Unsteady Turbulence Characteristics in an Undular Bore

When a river mouth has a flat converging shape with a tidal range exceeding 6 to 9 m, the river may experience a tidal bore. A tidal bore is a positive surge, and the aim of the study is to detail the turbulent field beneath an undular bore. New unsteady experiments were conducted in a large channel. Turbulence measurements were performed with high-temporal resolution using side-looking acoustic Doppler velocimetry. Detailed turbulent measurements were conducted along a vertical profile for a Froude number of 1.4. Instantaneous velocity measurements showed a marked flow deceleration at all vertical elevations. Turbulent stresses were deduced from high-pass filtered data. Maximum Reynolds stresses were observed beneath the whelps, under and just before each crest. The findings suggest that preferential bed erosion takes place beneath each wave crest, and the eroded material is advected in the undular wave motion behind the bore front. tions and sometimes free-surface measurements. These rarely encompassed turbulence but a few limited studies (e.g. Hornung et al. 1995). Field measurements in tidal bores are few: e.g., Lewis (1972) and Huntley (2003) in the Dee river (UK), Wolanski et al. (2004) in the Daly river (Australia), Kjerfve and Ferreira (1993) in Rio Mearim (Brazil). All these studies were limited to a very small number of occurrences. (A) Undular tidal bore of the Dordogne river (France) at St Pardon on 6 Aug. 2004 (Courtesy of Pierre-Yves Lagrée) View from left bank with bore propagating from left to right (B) Tidal bore of the Sélune river (France) on 7 April 2004 at Roche-Torin (Photograph by Hubert Chanson) The bore front disappeared briefly in the deep channel section while an undular bore was seen besides, with breaking bores in shallower waters and the bore front advancing over dry bed in foreground Fig. 1 Photographs of undular tidal bores 2 EXPERIMENTAL FACILITIES 2.1 Channel and instrumentation Experiments were performed in a 0.5 m wide 12 m long horizontal flume (Fig. 2). Waters were supplied by a constant head tank. A tainter gate was located next to the downstream end of the channel (x = 11.15 m). Its controlled and rapid closure induced a positive surge propagating upstream. Steady flow rates were measured with bend meters which were calibrated in-situ with a large V-notch weir. The percentage of error was expected to be less than 2%. In steady flows, the water depths were measured using rail mounted pointer gauges and acoustic displacement meters. Unsteady water depths are measured with acoustic displacement meters MicrosonicTM Mic+25/IU/TC with an accuracy of 0.18 mm and a response time of 50 ms. The acoustic displacement readings were compared with instantaneous freesurface profiles captured with a high-speed camera. The results were found to be within the accuracy of the systems, although a few spurious points were sometimes observed. The displacement meter output was a function of the strength of the acoustic signal reflected by the free-surface. When the free-surface was not horizontal, some erroneous points were recorded. These were relatively isolated and easily ignored. In steady flows, velocity measurements were conducted with a Prandtl-Pitot tube (3.3 mm ∅) previously calibrated as a Preston tube based upon in-situ experiments (Chanson 2000). Turbulent velocity measurements were conducted with an acoustic Doppler velocimeter SontekTM 16 MHz micro-ADV at x = 5 m. The probe sensor had a two-dimensional side-looking head with a distance to sampling volume of 5 cm. With this arrangement, the closest measurement distance from the bed was 7.2 mm. The Vx velocity component was aligned with the longitudinal flow direction and positive downstream, while the transverse velocity component Vy was oriented normal to the channel sidewall and positive towards the left sidewall. The velocity range was 1.0 m/s, most unsteady flow experiments were conducted with 50 Hz sampling rate and the data accuracy was 1%. The translation of Pitot tube and ADV probe in the vertical direction was controlled by a fine adjustment travelling mechanism connected to a MitutoyoTM digimatic scale unit. The error on the vertical position of the probe was ∆z < 0.025 mm. The accuracy on the longitudinal position was estimated as ∆x < +/2 mm. The accuracy on the transverse position of the probe was less than 1 mm. Additional informations were obtained with digital cameras PanasonicTM Limux DMC-FZ20GN and CanonTM A85, and a digital video-camera SonyTM DV-CCD DCR-TRV900. Further details on the experimental facility were reported by Koch and Chanson (2005). Fig. 2 Sketch of experimental channel 2.2 Tidal bore generation For each experiment, the initial steady flow was uncontrolled and gradually-varied. It was established for at least 10 minutes prior to measurements. A bore was generated by the rapid partial closure of the downstream gate. The gate closure occurred in less than 0.1 sec. Flow measurements and data acquisition were started for 2 minutes prior to gate closure. After gate closure, the travelling bore propagated upstream against the gradually-varied flow over the full channel length. Each experiment was stopped when the bore front reached the intake structure. Tests were repeated systematically for different gate closures (Table 1). Detailed velocity and free-surface elevation measurements were performed with the acoustic Doppler velocimeter (ADV) located at x = 5 m from the channel intake and at several transverse positions y/W = 0.5, 0.75, 0.90 and 0.95, where x is the distance from the upstream channel end, y is the transverse distance measured from the right sidewall and W is the channel width (W = 0.5 m). The acoustic displacement meters were located at x = 10.95 m, 7.25 m, 6 m, 5.1 m and 5 m. The latter displacement meter sampled the free-surface elevation immediately above the ADV sampling volume, while the other sensors were placed on the channel centreline. Table 1. Experimental flow conditions ________________________________________________ Q do U dconj Fr Remarks m/s m m/s m ________________________________________________ 0.0403 0.0795 0.140 0.0957 1.31 Undular bores 0.0403 0.0795 0.235 0.103 1.41 ADV measurements. 