Geoscience Reference
In-Depth Information
and Rarity
[1967] found that the arms of the cross-pattern
of waves formed a fixed angle
from the vertical that was
related to the ratio of
ω
to
N
by
horizontal black-and-white lines resulting when a set of
model sinusoidal “hills” are towed from left to right over
the surface of a tank filled with uniformly stratified fluid.
In the initial image, shown in Figure 10.3a, the hills
immersed in the ambient are apparent near the top of the
frame. The black-and-white lines are not in the tank, how-
ever. The image is situated approximately 10 cm behind
the tank. After the hills are set in motion, various dis-
turbances in the ambient can be seen as a result of the
distortion of the image (Figure 10.3b). In the lee of each
hill, boundary layer separation results in large perturba-
tions that warp and blur the lines. Furthermore, below the
hills the eye can barely make out smaller undulations of
lines in the image.
These alterations can be enhanced through digital image
processing. Each snapshot can be represented as an array
of pixels with each pixel given a number corresponding to
its intensity (e.g., 0 for black, 1 for white, and in between
for gray). The image in Figure 10.3c is produced by taking
the difference of the digitized snapshot in (b) from that
in (a), then taking the absolute value and multiplying the
result by an enhancement factor, typically 10. Thus even
small changes to the image become obvious.
One advantage of synthetic schlieren is that its sensitiv-
ity can be increased by widening the distance between the
test section and the image behind it. For example, it is easy
to observe heat rising off one's hand if the image is several
meters away.
= cos
−
1
(ω/N)
.
Color filters have allowed schlieren to be more quanti-
tative [
Howes
, 1984;
Teoh et al.
, 1997;
Chashechkin
, 1999].
But the expense and physical constraints imposed by the
need for well-aligned pairs of parabolic mirrors has lim-
ited the use of schlieren until recently.
Schlieren technology has advanced enormously since
the mid-1990s. As a result of digitization technology
and computers, “synthetic schlieren” was developed as
an inexpensive, versatile and, most importantly, quanti-
tative tool for sensitively measuring density perturbations
in stratified fluids.
In what follows we examine how synthetic schlieren has
been used to test theory and to develop new insights into
thedynamicsof internalwaves.Intheprocesswereviewan
analysis method for separating out waves propagating in
different directions and we describe a recently developed
mechanism for generating waves that does not suffer some
of the drawbacks of oscillating or towed rigid objects.
Section 10.2 briefly discusses how synthetic schlieren
visualizes disturbances in a fluid through contrasting
snapshots taken by a digital camera looking through the
fluid at a black-and-white image of lines or dots. If the
disturbances are small, the displacements of objects in
the image can be computed and, from these, the magni-
tude of the disturbance calculated. This is described in
Section 10.3 with the assumption that the disturbance in
the tank is uniform across the line of sight. The treatment
of axisymmetric and fully three-dimensional disturbances
is described in Section 10.4. Other advances in gener-
ating internal waves and analyzing them using PIV are
described in Section 10.5. Future directions are described
in Section 10.6.
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10.3. SPANWISE-UNIFORM DISTURBANCES
10.3.1. Quantitative Synthetic Schlieren
When light passes through a medium whose refractive
index changes in space, it is deflected in a manner well
predicted by Snell's law. In the particular case of stably
stratified fluid, the density
ρ
and hence refractive index
n
change with height
z
. The path of light passing in the
y
direction through the fluid at a small angle to the vertical
from the
y
axis is given by [
Sutherland et al.
, 1999]
10.2. QUALITATIVE USE OF SYNTHETIC
SCHLIEREN
Synthetic schlieren [
Dalziel et al.
, 2000] makes away
with the need for parabolic mirrors to straighten and refo-
cus a localized light source. Instead, a camera is focused
upon an image behind a tank filled with salt-stratified
fluid.
1
Disturbances in the fluid displace isopycnal sur-
faces and so locally change the refractive index of the
salt water through which light passes from a point on
the image through the tank to the camera. The image
apparently distorts as a result.
For example, Figure 10.3 shows how qualitative syn-
thetic schlieren observes distortions of an image of
d
2
z
dy
2
1
n
0
∂n
∂z
.
(10.2)
Here
n
0
is the characteristic refractive index of the fluid
(e.g.,
n
0
= 1.3330 for pure water).
In uniformly stratified fluid, the vertical gradient of
the refractive index can be related to the vertical density
gradient:
∂n
∂z
=
dn
∂ρ
T
∂z
.
(10.3)
dρ
1
Synthetic schlieren has also been called “background oriented
schlieren” by
Meier
[2002], who used it to visualize and measure shock
waves in air.
¯
Here
ρ
T
denotes the sum of the ambient density
ρ(z)
and
the perturbation density
ρ(
x
,
t)
.
