92 −90
−6
−4
−2 0 2 4 6
Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
Win13b x = −101 cm
(s−1)
−100 −50 0 50 100
Figure 8.4: Contour plots of instantaneous vorticity,ωy, under the wave crests, measured at the five stations.
layer overlaying a slower layer of fluid (Misra et al.[29]). The co-rotating instantaneous eddies observed earlier get coalesced to become a larger and stronger single vortex. The shear layer was earlier seen to arise from opposing flow of the fast moving mixture of crest water/bubbles and the slow moving water near the trough. The formation of the positive vortical layer represents shear resulting from the incoming uprush flow and receding downwash flow.
−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
−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 = 0.05
−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 = 0.10
−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 = 0.15
−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 = 0.20
−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 = 0.25
(s−1)
−60 −40 −20 0 20 40 60 80 100
Figure 8.5: Contour plots showing the evolution of the vorticity of the mean flow.
Averaging the instantaneous data makes small scale eddies vanish so the contours of the mean flow vorticity,∇ ×~u, show the development of large scale structures within and around the shear layer, which develops and moves downstream. The fluid beneath the elevation ofz= -5 cm is relatively vorticity-free
for the first two phases but for the last, it is observed that positive vorticity diffuses downwards towards the flume bed. As can be observed for phases 0.10 to 0.25, the fluid immediately behind the crest, at elevations centered around z = -5 cm, is characterized by negative vorticity that ride above positive vorticity. As pointed out by Dabiri & Gharib [203] the negative vorticity seen on the wave, below the surface, and above the positive shear layer abovez= 0 cm, indicate the existence of a stagnation point at that location. In agreement with observations bySou &Yeh [12] the maximum intensity of vorticity occurs around the shear layer and the intensity decreases in magnitude as flow progresses. It is also interesting to note that even though the flow between the shear layer and the free surface is turbulent, its vorticity field is quite weak with respect to the vorticity within the shear layer. This is consistent with observations by Lin & Rockwell [54]. Thus maximum positive vorticity will remain in the shear layer region between the upper, faster moving part of the breaking wave and the quiescent region below.
The contour plots also reveal the phenomenon of vorticity shedding at later phases of the flow in which the tail of the initially strong boundary layer vorticity breaks up or peels off, weakens and diffuses from the shear boundary layer, reaching the flume bed as phase progresses. This results in bleeding most of the vorticity from the neighbourhood of the initially stronger region (Jimenez [202]). The original layer breaks in this way into approximately circular cores. The strong negative vorticity patches near free surface directly above regions -255 cm< x < -242 cm for phase 0.10, and -242 cm< x < -232 cm for phase 0.15 may be responsible for the vortex shedding observed. The turbulent flow studied here is also in some sense a decaying flow since the mean flow vorticity and root-mean-square velocity decrease slowly with time or phase. The explanation for the observed decay is that at later phases, the effects of small-scale mixing due to the strong turbulence in the flow have greatly reduce the presence of patches of vorticity in the flow. It was shown by other researchers (e.gStanely [204]), that while the large scales in the flow field adjust slowly to variations in the local mean velocity gradients, the small scales adjust rapidly. Intense vorticity structures are observed inside the shear layer region, which is the interface separating the turbulent and the irrotational flow regions. Near the trough level, there are occasional regions devoid of strong vorticity.
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−15
−10
−5 0 5 10 15
Elevation, z, relative to SWL (cm)
Vorticity, (s−1)
bed position phase = 0.00 phase = 0.05 phase = 0.10 phase = 0.15 phase = 0.20 phase = 0.25
Figure 8.6: Profiles of the evolution of vorticity of the mean flow as a function of depth, measured at x=-238 cm as flow progresses.
Figure 8.6 shows the vertical variation of the evolution of mean flow vorticity in one frame, measured
at x= -238 cm, as phase progresses. From the flume bed up to an elevation of z = -5 cm, mean flow vorticity is about zero and increases sharply to peak values of about 150s−1 just above this elevation, before oscillating between -20s−1 and 20s−1 towards the crest. Peak vorticity is observed near shear- layer as a result of the interaction between the downwash and uprush flows. The flow below the shear layer remain relatively irrotational for early phases of the flow. These results are also consistent with phase averaged vorticity results by Sou & Yeh [12] who observed that in the surf zone, the maximum intensity of vorticity occurs at the shear layer, with peak values of up to 200s−1. They also observed that an internal flow circulation is generated at the flow reversal phase as the flow near the bed responds to the gravitational force earlier than the flow in the upper water column, where the uprush momentum is sustained later in phase. Similar to results presented here, they also observed that in the surf zone, the maximum intensity of the phase averaged vorticity occurs at the shear boundary layer and the strength of vorticity in the water column decays as phase advances.Melville et al.[3] also observed that breaking generates at least one coherent vortex that slowly propagates downstream.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
−20 0 20 40 60 80 100
Phase t/T
Vorticity, (1/s)
z = −8.0 cm z = −3.0 cm z = +2.0 cm
Figure 8.7: Phase variation of the mean flow vorticity,hωyimeasured at elevationx= -238 cm as flow progresses for three different elevations.
Figure 8.7 shows the profiles of mean flow vorticity as a function of depth measured at three different elevations,z= -8 cm, -3 cm and + 2 cm. For elevations close to the flume bed (z = -8 cm and -3 cm), most of the observed mean flow vorticity is positive for all phases. At elevationz = + 2 cm, mean flow vorticity is positive during the early phases of the flow and then becomes negative after phaset/T = 0.15. Again only a few phases have profiles that go up toz= +2 cm, which corresponds to 15 cm above the bed.
Figure 8.8 shows contour plots of the vorticity of the mean flow under the crests, measured at different cross-shore positions along the flume. The position of the SWL is at elevationz= 0 cm in all the plots.
Vorticity intensity near the shear boundary layer decreases away from the break point towards the shore.
As seen from the plots, this is a result of vorticity shedding as the flow approaches the shore.
−300 −295 −290 −285 −280 −275 −270
−10
−5 0 5 10
Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
Win11b x = −286 cm
−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)
Win12a x = −238 cm
−210 −205 −200 −195 −190 −185 −180
−10
−8
−6
−4
−2 0 2 4 6 8 10
Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
Win12b x = −193 cm
−160 −155 −150 −145 −140
−8
−6
−4
−2 0 2 4 6 8
Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
Win13a x = −147 cm
−110 −108 −106 −104 −102 −100 −98 −96 −94 −92 −90
−6
−4
−2 0 2 4 6
Distance from still water mark (cm)
Elevation, z, relative to SWL (cm)
Win13b x = −101 cm
(s−1)
−60 −40 −20 0 20 40 60 80
Figure 8.8: Contour plots of the vorticity of mean flow under the crests, measured at different cross-shore positions along the flume. The SWL is at elevationz= 0 cm in all the figures.