Árbók VFÍ/TFÍ - 01.06.2004, Page 214

of a Tantalum rod for a capacitance gauge was provided by Chapman and Monardo
(1991). The gauge was proven to be stable and precise; see Yeh and Chang (1994) for
detailed description of the gauge.
In order to examine temporal and spatial variations of the water surface response, a laser-
induced fluorescent imagery technique was used. In this technique, a 4-W Argon-ion
laser beam is converted to a thin laser sheet by using a resonant scanner. With the aid of
fluorescein dye dissolved in water, the vertical laser sheet illumination from above
induces the dyed water fluorescent and identifies a water surface profile as well as a gra-
dient of the water surface directly and non-intrusively. The illuminated images were
recorded by video camera. A fast shutter speed, 1 /30 s, was used to freeze the fast mov-
ing wave actions. The captured images were processed including the correction for image
distortions; hence, the resulting images can be analyzed quantitatively. More detailed
descriptions of the image process and the experimental setup can be found in Gardarsson
(1997).
The fundamental natural frequency of a water sloshing motion based on the linearized
water-wave theory for a rectangular tank i
(2)
where /0 is the fundamental frequency; g is the acceleration of gravity; h0 is the water
depth at rest; and L is the tank length. The normalized frequency of the oscillations of the
table is noted by (S and defined in the terms of the fundamental frequency as fS = f / /D,
where/is the frequency of the shaking of the table. The experiments focused on investi-
gating response of water sloshing for relatively large shaking amplitude which in many
cases results in wave breaking. Therefore, the maximum response will not happen at
f3 = 1.00, but a frequency shift will occur, consistent with a hardening spring effect (see
e.g. Reed et al. 1998). Hence, the linerized theory is only used as a reference point.
The experiments were carried out by starting the oscillation of the table at a low fre-
quency, about [S = 0.6-0.7. The sloshing in the tank was allowed to reach steady state for
each fS and then measurements were taken. The data acquired were wave height close to
the end wall and at the middle of the tank by wave gages, video recording capturing the
shape of the water surface illuminated by a laser sheet and forces resulting from the wave
action which were measured by the load cell underneath the tank. The results from the
force measurements can be found in Gardarsson (1997).
Experimental results
Several instances of hysteresis were observed in the experiments. In this paper the results
for a rectangular tank of length, L = 590 mm, width h = 335 mm, water depth h0 = 22.5
mm under shaking of amplitude a = 20 mm are discussed. It demonstrates the general char-
acteristics of the observed hysteresis as well as the specific results for that particular case.
Figure 3 shows the wave heights at the end wall and the middle of the tank for four dif-
ferent frequencies. The vertical axis on the plots shows the wave normalized wave height,
r? / h0, where r\ = h-h0 and h is the water depth with h0 as the quiescent water depth. For
the lowest shown frequency, /3 = 0.7, wave heights are relatively small at the end wall and
the wave height in the middle of the tank is barely measurable. For this frequency the
waves are smooth and do not break. The dashed line shows the movement of the shak-
ing table so the phase shift is apparent. When the frequency is increased the wave heights
increase and the wave starts to break. This is apparent from the second plot in the figure
that shows the wave heights for fS = 1.00. In this case the wave heights are more than three
times larger than for fí = 0.70 and the wave heights in the middle have also increased
2 1 2
Arbók VFl/TFl 2004