Geoscience Reference
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(a)
(b)
25
25
20
20
15
15
10
10
5
5 0
0
5
10
15
20
25
5
10
15
20
25
x
(cm)
x
(cm)
(c)
25
20
15
10
5 0
5
10
15
20
25
x (cm)
Figure 10.3. (a) Side view looking through tank filled with salt-stratified fluid with model inverted sinusoidal hills at the surface
and an image of horizontal black-and-white lines placed behind the tank. (b) Side view after hills have been towed slowly a
distance of one hill width. (c) Qualitative synthetic schlieren image produced by taking the absolute value of the difference of
the digitized images shown in (a) and (b). Also evident in (a) and (b) is a dark vertical streak above x
20 cm. This is a vertical
dye line suspended in the fluid itself. Its displacement can be used to determine mean horizontal flow, which is retrograde to the
towing direction of the hill.
In computing image displacements, it is sometimes
more intuitive to compute them in terms of the squared
buoyancy frequency rather than density gradients. The
local stratification resulting from both the background
and perturbation density is expressed by the total squared
buoyancy frequency:
Thus vertical variations of the refractive index can be
written in terms of N T by
∂n
∂z =
n 0 γ N T 2 ,
(10.5)
in which the coefficient γ is defined so that
1
g
ρ 0
n 0
dn
g
ρ 0
∂ρ T
∂z .
10 4 s 2 / cm.
N T 2 =
γ
1.878
×
(10.6)
(10.4)
 
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