0.0403 0.0785 0.238 0.109 1.44 0.0406 0.0790 0.286 0.117 1.49 0.0403 0.0785 0.315 0.120 1.53 0.04015 0.0790 0.456 0.135 1.67 Some breaking at 1st wave crest ________________________________________________ 0.0406 0.0795 0.549 0.145 1.77 Breaking bore. ________________________________________________ * do: initial flow depth dconj: measured conjugate flow depth; Q: steady discharge; U: bore celerity.. 2.3 Initial steady flow conditions The initial steady flow was partially-developed with δ/do = 0.6 to 0.8 at the sampling location (x = 5 m). Both ADV and Prandtl-Pitot tube data compared favourably with a 1/7th power law in the boundary layer. The shear velocity was estimated using the Preston-Prandtl-Pitot tube and a match between velocity data and logarithmic velocity law in the inner flow layer. The results were close and yielded : V* = 0.044 m/s. Importantly, the data, including the vertical distributions of Reynolds stresses, showed good qualitative and quantitative agreement with the detailed experiments of Xie (1988) and Tachie (2001) in smooth open channel flows. Further details on the initial flow properties were described in Koch and Chanson (2005, pp. 21-37). 2.4 Acoustic Doppler Velocity Metrology Acoustic Doppler velocimetry (ADV) is designed to record instantaneous velocity components at a single-point with relatively high frequency. Past and present experiences demonstrated many problems. In steady turbulent flows, the ADV velocity fluctuations characterise the combined effects of the Doppler noise, signal aliasing, velocity fluctuations, turbulent shear and other disturbances (Lemmin and Lhermitte 1999, McLelland and Nicholas 2000, Chanson et al. 2005). For all experiments, present experience demonstrated recurrent problems with the velocity data, including low correlations and low signal to noise ratios. The situation improved by mixing some vegetable dye (Dytex DyeTM Ocean Blue) in the entire water recirculation system. Other problems were experienced with boundary proximity. In steady flows, detailed comparisons between ADV and Prandtl-Pitot tube data were conducted at y = 0.473, 0.450, and 0.375 m (or 27, 50 and 125 mm from the left sidewall) with the micro ADV sensors facing the left sidewall, where y is the transverse distance from the right wall. Experimental data indicated that the streamwise velocity data were not affected by the presence of the channel bed at y = 0.450 and 0.375 m as observed at y = 0.250 m. But the ADV data underestimated the velocity in the vicinity of a sidewall (y > 0.455 mm). This was associated with a drastic decrease in average signal correlations, average signal-to-noise ratios and amplitudes next to the wall (Koch and Chanson 2005). While several ADV post-processing techniques were devised for steady flows (e.g. Goring and Nikora 2002, Wahl 2003), these post-processing techniques are not applicable to unsteady flows (e.g. Nikora 2004, Person. Comm., Chanson et al. 2005). In the present study, unsteady flow post-processing was limited to a removal of communication errors and a replacement by interpolation. Beneath the undular surge, the ADV probe outputs showed systematically a lower proportion of errors and "spikes" while the bore front passage was associated with some increase in average signal-to-noise ratios, average signal correlations and to a lesser extent signal amplitudes. Although these observations were not "true" validation, they tended to support the use of Acoustic Doppler devices in such a highly unsteady flow situation. 2.5 Reynolds stress calculation in rapidly-varied flow motion In turbulence studies, the measured statistics are based upon the analysis of instantaneous turbulent velocity data : v = V V ⎯, where V ⎯ is a timeaverage velocity. If the flow is "gradually timevariable", V ⎯ must be a low-pass filtered velocity component, or variable-interval time average VITA (Piquet 1999). The cutoff frequency must be selected such that the averaging time is greater than the characteristic period of fluctuations, and small with respect to the characteristic period for the timeevolution of the mean properties. In undular surge flow, the Eulerian flow properties showed an oscillating pattern with a period of about 2.4 s that corresponded to the period of the free-surface undulations. The unsteady data were therefore filtered with a low/high-pass filter threshold greater than 0.4 Hz (i.e. 1/2.4 s) and smaller than the Nyquist frequency (herein 25 Hz). The cutoff frequency was selected as 1 Hz based upon a sensitivity analysis (Koch and Chanson 2005, pp. A51A55). The same filtering technique was applied to both streamwise and transverse velocity components, and Reynolds stresses were calculated from the high-pass filtered signals. 3 UNDULAR BORE FREE-SURFACE PROFILES