Velocity distribution in the transverse direction of ( u ) along sections A to D for cases A1: emerged groynes, A2 and A3: submerged groynes (measured using EMF — time-averaged) 

Contexts in source publication

Context 1

... considered representative of groyne fields in a straight reach with similar aspect ratio. The bed of the model is fixed and flat in the main channel; and slopes toward the bank in the area between the groynes [Fig. 2(b)]. The water level is controlled downstream by a manually controlled tailgate. In all tested cases, the Froude number ( F ) was around 0.2 to obtain subcritical flow as observed in the prototype, and the Reynolds number ( R ) was high enough to ensure turbulent flow in both the main channel region ( R 6 × 10 ) and the groyne fields region ( R ≅ 10 4 ). This paper considered only one of the tested groyne types, which represent a typical groyne as found in the Dutch Rhine branches. This groyne type is a straight, impermeable structure perpendicular to the riverbank with a crest length of 1.5 m and with slopes of 1 ∶ 3 on all sides, and the beach slope of the groyne fields is 1 ∶ 30 [see Fig. 2(b)]. The aspect ratio of the groyne fields (spacing between groynes/length of groyne) is 3.3. Uijttewaal (2005) rovides an overview of the effect of other tested geometries on the flow in groyne fields. Velocity measurements carried out during each test comprised two measurement techniques: electromagnetic flowmeters (EMF), and particle-tracking velocimetry (PTV). Four EMFs were used, meas- uring simultaneously the u -and v -components of the velocity in the horizontal plane (EMF sensor: electromagnetic, biaxial, 4-quadrant ellipsoid 11 × 33 mm; For this type of probe, the influence area has a cylindrical shape with approximately a thickness of 5 mm and 50 mm diameter, situated just below the electrodes). The measurements covered four sections, A to D as indicated in Fig. 2(a). The sections extended over 2.6 m in the transverse direction, and they were spaced at an equal distance of 0.75 m. Each section consisted of 12 points. At each point, velocities at two vertical elevations, located at 0.2 h and 0.8 h from the surface were recorded to dis- tinguish the difference between the near bed and the near surface velocities (little difference was observed in the velocity fluctuation pattern). PTV was used to measure the instantaneous surface velocity without causing disturbance and characterized the global structures of a complicated unsteady flow field. PTV was applied in four areas of 1 : 5 × 1 : 5 m 2 ; these areas are indicated as P1 to P4 in Fig. 2(a). Each time series lasted at least 5 min with a recording frequency of 30 Hz. Each frame contains about 2,000 particles of 2 mm diameter, floating on the free surface. The velocities were determined using a PTV-algorithm according to Bastiaans et al. (2002). The unstructured data were then interpolated onto a uniform rectangular grid with a characteristic spatial resolution of 5 cm. This resolution is, however, not sufficient to resolve the full spectrum of turbulent fluctuations, and so conclusions to be drawn from these measurements only apply to the large-scale turbulence structures. The absolute accuracy of the used EMF is less than 1 : 0 cm = s. When evaluating time-averaged velocities the uncertainty reduces because of averaging large number of samples. The accuracy of the PTV system is much less than the EMF. Accordingly, only quali- tative information is deduced from the PTV results. The test series discussed in this paper, Series-A, investigates the dynamics of the flow in the vicinity of a series of groynes at two different flow stages; namely, the emergent-and submerged groynes stages. The effect of flow stage is studied by changing the flow depth and keeping the main channel mean velocity constant at about 0 3 m s. Three water levels were tested; see hydraulic conditions in Table 1. A water level of 0.25 m represented the emergent condition (case A1), while two high water levels of 0.30 m and 0.35 m (cases A2 and A3), represented two submerged cases. The measurement locations covered the entire width of the mixing layer from section A to section D. The sampling time was guaranteed to be long enough to ensure a full coverage of the largest turbulence structure; the total recording period using EMF for a single point was 600 s, with a sampling rate of 10 Hz. The inflow conditions were adapted to the cross-section velocity profile far downstream such that beyond the first two groyne fields the flow can be considered as fully developed; this has been checked in the model using dye visualization. EMF velocity samples were measured throughout sections A to D. The time series (Fig. 3) taken at the center of the mixing layer at section A (at 0.2 h) gives an impression of the amplitude and the timescale of the velocity fluctuations. In all three cases, the velocity fluctuations in the transverse y -direction are slightly more pronounced than those in the streamwise direction. Comparison of the time signals of the different cases reveals that