7.6. IRREGULAR (2-D) WAVE GENERATION
411
Correct Reproduction of Bound Long Waves
It has long been known that naturally occurring irregular wave trains exhibit “groupiness”, with a series of consecutive waves being greater in height
than waves immediately preceding or following the wave group. Associated
with the wave group is a set-down in the mean water level that travels with
the group. This set-down has become known as the bound long wave
because, instead of obeying the usual dispersion relationship, it travels at
the group velocity, and thus, is bound to the wave group. Bound long waves
are one source of long-wave energy that can create problems for coastal engineers. Commonly cited problems induced by long-wave energy include
oscillation of moored structures, seiching in harbors and basins, and wave
runup.
Ottesen Hansen (1978) gave a method for quantifying naturally occurring bound long waves in terms of the irregular short-wave components.
He assumed the short waves could be adequately described by first-order
wave theory, and the bound long waves arose as a second-order phenomenon
when two first-order short waves of different frequencies were superimposed.
Other assumptions included a flat bottom, two-dimensional waves propagating in one direction, and negligible frictional effects.
It was immediately recognized that laboratory model studies sensitive
to energy at long-wave frequencies would benefit from correct laboratory
reproduction of group-induced bound long waves, and this lead to several
pioneering studies into the formulation of the required wave board motion.
Flick and Guza (1980) showed theoretically and with experiments that
laboratory tests using first-order irregular wavemaker theory also generates
unwanted long-wave energy that might influence the experiment outcome.
Ottesen Hansen, et al. (1980) identified the causes and components of
unwanted long-wave energy that appears in a wave flume when irregular
short waves are generated by first-order theory, and they derived a secondorder method to compensate for the unwanted long waves for the case of a
piston-type wave board.
Sand (1982) elaborated on Ottesen Hansen, et al.’s procedure; and for
the case of a piston, he gave practical advice for laboratory implementation of the second-order procedure for suppressing the unwanted long-wave
energy. Barthel, et al. (1983) provided a detailed derivation for the correct
reproduction of irregular waves and the associated bound waves for the
more general case of a wave board hinged a distance, /, below the bottom
as depicted in Figure 7.1. They also described tests that demonstrated the
successful suppression of unwanted long-wave energy.
Sand and Donslund (1985) gave examples of model studies that illustrated model response differences between first-order irregular waves, and
411
Correct Reproduction of Bound Long Waves
It has long been known that naturally occurring irregular wave trains exhibit “groupiness”, with a series of consecutive waves being greater in height
than waves immediately preceding or following the wave group. Associated
with the wave group is a set-down in the mean water level that travels with
the group. This set-down has become known as the bound long wave
because, instead of obeying the usual dispersion relationship, it travels at
the group velocity, and thus, is bound to the wave group. Bound long waves
are one source of long-wave energy that can create problems for coastal engineers. Commonly cited problems induced by long-wave energy include
oscillation of moored structures, seiching in harbors and basins, and wave
runup.
Ottesen Hansen (1978) gave a method for quantifying naturally occurring bound long waves in terms of the irregular short-wave components.
He assumed the short waves could be adequately described by first-order
wave theory, and the bound long waves arose as a second-order phenomenon
when two first-order short waves of different frequencies were superimposed.
Other assumptions included a flat bottom, two-dimensional waves propagating in one direction, and negligible frictional effects.
It was immediately recognized that laboratory model studies sensitive
to energy at long-wave frequencies would benefit from correct laboratory
reproduction of group-induced bound long waves, and this lead to several
pioneering studies into the formulation of the required wave board motion.
Flick and Guza (1980) showed theoretically and with experiments that
laboratory tests using first-order irregular wavemaker theory also generates
unwanted long-wave energy that might influence the experiment outcome.
Ottesen Hansen, et al. (1980) identified the causes and components of
unwanted long-wave energy that appears in a wave flume when irregular
short waves are generated by first-order theory, and they derived a secondorder method to compensate for the unwanted long waves for the case of a
piston-type wave board.
Sand (1982) elaborated on Ottesen Hansen, et al.’s procedure; and for
the case of a piston, he gave practical advice for laboratory implementation of the second-order procedure for suppressing the unwanted long-wave
energy. Barthel, et al. (1983) provided a detailed derivation for the correct
reproduction of irregular waves and the associated bound waves for the
more general case of a wave board hinged a distance, /, below the bottom
as depicted in Figure 7.1. They also described tests that demonstrated the
successful suppression of unwanted long-wave energy.
Sand and Donslund (1985) gave examples of model studies that illustrated model response differences between first-order irregular waves, and