Árbók VFÍ/TFÍ - 01.06.2004, Qupperneq 217

Figure 6:Temporal and spatial water surface profiles, processed from the experimental image data,for p = 1,397,for (a)
the lower branch and (b) the upper branch.
0.3
t /T
a gently sway back and forth with no wave breaking. There is hardly any run-up at the
end wall and the surface is smooth at all times.
Discussion
In the above analysis it is demonstrated that a sloshing of shallow water in a rectangular
tank under relatively large shaking amplitude does not necessarily behave in a unique
way for exactly the same conditions but the behavior is dependent on the history of the
sloshing. This is not necessarily an expected or intuitive result. Hysteresis is known for
example in a response of a material to an external force where it is forced past its elastic
limit. In that case it can be thought of as a different deformation behavior in the material
due to different stresses. For liquid this is not as easy to imagine as the liquid will not take
up any shear stresses. It is easier to think about the double solution as two different, but
equal, energy states, that the sloshing can exhibit close to the jump frequency. In the
experiments it was found that it was relatively easy to change the sloshing from the lower
branch to the upper branch by simply sweeping the smooth water body with a board
forcing an appearance of a breaking wave which then would be transformed to a break-
ing wave in accordance to the upper branch. However, it did not seem possible to „quiet"
the sloshing down from the upper branch to the lower branch. This could indicate that
the lower branch is more unstable than the upper branch.
Although it may not be expected that a sloshing of water would exhibit two states of
energy there is a parallel in hydraulics that is well known, namely, flow in an open chan-
nel can be either super critical or sub critical for the same specific energy. This may not
be a direct parallel to the sloshing of water in a tank but shows that a two state energy
solution is possible for fluids in some instances.
The width of the hysteresis is fairly narrow even though it was possible to measure many
points in the experiments for both branches due to the high quality of the experimental
equipment. The relatively narrow range of the bifurcation indicates that it is probably not
very important for the application of a tuned liquid damper in the case of an earthquake
load as the response typically covers a wide range of frequencies but does not stay at con-
stant frequency for long periods. However, it could be important for wind application,
especially if the wind response is allowed to be close to the shifted resonant frequency.
However, it is not advisable to design the TLD for wind application so the wind response
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