the velocity fluctuations in the submerged condition have a longer timescale than those in the emerged condition. Fig. 4 presents the time-averaged velocity distribution in the transverse direction of the streamwise velocity ( u ), measured at sections A through D for the three test cases A1, A2, and A3. A comparison between the two submerged cases shows little differences between the velocity profiles, whereas, larger differences are observed if they are compared with the emerged case. Moreover, the transverse velocity distribution in the emerged case [Fig. 4(a)] converges from section A to B, to reach a rather stable time- averaged distribution at sections C and D. In the submerged cases [Figs. 4(b) and 4(c)] the time-averaged velocity distribution converges within a rather short distance, as it is nearly the same for sections B, C, and D. Fig. 6 gives the transverse shear stresses ( τ xy ), and is a representation of the time-varying component of the velocity. The variation between the profiles of τ xy is a manifestation of changes in turbulence intensity due to the variation in the mixing layer. Fig. 5 presents the total turbulence intensity extracted from the PTV measurements for the three test cases A1, A2, and A3. The figure indicates the extent of the mixing layer in the different cases. In the emerged stage (case A1), the mixing layer starts with flow separation at the tip of the groyne and grows in width in the downstream direction. The total turbulence intensity and the transverse shear stress ( τ xy ), have their maxima around 1.5 m downstream of the tip of the groyne [see Figs. 5(a) and 6(a)]. Fig. 6 is based on measurements at 0.2 h from the surface; similar behavior, yet slightly less pronounced, is observed from the analysis of the measurements near the bottom. In the submerged stage, the mixing layer develops because of the steep velocity gradient between the fast stream in the main channel and the slow stream in the groyne fields region. It has a constant width [see Figs. 5(b), 5(c), 6(b), and 6(c)]. The width of the mixing layer is maintained because of the existence of a series of groynes that maintain the velocity difference between the fast stream (main channel), and the slow stream (groyne fields region). The nearly constant velocity difference maintains a constant velocity gradient across the mixing layer, thus keeping it constant in width. We can think of it (with reservations), to be analogous to a compound channel case with the mixing layer forming on the interface between the main channel and the floodplain (for example, see Van Prooijen et al. 2005). A comparison between the two submerged cases, A2 and A3 shows that with increasing submergence, the magnitude of the total turbulence intensity and the transverse shear stress decrease, while the width of the mixing layer remains the same [see Figs. 5(b), 5(c), 6(b), and 6(c)]. When the groynes are not submerged, the flow inside the groyne fields, in the horizontal plane, shows the circulation pattern, as reported previously by Uijttewaal et al. (2001) for a similar aspect ratio (see as well Uijttewaal 2005; Yossef 2005). Fig. 7 gives an illustration of the flow pattern, which is characterized by: • A primary eddy that forms in the downstream part of the groyne field and covers nearly two thirds of its spacing; the magnitude of the circulation velocity is about 30% to 40% of the main channel mean velocity; • A secondary eddy driven by the primary one with an opposite sense of rotation and a much smaller flow velocity; and • A dynamic eddy that sheds regularly from the tip of the upstream groyne. This eddy migrates in downstream direction and merges with the primary one, which in return changes in size due to the interaction with the migrating eddy. The whole circulation pattern is driven by the main stream via exchange of momentum through the interfacial mixing layer. Fig. 8 presents the autocorrelation functions of the transverse velocity for test case A1 (emergent groynes) measured using EMF at different locations. The large turbulence structures can be recognized through a correlation that extends over large time lags, and the characteristic time of the modulation is related to the timescale and consequently the length-scale of the turbulent structure. Inside the groyne fields [Fig. 8(a)], the presence of positive and negative correlations at large time lags corresponding to large structures is clear. Near the detachment point of the dynamic eddy [Fig. 8(b); section A], strong modulation with a shorter time span is visible, corresponding to the dynamic eddy. At section D, the autocorrelation shows the same characteristics as that inside the groyne field, implying that the same structure exists in these two points; evidence that it is the primary eddy. In the main stream [see Fig. 8(d)], the autocorrelations at large time lags are negligible. This suggests that only bottom-induced turbulence is present in the main stream far from the groynes. Unlike a free mixing layer, which is characterized by a single dominant peak in the energy ...

