7.3. FIRST-ORDER WAVE GENERATION
353
nite amplitude waves generated by the first-order wavemaker equation are
smaller than predicted by first-order theory. Ursell, et al.’s tests were the
first verification of first-order wavemaker theory for the case of a pistontype board. They conjectured that first-order theoretical expressions for
more complicated wave boards (and also board forces) also were probably
correct.
Madsen (1970) surmised that leakage around the wave board played
a significant role in the variations found between measurements and firstorder wavemaker theory, and he performed an analysis of the leakage problem. He also noted that Ursell, et al. tried to seal the gap around the wave
board in their experiment, but it may have been possible that the seal
was less effective for the steeper waves, thus causing the deviation between
measurements and theory.
Flick and Guza (1980) measured values of wave amplitude-to-stroke for
a flap-type wave board in a 50-cm-wide wave channel. They also obtained
good correspondence to first-order theory after sealing leaks on the sides of
the wave board.
The wave height capability of a particular wavemaker (assuming adequate power to drive the wave board) is a function of its maximum usable
stroke, coupled with water depth and wave period. Figure 7.4 displays the
maximum regular wave height operating envelope for a piston-type wavemaker at the Waterways Experiment Station. The dashed line labeled
“First-Order Theory” is simply a plot of Eqn. 7.58 for the specified water
depth and maximum board stroke. Notice how the wavemaker theory increases very rapidly as wave period decreases below about 2 s. The dashed
line labeled “H/Lo = 0.142” is the theoretical wave steepness limit, and
the horizontal dashed line is the theoretical shallow water wave breaking
condition.
The solid data points on Figure 7.4 are measured wave heights produced
at maximum stroke. Data were collected at three gage locations over a flat
bottom and then averaged. The hollow data points are also measured
wave heights, but in these cases, the breaking limit was reached before the
maximum stroke limit. Increasing the stroke further would not produce
any increase in wave height. Additional curves could be generated for
different water depths, and they would show that wave generating capability
decreases as the water depth decreases.
Example 7.1. First-Order Two-Dimensional Wavemaker |
A wavemaker with water on only one side is to be used to generate uniform waves
having a height of H = 6 cm (2.4 in) and a period T = 2 s in water depth of h = 25
353
nite amplitude waves generated by the first-order wavemaker equation are
smaller than predicted by first-order theory. Ursell, et al.’s tests were the
first verification of first-order wavemaker theory for the case of a pistontype board. They conjectured that first-order theoretical expressions for
more complicated wave boards (and also board forces) also were probably
correct.
Madsen (1970) surmised that leakage around the wave board played
a significant role in the variations found between measurements and firstorder wavemaker theory, and he performed an analysis of the leakage problem. He also noted that Ursell, et al. tried to seal the gap around the wave
board in their experiment, but it may have been possible that the seal
was less effective for the steeper waves, thus causing the deviation between
measurements and theory.
Flick and Guza (1980) measured values of wave amplitude-to-stroke for
a flap-type wave board in a 50-cm-wide wave channel. They also obtained
good correspondence to first-order theory after sealing leaks on the sides of
the wave board.
The wave height capability of a particular wavemaker (assuming adequate power to drive the wave board) is a function of its maximum usable
stroke, coupled with water depth and wave period. Figure 7.4 displays the
maximum regular wave height operating envelope for a piston-type wavemaker at the Waterways Experiment Station. The dashed line labeled
“First-Order Theory” is simply a plot of Eqn. 7.58 for the specified water
depth and maximum board stroke. Notice how the wavemaker theory increases very rapidly as wave period decreases below about 2 s. The dashed
line labeled “H/Lo = 0.142” is the theoretical wave steepness limit, and
the horizontal dashed line is the theoretical shallow water wave breaking
condition.
The solid data points on Figure 7.4 are measured wave heights produced
at maximum stroke. Data were collected at three gage locations over a flat
bottom and then averaged. The hollow data points are also measured
wave heights, but in these cases, the breaking limit was reached before the
maximum stroke limit. Increasing the stroke further would not produce
any increase in wave height. Additional curves could be generated for
different water depths, and they would show that wave generating capability
decreases as the water depth decreases.
Example 7.1. First-Order Two-Dimensional Wavemaker |
A wavemaker with water on only one side is to be used to generate uniform waves
having a height of H = 6 cm (2.4 in) and a period T = 2 s in water depth of h = 25