1DH Boussinesq Wave Module - Examples
103
beach profile is taken from a 2D-bathymetry map covering the area north of
Torsminde harbour, see Figure 5.6.
Model setup
The model setup is illustrated in Figure 4.73. In the first part of the profile the
slope is approximately 1:100, which is increased to approximately 1:50 on the
first bar and further to approximately 1:30 on the second bar. The slope of the
still water shoreline is approximately 1:15. Waves are generated at internal
points by source terms representing the volume flux in progressive waves (at
water depth 13.7 m). The irregular wave time series is generated on basis of
a mean JONSWAP spectrum. The spectral peak wave period is 9.0 s and the
significant wave height 3.0 m. The minimum wave period included in the time
series is 2.5 s.
As the surf similarity parameter is less than 0.5 spilling breakers would also
occur in this example. The surf similarity parameter () is defined as the
beach slope divided by the square root of the deep water wave steepness.
Based on the classification of Galvin (1968) of wave breaking, Batjjes (1974)
found that spilling breakers would occur for , see Madsen et al
(1997a)
(1)
p. 295.
The seaward boundary is treated as nonreflective, using sponge layer (100
points). Also an absorbing sponge layer is used at the shoreline in this exam-
ple, see Figure 4.73, i.e. the moving shoreline is not modelled in this exam-
ple. With respect to the parameters of the breaker model the following
standard (default) values are applied: initial breaking angle
b
= 20, final
breaking angle
o
= 10, half-time for cut-off roller t
1/2
= T
p
/5 = 1.8 and roller
form factor f
d
= 1.5. Also in this example an explicit filter is introduced near
the still water shoreline to remove potential.
A structured mesh
with elements with an fixed edge length of 1.0 m is used.
For the 1980 m long channel this results in 1980 elements and 1981 nodes.
Significant wave breaking will occur at the two bars. At the first bar (water
depth about 4 m) approximately 54 nodes resolve the most energetic and
breaking waves (9 s). At the shallower bar (depth 2.1 m) approximately 41
nodes resolve the waves (9 s). The time step is 0.05 s (results in a maximum
Courant number of 0.58) and the simulation duration 1/2 hour (36001 time
steps). As usual the enhanced Boussinesq equations are solved (i.e. deep-
water terms included) in 1DH applications.
1 Paper included in the Scientific Background
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