Context 2

... groynes. Unlike a free mixing layer, which is characterized by a single dominant peak in the energy density spectrum (at a given location, see Van Prooijen 2004), the mixing layer from a series of groynes contains more peaks caused by the interaction between the shedding eddies from the groyne tips and those migrating from upstream groynes, see Figs. 9(a) – 9(c). Inside the groyne fields [Fig. 9(a)], two peaks can be observed in the energy density spectrum at section A. The peak at the higher frequency has faded away in section D, where the lower frequency dominates. This can be related to the difference in length-scale between the eddy at section A and that at section D. The existence of the two peaks is caused by the interaction between the primary and the secondary eddies. Near the center of the mixing layer (point #2), Fig. 9(b) shows that near the groyne tip at section A, in addition to the two peaks that are present at point #1, another sharp peak at a higher- frequency is found. The presence of this peak is caused by the dynamic eddy that sheds from the tip of the groyne at a high- frequency; it appears only near the tip of the groyne and not at section D. The same pattern can also be inferred from the autocorrelations presented in Fig. 8(b). The effect of the groynes further upstream is visible in the presence of the low-frequency peaks at section A. Point #3 at section A is located just outside the mixing layer near the groyne, but still within the mixing layer of the upstream groyne. The energy density spectra at that point [Fig. 9(c)] show the existence of only a low-frequency peak with relatively low energy content at section A, caused by the mixing layer of the upstream groyne. At section D, two peaks can be observed; the higher- frequency peak is due to the mixing layer that forms because of the nearby groyne and the low-frequency peak is attributed to the interaction of the migrating eddy from the upstream groyne. In the main stream (point #4), the large structures nearly disappear and only small-scale turbulence can be observed [see Figs. 8(d) and 9(d)]. When the groynes are submerged, the flow in the groyne fields region does not show the horizontal circulation pattern that is observed in the emerged case. The visual observations of no circulation are supported by the cross-section velocity profiles where reverse flow was not observed in the submerged groyne cases; Figs. 4(b) and 4(c) show no -ve velocity in the groyne field region. The groyne fields can be characterized as a low-velocity region. The momentum transfer by the water flowing over the groynes is sufficient to balance the momentum transfer through the mixing layer, that otherwise would have caused a recirculation inside the groyne field. As the groynes are submerged, the flow over the groynes hinders the horizontal recirculation, causing it to disappear after relatively low submergence. Generally speaking, the flow pattern in the submerged stage shows an alternating accelerating and decelerating pattern between flow over and around the groynes. From Fig. 10, we see that the turbulence characteristics in the submerged condition are different from that of emergent conditions. There is a slow periodical behavior with a timescale of around 25 s, which is present in all locations, illustrated in Figs. 10(a) – 10(d). This suggests a phenomenon that occupies the whole length of the groyne field. Yet this phenomenon does not seem to have a free-surface signature, in the sense that no significant free-surface waves were observed. The energy density spectra presented in Fig. 11 shows a distinct single peak at a similar frequency for both sections A and D, meaning the same fluctuation is present throughout the length groyne field. From Fig. 11(d), one can observe the existence of large structures at point #4 far into the main stream. Thus, the submerged case the mixing region extends further into the main channel than in the emerged case. In this section we parameterize the complex flow field near groynes in terms of depth-averaged components. The parameterization provides some building blocks that may serve further analysis of, for example, the sediment exchange process between the main channel and the groyne fields of a river (see Yossef 2005; Yossef and De Vriend 2010). In the previous section, large-scale velocity fluctuations in both horizontal directions were observed and the velocity field indicated a periodical behavior. The case of submerged groynes has an anal- ogy with the free mixing layer between a fast stream and a slow stream (see, for example, Uijttewaal and Booij 2000), where the fast stream is the main channel flow and the slow stream is the flow far inside the groyne field, away from the mixing layer. The case of emerged groynes includes more dynamics; viz, a dynamic eddy detaching from the tip of the groyne and the large circulation cell inside the groyne field. However, the time-averaged velocity profiles given in Fig. 4 and the transverse shear stresses given in Fig. 6 both indicate a level of similarity with free mixing layer. Accordingly, we may apply the same treatment as in the case of free mixing layer. Representing the fluctuating velocity component of the coherent structures in the mixing layer with a periodical function with prescribed amplitude, period and phase difference seems a natural choice (cf., Lyn and Rodi 1994). Assuming the full velocity signal takes the form u 1⁄4 u þ u 0 þ u 00 ð 1 Þ where u , v = time-averaged components; u , v = large-scale turbulence components; and u 00 , v 00 = small-scale (bottom) turbulence components. The large-scale turbulent part is represented as u 0 1⁄4 û · sin ð ω · t Þ ð 2 ...