Theoretical and experimental studies of three-dimensional wavemaking in narrow tanks, including nonlinear phenomena near resonance

Yao, Yiyang; Tulin, Marshall P.; Kolaini, Ali R.

doi:10.1017/s0022112094002533

Cited by 7 publications

(8 citation statements)

References 7 publications

(17 reference statements)

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“…A pump at the downstream end of the flume drove a return flow through a pipe beneath the flume that entered the main flume at the upstream end, forcing a steady current along the test section. Waves were generated at the upstream end of the flume using a plunger-type wavemaker based on the design of Yao (1992). At the downstream end, waves passed over a shallow weir designed to limit reflections.…”

Section: Methodsmentioning

confidence: 99%

Interaction of waves and currents with kelp forests (Macrocystis pyrifera): Insights from a dynamically scaled laboratory model

Rosman

Denny

Zeller

et al. 2013

Limnology & Oceanography

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The interaction of surface waves and currents with kelp forests was examined under controlled conditions using a dynamically matched 1/25-scale physical model in a laboratory flume. In experiments with kelp mimics, waves increased the time-averaged drag by a factor of 2 and altered the shape of current profiles. Relative motion between model kelp and water under waves increased wake generation of turbulence, resulting in turbulent kinetic energies 2-5 times larger, and eddy viscosities 20-50% larger, than for experiments without waves. Because mixing lengths were reduced to wake-scales in the model kelp forest, eddy viscosities were 25-50% smaller than when kelp was absent. In the model kelp-forest surface canopy where solid obstacles were most densely spaced, wave orbital velocities were reduced by , 10% from linear wave theory predictions. This decrease in wave orbital velocities is thought to result primarily from inertial forces exerted on water by model kelp. Stokes drift was reduced by , 20% as a result of the change in wave orbital velocities. Although hydrodynamics within kelp forests are more complex than in the laboratory experiments and a wide range of flow conditions can occur, laboratory results suggest that (1) kelp forest drag is increased by waves; (2) wave properties can be altered by drag and inertial forces; and (3) wake production of turbulence caused by waves may be the main source of turbulence in dense kelp stands. Interactions between kelp and waves must therefore be taken into account when developing models for drag and mixing in these systems.

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Section: Methodsmentioning

confidence: 99%

Interaction of waves and currents with kelp forests (Macrocystis pyrifera): Insights from a dynamically scaled laboratory model

Rosman

Denny

Zeller

et al. 2013

Limnology & Oceanography

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“…. ), and, therefore, the cross-wave (or the sloshing wave) studied by Jones (1984), Kit, Shemer & Miloh (1987) and Yao, Tulin & Kolaini (1994), or the oblique waves studied by Trulsen, Stansberg & Velarde (1999) were not excited directly. As a comparison, the off-resonant case was tested as well.…”

Section: Experimental Conditionsmentioning

confidence: 98%

“…The corresponding wavelength is 6.67 m, which is 2/3 of the tank width. Because the secondary wave propagates across the tank, it will inevitably excite a sloshing mode in the tank (Jones 1984;Kit et al 1987;Yao et al 1994). By intentionally exciting this cross-wave, the detection of the third-order wave resonance should become easy (case 1, figure 3a).…”

Section: Current Field In the Tankmentioning

confidence: 99%

Third-order resonant wave interactions under the influence of background current fields

et al. 2015

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A series of experiments were conducted in a wave basin (50 m long, 10 m wide and 5 m deep) generating two waves propagating at an angle by a directional wavemaker. When the two waves were selected from a resonant triplet, an initially non-existing wave grew as the waves propagated down the tank. The linear growth rate of the resonating wave agreed well with third-order resonance theory based on Zakharov's reduced gravity equation. Additional experiments with opposing and coflowing mean current with large temporal and spatial variations were conducted. As the flow rate increased, the linear growth was suppressed. As reproduced numerically with Zakharov's equation, the resonant interaction saturated at time scales inversely proportional to the magnitude of the forced random resonance detuning. It is conjectured that the resonance is detuned by the variation and not by the mean of the current field due to wavelength-dependent Doppler shift and to the refraction of wave rays. Further analysis of the spectral evolution revealed that while discrete peaks appear at high frequencies as a result of dynamical cascading, a continuously saturated spectrum develops in the background as the current speed increases. Additional experiments were conducted studying the evolution of the random directional wave on a dynamical time scale under the influence of current. Due to random resonance detuning by the current, the spectral tail tended to be suppressed.

