Geoscience Reference
In-Depth Information
(a)
(b)
0.07
0.07
0.06
0.06
0.05
0.05
0.04
0.04
0.03
0.03
0.02
0.02
0.01
0.01
1
1.5
2
2.5
3
1
1.5
2
2.5
3
f
(rad/s)
f
(rad/s)
(c)
0.07
0.06
0.05
0.04
0.03
0.02
0.01
1
1.5
2
2.5
3
f
(rad/s)
Figure 12.8.
Contour plots of (a) the time of wave breaking in seconds, (b) the breaking wavelength in centimeters, and (c) the
breaking wave amplitude in centimeters, calculated using the nondispersive (
γ
= 0) wave equation (12.28). The contours have
been interpolated linearly between data points, which are indicated by crosses.
and the filtering must be adjusted to each experiment due
to variations in the color of the dye line and the hues of
the images.
theory, numerical solutions, and experiments, we define
T
B
as the smallest
t
for which the corresponding wave-
breaking condition is satisfied. In Figures 12.8a, 12.9a,
and 12.10a, we plot
T
B
over our experimental ranges of
f
and
f
, as calculated from our nonlinear wave theory, our
numerical solutions, and our experiments, respectively.
The variation of
T
B
with
f
and
f
is qualitatively
similar in our nonlinear wave theory and QG numeri-
cal solutions: A swift coastal current or strong rotation
leads to the wave breaking much more rapidly than a
slow current or weak rotation. However, solutions of
the nonlinear wave equation break more than twice as
12.6.2. Onset of Wave Breaking
The time at which the wave first breaks serves as a
direct quantitative comparison of our theoretical, numer-
ical, and experimental results. It is also an indication of
how effectively PV is conserved as fluid crosses the shelf
line, as waves of the same length will tend to steepen more
quickly if they entrain a larger relative vorticity. In our
