Geoscience Reference
In-Depth Information
49
-49
100
200
t
, s
300
400
Figure 5.8.
Hovmöller diagram showing the time line of the
x
component of velocity of the flow shown in Figure 5.5 measured
along the
y
axis across the tank. The gray scale shows velocity in the range from -0.8 to 0.8 cm/s. The
y
axis crosses the wall of the
tank at
y
=
49 cm and
y
= 49 cm (6 o'clock and 12 o'clock, respectively). The meanders of the coastal current passing through
these two points are clearly visible along the bottom and the top of the diagram. Inertial waves emitted by the meanders can be
seen in the interior in the form of lighter and darker bands.
−
interact with each other by pairing. Video sequences of
this flow reveal that spontaneous bursts of wave radiation
occur in this flow. The waves are radiated by the evolv-
ing meanders and then propagate toward the center of
the tank. Fluid in the interior of the tank away from the
stratified coastal current at the wall is unstratified.
The waves propagating in the interior have frequency
below the inertial frequency and are pure inertial waves.
Their amplitude is quite low, and it is difficult to see them
in still images. The area where the waves can be seen is indi-
cated by the arrow in Figure 5.7a. To visualize the waves
more clearly and to follow their evolution in time, a Hov-
möller diagram can be used (see Figure 5.8). The diagram
shows the time evolution of velocity measured along a line
across the tank. The dynamical range of velocities is inten-
tionally reduced in the diagram to reveal low-amplitude
waves. The bursts of inertial waves in the interior can be
traced to meanders of the coastal current at the wall of
the tank (top and bottom of the diagram). It is clear that
the waves are mostly emitted by small-scale meanders (see
top half of Figure 5.8, where most of the inertial waves
are visible and where the meanders are smaller than on
the bottom), which indicates that a certain match in scale
and synchronization in time between meanders and waves
must be realized for the effective emission. One might
expect that the size of the meanders determines the wave-
length of the wave while the translation velocity of the
meander is matched to the phase speed of the wave, similar
to that described by
Afanasyev
[2003].
Figure 5.9 shows velocity profiles measured across the
coastal current and across the wave at three different times
separated by small time intervals. One can see that the
crest of the wave (indicated by the arrows in Figure 5.9)
propagates toward the wall. This might seem counterin-
tuitive because the source of the wave is the meander at
the wall so the wave might be expected to propagate away
from the source (similar to the way that gravity waves on
the surface of a pond propagate away from a thrown rock).
However, this is in fact one of the peculiarities of iner-
tial waves. Their phase speed is directed
toward
the source
while the group velocity is of course directed away from
the source such that the energy propagates away.
Another example of the interesting interplay between
vortices and waves is provided by our recent experi-
ments with rotating (nearly) two-dimensional turbulence
[
Afanasyev and Craig
, 2013;
Zhang and Afanasyev
, 2014].
Rotating turbulence is relevant to a wide range of
applications, including geophysical, astrophysical, and
engineering flows. It has been the subject of theoreti-
cal and experimental studies for quite a long time [e.g.,
Ibbetson and Tritton
, 1974;
1974;Hopfinger et al.
, 1982;
Jacquin
et al.
, 1990;
Morize et al.
, 2005;
Bewley et al.
, 2007],
yet it is not completely understood. In our experiments
it was desirable to avoid the
β
-effect by using the
f
-
plane setup, namely a uniformly rotating fluid of constant
depth. Since it was also desirable to take advantage of the
AIV technique, which requires the paraboloidal surface,
a paraboloidal bottom was employed. The null rotation
of the table was such that the form of the free surface of
water was approximately the same as that of the bottom,
thus providing a layer of constant depth. The container
with paraboloidal bottom was of diameter
D
=90cmand
was inserted into the main tank.
The flow was forced electromagnetically [e.g.,
Marteau
et al.
, 1995;
Afanasyev and Wells
, 2005]. For this pur-
pose over 300 permanent rare earth magnets (size 2.5
×
2.5cm
2
)
of alternating polarity were attached under the
bottom of the container such that the distance between
the magnets was 4.5 cm. The water in the tank was
saline to allow electric current to flow between two elec-
trodes placed at the sides of the container. The Lorentz
force on the ions occurs due to the vertical magnetic
