Spurious Waves During Generation of Multi-Chromatic Waves in the Wave Tank in Shallow Water

Abstract

Accurate generation of the primary waves and the reproduction of the group-induced second-order low and high frequency waves have been considered essential for physical i.e. model test in the laboratory. In the laboratory when multi-chromatic primary waves are generated the required bounded waves will be generated naturally at the difference frequencies. In addition to that several unwanted free waves are also generated. The free waves, having the same frequencies of the bounded waves are reproduced due to mismatch of the boundary conditions at the wave paddle. The other two types of free waves are due to the wave paddle displacement and the local disturbances. We carried out physical experiments to identify the second order spurious waves in shallow water in the Offshore Engineering Basin (OEB) at the Institute for Ocean Technology (IOT) of National Research Council (NRC) Canada. In the basin water depths in the range of 0.4m to 0.6m are used for the experiments. The peak wave periods also have varied from 1.133s to 2.145s. In the experiments multi-chromatic waves are used. The drive signals of the wave-makers are generated using first-order and second-order wave generation techniques. Total 14 wave probes are used to capture the data in the wave tank. A NRC-IOT code is used to isolate the primary waves, the bounded waves and the unwanted free waves from the measured data at each wave probe. The measured data are analyzed in this paper to illustrate the differences in the waves generated by two different generation techniques. KEYWORDPhysical experiments, multi-chromatic shallow water waves, second order waves, Bounded waves, second-order spurious waves, data comparisons.

Behavior of the Residual Wave Components in a 3D Wave Basin After the Termination of the Wave Maker

“…In this paper only three cases of monochromatic and three cases of bi-chromatic waves are presented and discussed but more emphasis is given to Case-2 and Case-4. In an earlier analysis it was observed that the total unwanted free wave components are in the range of 1 to 4% (Zaman et al, 2011) of the incident wave height and not discussed here. For Case-2 (mono-chromatic) it is observed that the tank's natural frequency energy components are very small compare to the total energy and is of O(10 -3 ) or less.…”

“…Very limited results are also incorporated on irregular waves in this paper. Wave splitting described Mansard et al (1987) and Zaman et al (2010Zaman et al ( , 2011) was used to separate the different wave components -primary wave(s), bounded wave(s) and free wave(s). Natural frequency components in the longitudinal and transverse directions were identified using Equations 9 to 14.…”

“…So we have to be sure that the available surface undulation is already small enough not to contaminate the next "run". When we generate waves in the tank we obtain the primary wave components, bounded waves, interacted wave components, unwanted free wave components [Zaman et al (2010 and2011), Zaman and Mak (2007), Mansard et al(1987), Sand and Mansard (1986)] and some contribution of natural frequency energy components of the wave tank. Interactions of the wave components are numerous but are not necessarily important due to their small amplitudes.…”

Validation of a hydrodynamic model for a curved, multi-paddle wave tank

“…In practice, second-order, directional wave generation techniques are found to be rather complex to implement, and only limited experimental results have so far been published for these techniques. Whilst Zaman et al [ 25 ] investigate second-order generation in a wave tank, only straight waves are considered. It is also important to note that all the studies on 3D tanks noted above (in effect) assume positioncontrolled wavemakers (with given motions imposed) rather than absorbing, force-feedback generators.…”

“…There have been no studies to date looking at second-order free waves in the curved tank, but experimental results for a rectangular, shallow water tank can be found in Zaman et al [ 25 ]. Second-order free waves are shown in the context of a numerical, rectangular wave tank in Le Touze et al [ 35 ].…”