Geoscience Reference
In-Depth Information
sidewalls whose influence upon the path of light rays could
be accounted for. In attempts to study non-axisymmetric
waves generated (e.g., by a horizontally towed object) in
a square tank, at most two perspectives at 90
◦
might
be recorded simultaneously, each with a camera on one
side and the image on the other. To gain more perspec-
tives, the experiment must be repeated but the generation
mechanism reoriented within the tank to give the cam-
eras a different perspective. This method requires perfect
repeatability. Small changes can lead to large errors in the
computation of
∇
ρ
.
10.5. OTHER ADVANCES
Thus far we have focused upon the use of schlieren to
examine internal waves in the laboratory. Here we mention
other techniques used to generate and analyze internal
waves.
10.5.1. Particle Image Velocimetry
Particle image velocimetry is now a well-established
method used in the laboratory to measure flow fields
nonintrusively. In this method, small particles are illu-
minated by a laser light sheet. Their displacements (or,
more precisely, displacements of patches of particles in
a window) are tracked between pulses of the laser. The
technique has revolutionized laboratory experiments by
providing a nonintrusive method that measures velocity
at all points in the plane of the light sheet [
Fincham and
Spedding
, 1997]. Using an oscillating mirror, one can also
make multiple parallel light sheets that sequentially illumi-
nate on a fast (typically microsecond) time scale [
Fincham
,
2006]. Thus the flow field can be reconstructed in three
dimensions to within the resolution set by the separation
between successive light sheets and the digital camera.
Using PIV in the study of internal waves poses addi-
tional challenges. Because light bends as it passes through
stratified fluid, the position of particles in the flow can be
misrepresented [
Dalziel et al.
, 2007]. One can try to elim-
inate particle distortions by adding another fluid to the
ambient (e.g., alcohol) that cancels the refractive index
change due to salinity, but this can also lead to problems
with double diffusive behavior.
Without resorting to adding refractive index matching
fluids, schlieren can be used to predict the distortion and
so provide a correction to the digitized image of particles
before they are processed to compute displacements.
For example, in the study of solitary waves by
Dalziel
et al.
[2007], the direct application of PIV was hindered
by distortions resulting from the sharp density gradient at
the interface between the fresh and underlying salty water.
Figure 10.14 shows the smearing and significant apparent
particle displacement at a sharp density gradient. This is
Figure 10.14.
Image of random dots distorted by strong stratifi-
cation at a density interface in an approximately two-layer fluid.
Reproduced from Figure 6c of
Dalziel et al.
[2007].
not due to the vertical motion of the wave. It results from
photons between the laser light sheet and observer being
deflected as they pass through the interface.
Dalziel et al.
[2007] addressed the issue by using
schlieren to measure the density gradient and then using
this information to correct for the apparent in situ parti-
cle displacement. The experimental configuration strobed
between the camera recording the positions of particles in
a laser light sheet in the fluid and it recording images of
random dots on a screen behind the tank. This effectively
rendered the schlieren and PIV measurements simultane-
ous. The result is shown in Figure 10.15. The corrected
PIV image gives values of velocity and the schlieren mea-
surements predicted the density. Importantly, the com-
bined results measured the gradient Richardson number
and so assessed the stability of internal solitary waves.
If the stratification is not too strong and disturbances
in the fluid are not too large, then the distortion due
to refractive index changes can be ignored and PIV can
be applied directly. This method was used successfully in
the measurement of internal waves generated by oscil-
latory flow over cylinders [
Zhang et al.
, 2007] spheres
[
King et al.
, 2009] and a Gaussian-shaped hill [
Echeverri
etal.
, 2009]. In these cases the distortions due to isopycnal
