Geoscience Reference
In-Depth Information
(a)
(d)
I
II
I
II
0.15
0.15
0.10
0.10
0.05
0.05
0
0.1
0.2
0.3
0
0.1
0.2
0.3
(b)
(e)
0.15
0.15
0.10
0.10
0.05
0.05
0
0.1
0.2
0.3
0
0.1
0.2
0.3
(c)
(f)
∣
u
/
U
∣
1.8
0.15
0.15
1.2
0.10
0.10
0.6
0.05
0.05
0
0.1
0.2
0.3
0
0.1
0.2
0.3
x
(m)
x
(m)
Figure 10.16.
Experimental measurements (top), numerical results (middle), and theoretical predictions (bottom) of internal waves
generated by oscillatory flow over a Gaussian hill in cases where the frequency of oscillation is subcritical (left) and supercritical
(right). Reproduced from Figure 2 of
Echeverri et al.
[2009].
Consequently, this can be used to assess mixing and trans-
port in fluids.
The technique has been used somewhat differently in
the study of internal waves generated by a moving sphere
in uniformly stratified fluid. Following the technique
originally devised by of
Hopfinger et al.
[1991],
Voisin
et al.
[2011] (see also
Ermanyuk et al.
[2011]) made thin,
evenly spaced horizontal dye lines by soaking threads with
fluorescein dye and slowly dragging them horizontally
through a tank filled with uniformly stratified fluid. This
created very thin markers of isopycnal surfaces that were
clearly revealed as a sequence of lines in a vertical plane
illuminated by a laser light sheet. The position of each line
could be determined to subpixel accuracy by assuming a
Gaussian vertical distribution of intensity.
An example of the displacement computed from suc-
cessive dye lines in a plane passing through the center of
a horizontally oscillating sphere is shown in Figure 10.17.
Even where the displacement of lines is not obvious to the
naked eye, they are clearly discerned by the digital analysis
technique.
10.5.3. Novel Wave Generator
Typical methods for generating internal waves in the
laboratory include oscillating a rigid body at constant
frequency or towing a body horizontally at a constant
speed. The former has the disadvantage that it creates four
wave beams, as in Figure 10.2, or at least two if oscillated
against a side boundary. Towed objects along a top or bot-
tom boundary produce unidirectional waves, but towing
piles up the stratified fluid ahead of the object forming
what is called a “columnar mode.”As a result, the endwall
of the tank can influence the dynamics of flow over the
obstacle [
Baines
, 1995].
A new mechanism for the generation of internal waves
avoids these deficiencies [
Gostiaux et al.
, 2007;
Mercier
et al.
, 2010]. In it vertically stacked flat plates periodically
move back and forth providing forcing on the stratified
fluid from the side. If the forcing is driven by a rotat-
ing spiral camshaft, as in Figure 10.18, the plates effec-
tively move collectively as a vertically propagating wave
whose vertical wavelength and amplitude are set by the