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“…12,13 We predict that quadratic NLS solitary waves can occur in a pendulum lattice with double cylindrical interrupters, or any lattice with nonanalytic nonlinearities in the broad class mentioned above. Furthermore, because the mathematical description of a lattice of coupled oscillators near the lower cutoff mode is closely related to that of acoustic, 14,15 model, 16 and surface [17][18][19][20][21] waveguides near a cutoff mode, these solitary waves can occur in waveguides with similar nonanalytic nonlinearities. In particular, we show that compressional waves in sandstone can be modeled by such a softening nonanalytic nonlinearity, and that the transverse displacement in a waveguide of this medium is described by a quadratic NLS equation.…”

Section: And a Force Proportional Tomentioning

confidence: 99%

“…For example, essentially the same equations arise in the description of modulations of transverse modes in acoustic 14,15 and model 16 waveguides, as well as surface cross modes in a channel of liquid. [18][19][20][21] To determine the equations that describe the modulations ͑24͒ for the nonanalytic lattice represented by Eqs. ͑23͒, we first note that the linear terms must be identical to those in the cubic NLS equations ͑25͒.…”

Section: Lattices and Nonlinear Schrö Dinger Equationsmentioning

confidence: 99%

Nonanalytic nonlinear oscillations: Christiaan Huygens, quadratic Schrödinger equations, and solitary waves

Denardo

1998

The Journal of the Acoustical Society of America

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An example of an oscillatory system with a time-reversible nonanalytic nonlinearity is shown to be a pendulum with a flexible cord sandwiched between two identical circular disks, in contrast to the analytic case of a pendulum interrupted by a single circular disk. The amplitude-dependent frequencies of both cases are perturbatively calculated, and are compared to numerical simulations over the entire range of amplitudes. The nonanalyticity causes the unusual effect of the frequency to vary linearly with amplitude for small amplitudes, which has also been observed in the resonant frequencies of compressional standing waves in sandstone. A general condition for a nonanalytic nonlinearity to yield this behavior is presented. The amplitude-dependent frequency for the double-interrupted pendulum allows an explanation for Huygens'surprising observation that circular interrupters were as effective as cycloidal interrupters in achieving isochronous motion. A lattice of linearly coupled double-interrupted pendulums is described near the lower and upper cutoff modes by quadratic nonlinear Schrödinger ͑NLS͒ equations, in contrast to cubic NLS equations which arise for analytic pendulum lattices as well as typical acoustic and surface waveguides. Solitary breather and kink solutions to the quadratic NLS equations are presented, and are compared to the known soliton solutions of the corresponding cubic NLS equations. Compressional waves in sandstone are shown to be modeled by the inclusion of a nonanalytic quadratic nonlinearity in the stress-strain relationship. Quadratic NLS breathers are predicted to occur in a waveguide of sandstone, and an analysis indicates that such an observation is feasible.

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Theoretical and experimental studies of three-dimensional wavemaking in narrow tanks, including nonlinear phenomena near resonance

Cited by 7 publications

References 7 publications

Interaction of waves and currents with kelp forests (Macrocystis pyrifera): Insights from a dynamically scaled laboratory model

Interaction of waves and currents with kelp forests (Macrocystis pyrifera): Insights from a dynamically scaled laboratory model

Third-order resonant wave interactions under the influence of background current fields

Nonanalytic nonlinear oscillations: Christiaan Huygens, quadratic Schrödinger equations, and solitary waves

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