2. Experimental set-up and imaging configuration
Experiments are conducted in a hydraulic flume having the following
dimensions: length = 6 m; width = 50 cm; side wall height = 40
cm. The flume is tilted to obtain a bottom slope of 1 %. A 5 cm
deep layer of loose sediment covers the flume bottom and is
replenished during the flow by an upstream silo. Sand of nearly
uniform size distribution is used as sediment material, and has the
following characteristics: mean grain diameter = 1.65 mm;
density = 2615 kg/m3. For the proof-of-concept
experiments presented hereafter, the water inflow was not tightly
controlled but rather loosely operated in order to produce a variety
of patterns. Water discharges in the flume ranged from 15 to 35
l /s, yielding flow depths of 3 to 6 cm and Froude numbers in the
range Fr = 1.4 to 2. For such high Froude numbers, the water free
surface responds strongly to the underlying oscillatory topography of
the bedforms, up to the point of breaking at the wave crests when
antidunes are fully developed. The experimental parameters of the
three runs selected for analysis are listed in Table 1.
Starting from a plane bed, the antidunes emerge as longitudinal
trains of crests and troughs initiating from downstream but stationary
in phase. The antidunes are observed to respond to transient changes
in the flow rate (both increase and decrease) by temporarily growing
in amplitude. Amplitude responses and gradual shifts in pattern occur
on a time scale of tens of seconds. By contrast, on the shorter time
scale corresponding to the image acquisition (of the order of 2 s),
the hydrodynamics can be assumed to be quasi-steady and this is
exploited hereafter to derive a single surface from each measurement
sequence. The flow is however observed to exhibit small unsteady
pulses, and this physical source of noise may slightly affect the
results concurrently with measurement errors.
The short wavelength features of the water surface itself are not
suitable for either matching or tracking. Specular reflection changes
the appearance of these features when viewed from different
angles. They also continuously evolve in time under the action of
capillarity and gravity. Floating particles dispersed on the water
free surface are used instead as tracers. The tracer particles are
white wooden pearls 9 mm in diameter. The measurement section is
placed some 2 m upstream of the flume outlet. Further upstream and
moments before image acquisition, a uniform dispersion of floats is
dropped onto the mean surface by means of staggered metal meshes.
Image sequences are obtained using digital cameras placed above the
flow. The velocimetric and stereoscopic methods require rather
different image acquisition systems, hence some care is necessary in
order to operate them simultaneously and observe the same scene. Two
commercial digital cameras (miniDV, PAL, 25 frames per second) are
used for the stereoscopic measurements. These cameras offer good image
resolution (768 by 576 pixels) but cannot be synchronised with each
other during the acquisition. To avoid motion-stereo ambiguity, it
will thus be necessary to synchronise them a posteriori using an
interpolation procedure (see below). The stereo cameras are placed
above the flow with oblique optical axes contained in a vertical plane
parallel to the direction of flow (see Fig. 2). For the velocimetric
measurements, on the other hand, a high frame rate camera (250 frames
per second; resolution of 239 by 192 pixels) is placed directly over
the flow with a nearly vertical optical axis. Due to the high frame
rate, this camera requires strong lighting, obtained with four 2 kW
light sources. Such powerful lighting saturates the commercial cameras
even at maximum shutter speed, and these have to be fitted with
dimming filters.
Figure 2. Imaging configuration for the antidune experiments.
After positioning, the viewpoints of all three cameras are
determined by placing a calibration target in their shared viewing
volume. This is essential for stereo reconstruction and allows the
results of the two methods to be obtained in the same
three-dimensional referential. For ease of reference in the next
sections, we adopt labels V = L, R, and T to identify the three
viewpoints. Labels L and R designate the left and right oblique
cameras used for stereoscopic reconstruction, while label T refers to
the top camera used for velocimetric reconstruction. The camera
configuration shown on Fig. 2b is reconstructed based on actual
calibrated viewpoints.
| |
