EM 1110-2-1100 (Part II)
30 Apr 02
2π R
1
T '
(II-7-17)
kR
gd
(8) It is interesting to note that the resonant period increases as the aspect ratio increases, even for the
fully open harbor. The change is due to the effect of the confluence of the entrance and the open sea.
Resonant periods estimated from Figure II-7-30 generally differ from the simple approximation in
Equation II-7-12.
(9) The simple guidance has some important limitations relative to real harbors. Amplification factors
are upper bounds, since no frictional losses were modelled. Harbors that are not narrow experience transverse
oscillation modes that are not represented in the simple guidance. Harbors with asymmetric entrances
experience additional transverse modes of oscillation and possible increases in amplification factor (Ippen
and Goda 1963). In addition to introducing new resonant frequencies and modified amplification, transverse
oscillations change the locations of nodes, as illustrated in Figure II-7-32 based on numerical model
calculations.
(10) Harbor oscillation information is available for some other simple harbor shapes. Circular harbors
were investigated by Lee (1969) and reviewed by Raichlen and Lee (1992). Zelt (1986) and Zelt and
Raichlen (1990) developed a theory to predict the response of arbitrary shaped harbors with interior sloping
boundaries, including runup. The dramatic effect of a sloping rather than flat bottom on the behavior of a
rectangular harbor is illustrated in Figure II-7-33. The sloping bottom greatly increases A and greatly reduces
kR values at resonance. For example, kR for the second resonant peak drops from 4.2 for the flat bottom case
to 2.6 for the sloping bottom case. The first two resonant modes for six symmetric, fully open configurations
are given in Figure II-7-34. The A for the first mode is much more affected by the sloping bottom than by
the harbor planform. Details are available in Zelt (1986).
f.
Open basins - complex shapes.
(1) Real harbors never precisely match the simple shapes; usually they differ significantly. Complex
harbors can be analyzed with physical and numerical models. These modeling tools should be applied even
for relatively simple harbor shapes when the study has large economic consequences and accurate results are
essential. A combination of physical and numerical modeling is usually preferred for investigating the full
range of wave conditions in a harbor (Lillycrop et al. 1993).
(2) Physical models generally represent the shorter-period harbor oscillations more accurately. The har-
bor and immediately surrounding coastal areas are sculpted in cement in a three-dimensional model basin
(Figure II-7-35). Breakwaters and other structures that transmit significant amounts of long-wave energy are
properly scaled in the model for size and permeability. Currents can be introduced when needed to represent
field conditions. Limitations to physical modeling include cost, no direct simulation of frictional dissipation,
and the inherent difficulties in working with long waves in an enclosed basin. Special care is required to
properly generate long waves. Once generated, they tend to produce undesirable reflections from basin walls.
(3) Numerical models are most useful for very long-period investigations, initial studies, comparative
studies of harbor alternatives, and revisiting harbors documented previously with field and/or physical model
data. They are also most useful when unusually large areas and/or very long waves are to be studied. For
example, numerical models have been used effectively to select locations for field wave gauges (to avoid
nodes) and to identify from many alternatives the few most promising harbor modification plans for fine
tuning in physical model tests. Lillycrop et al. (1993) suggested that numerical modeling is preferable to
II-7-40
Harbor Hydrodynamics
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