7.8. ADDITIONAL WAVE GENERATION TOPICS
439
Trowbridge, Dalrymple, and Suh (1986) derived an approximate secondorder solution for spiral waves generated in a constant-depth basin by a
rotating circular cylinder. Their solution was limited to cases in which the
wave amplitude is small compared with the radius of the cylinder, which
in turn is small compared with the wavelength. This assumption allowed
them to neglect the quadratic term in the free surface boundary condition.
Trowbridge, et al.’s solution predicted free secondary waves which do
not propagate at the same speed or in the same direction as the first-order
waves. Furthermore, at large distances from the spiral wavemaker these
second-order free waves with amplitudes proportional to (l/^/r) dominate
over the nonlinear second bound harmonics which have amplitudes proportional to 1/r. Laboratory measurements indicated that the second-order
waves could be predicted with reasonable accuracy.
A key conclusion from Trowbridge, et al. (1986) is that studies conducted in a spiral wave basin should not be too sensitive to wave asymmetry because this second-order wave characteristic is incorrectly represented
in the basin. They cited longshore and cross-shore transport on relatively
steep beaches as littoral processes that are not significantly affected by wave
asymmetry.
Suh and Dalrymple (1987a) reported on small-scale movable-bed model
tests conducted in a circular basin with a spiral wavemaker. They examined the morphological development of salients behind single and multiple
offshore breakwaters. Although similitude of the sediment was not maintained, consistent relationships were noted between breakwater geometric
parameters and sediment depositional parameters.
Finally, Williams and McDougal (1989) performed a first-order analysis
of a spiral wavemaker with a variable draft. Their wavemaker consisted of
an “eccentrically-mounted, right circular cylinder rotating at constant angular velocity in a basin of arbitrary uniform depth, ” and they included
the effect of a finite-width gap between the underside of the cylinder and
the basin bottom. Numerically derived plots for wave amplitude and wavemaker force and moment were also presented in the paper.
7.8.2 Wave Absorbers
One of the most common laboratory effects that plague physical model
experiments is reflection of wave energy from boundaries or from model
structures, and dealing with wave reflection ranks right behind wave gen
eration in importance to high quality laboratory experiments (Ouellet and
Datta 1986). Unwanted reflections can alter significantly the incident wave
field, which in turn may impact test results. Well conducted model studies
attempt to minimize wave reflections by placing wave absorbers at reflective
439
Trowbridge, Dalrymple, and Suh (1986) derived an approximate secondorder solution for spiral waves generated in a constant-depth basin by a
rotating circular cylinder. Their solution was limited to cases in which the
wave amplitude is small compared with the radius of the cylinder, which
in turn is small compared with the wavelength. This assumption allowed
them to neglect the quadratic term in the free surface boundary condition.
Trowbridge, et al.’s solution predicted free secondary waves which do
not propagate at the same speed or in the same direction as the first-order
waves. Furthermore, at large distances from the spiral wavemaker these
second-order free waves with amplitudes proportional to (l/^/r) dominate
over the nonlinear second bound harmonics which have amplitudes proportional to 1/r. Laboratory measurements indicated that the second-order
waves could be predicted with reasonable accuracy.
A key conclusion from Trowbridge, et al. (1986) is that studies conducted in a spiral wave basin should not be too sensitive to wave asymmetry because this second-order wave characteristic is incorrectly represented
in the basin. They cited longshore and cross-shore transport on relatively
steep beaches as littoral processes that are not significantly affected by wave
asymmetry.
Suh and Dalrymple (1987a) reported on small-scale movable-bed model
tests conducted in a circular basin with a spiral wavemaker. They examined the morphological development of salients behind single and multiple
offshore breakwaters. Although similitude of the sediment was not maintained, consistent relationships were noted between breakwater geometric
parameters and sediment depositional parameters.
Finally, Williams and McDougal (1989) performed a first-order analysis
of a spiral wavemaker with a variable draft. Their wavemaker consisted of
an “eccentrically-mounted, right circular cylinder rotating at constant angular velocity in a basin of arbitrary uniform depth, ” and they included
the effect of a finite-width gap between the underside of the cylinder and
the basin bottom. Numerically derived plots for wave amplitude and wavemaker force and moment were also presented in the paper.
7.8.2 Wave Absorbers
One of the most common laboratory effects that plague physical model
experiments is reflection of wave energy from boundaries or from model
structures, and dealing with wave reflection ranks right behind wave gen
eration in importance to high quality laboratory experiments (Ouellet and
Datta 1986). Unwanted reflections can alter significantly the incident wave
field, which in turn may impact test results. Well conducted model studies
attempt to minimize wave reflections by placing wave absorbers at reflective