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(x, z)
Figure 7.25b Plotted in (b) are contours of the potential temperature at four uniformly
spaced times for the same parameters used. [After Seyler (2005). Reproduced with per-
mission of the American Geophysical Union.]
counterclockwise rotation. This implies a positive potential temperature pertur-
bation above and a negative perturbation below the center line. The streamline
contours before the vertical boundaries have begun to fall off exponentially so
that the effect of the periodic boundary conditions is negligible.
The structure of the bore flow and potential temperature fields in the Seyler
model is consistent with that proposed by Dewan and Picard (1998). Bores have
only odd symmetry (i.e., area varicose mode) in the flow field. This corresponds
to the odd-node number eigenmodes. Even eigenmode bores have not been
found in these numerical solutions. This is expected because the nonlinear
steepening process resulting from flow advection of the potential temperature
is not significant for even parity solutions. A property found in the simulations
that differs from that assumed by Dewan and Picard (1998) is the constancy
of the wavelength, or, perhaps more properly, the separation between crests.
Seyler finds that the wavelength decreases from the front to the back of the bore.
The variation in peak separation can be large, as in runs 5 and 7 or considerably
smaller, as in runs 1, 2, 3, and 4, and depends significantly on the time at which
the separation is measured.
The linear bore phase speed is close to that predicted by linear theory—namely,
1
h
2 hN 0
π
4
π
c
=−
2 |
k
|
For example, using k
=
2
π/
18
0
.
35 in run 1, the linear model phase speed
is c
=
0
.
55. This is very close to the simulation value for the bore speed, which
is 0.54.
 
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