scholarly journals CORRECT REPRODUCTION OF GROUP-INDUCED LONG WAVES

1980 ◽  
Vol 1 (17) ◽  
pp. 47
Author(s):  
N.E. Ottesen Hansen ◽  
Stig E. Sand ◽  
H. Lundgren ◽  
Torben Sorensen ◽  
H. Gravesen
Keyword(s):  
Second Order ◽  
Long Waves ◽  
Wave Problem ◽  
Wave Groups ◽  
Storm Waves ◽  
Slow Drift ◽  
Short Period ◽  
Harbour Resonance ◽  
The Waves ◽  
Wave Phenomena

In nature short period storm waves generate longer waves with periods corresponding to the wave group periods. The long waves are generally referred to as the wave set-down of water level. The set-down term is of second order in the height of the short waves. With first order reproduction of natural storm waves in the laboratory, the setdown bound to the wave groups is not reproduced. As a result, various free waves are generated, propagate towards the model and reflect from the boundaries. These so-called parasitic waves cause an exaggeration of long wave phenomena, such as harbour resonance and slow drift oscillations of moored ships. The parasitic waves can be eliminated by means of compensating free waves imposed on the system by second-order paddle motion reproducing the natural set-down. The control signal for this motion has been calculated and checked by testing. The agreement between calculated and measured results is found to be good. Further, an alternative method for reducing the parasitic wave problem is presented. Utilizing the shoaling properties of the various waves, the influence of parasitic waves can be diminished by generating the waves in somewhat deeper water before they propagate into the shallower model area.

Harbour excitations by incident wave groups

1990 ◽  
Vol 217 ◽  
pp. 595-613 ◽  
Author(s):  
Jiang-Kang Wu ◽  
Philip L.-F. Liu
Keyword(s):  
Incident Wave ◽  
Multiple Scales ◽  
Low Frequency ◽  
Second Order ◽  
Long Waves ◽  
Wave Groups ◽  
Order Of Magnitude ◽  
Harbour Resonance ◽  
Analytical Expressions ◽  
Multiple Scales Perturbation Method

By using the multiple-scales perturbation method, analytical solutions are obtained for the second-order low-frequency oscillations inside a rectangular harbour excited by incident wave groups. The water depth is a constant. The width of the harbour entrance is of the same order of magnitude as the wavelength of incident carrier (short) waves, but small in comparison with the wavelength of the wave envelope. Because of the modulations in the wave envelope, a second-order long wave is locked in with the wave envelope and propagates with the speed of the group velocity. Outside the harbour, locked long waves also exist in the reflected wave groups, but not in the radiated wave groups. Inside the harbour, the analytical expressions for the locked long waves are obtained. Owing to the discontinuity of the locked long waves across the harbour mouth, second-order free long waves are generated. The free long waves propagate with a speed of (gh)½ inside and outside the harbour. The free long waves inside the harbour may be resonated in a low-frequency range which is relevant to the harbour resonance.

On Sequence of High Waves in Nonlinear Groups

2008 ◽  
Author(s):  
Felice Arena ◽  
C. Guedes Soares
Keyword(s):  
Time Domain ◽  
Wind Wave ◽  
Narrow Band ◽  
Second Order ◽  
Wave Groups ◽  
Before And After ◽  
The Difference ◽  
Band Spectra ◽  
Two Peaks ◽  
The Waves

The structure of wave groups in time domain depends upon the spectrum. For narrow-band spectra, if a wave with a very large height H occurs, the waves that precede and follow the highest one have height (H′ and H″ respectively) very close to H. For real spectra, the difference between H and either H′ or H″ depends on the bandwidth of the spectrum: it increases as larger is the spectrum. For bimodal spectra, the authors have shown [1] that the wave groups are strongly modified and they are function of the energy associated to the swell and to the wind wave components, as well as of the distance between the two peaks. This paper analyzes the structure of the succession of three waves, given by the high waves and the two that come before and after the highest one, in time domain. The results are analyzed, up to the second-order, for wind wave unimodal and for bimodal spectra, by comparing the height H with H′ and H″.

scholarly journals SHOALING PROPERTIES OF BOUNDED LONG WAVES

1984 ◽  
Vol 1 (19) ◽  
pp. 54 ◽  
Author(s):  
E.P.D. Mansard ◽  
V. Barthel
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Second Order ◽  
Long Waves ◽  
Experimental Results ◽  
Wave Groups ◽  
Good Insight ◽  
Set Up ◽  
Theoretical Considerations ◽  
Insight Into

Group bounded long waves which appear as a set-down under a group of high waves and a set-up in between groups are well described for constant water depth. However, their propagation into shallow water and their interaction with the constituent wave groups are not well understood and theoretically described yet. Therefore, model investigations were carried out to study shoaling properties of these second order waves in terms of amplitudes and phases. The tests give a good insight into the phenomenon and suggest distinct shoaling properties. Moreover, experimental results provide a valuable basis for future theoretical considerations.

Effect of the Second-Order Potential in the Slow-Drift Oscillation of a Floating Structure in Irregular Waves

1986 ◽  
Vol 30 (02) ◽  
pp. 103-122
Author(s):  
J. A. P. Aranha ◽  
C. P. Pesce
Keyword(s):  
Water Depth ◽  
Narrow Band ◽  
Wave Spectrum ◽  
Low Frequency ◽  
Second Order ◽  
Irregular Waves ◽  
Leading Order ◽  
Floating Structure ◽  
Slow Drift ◽  
The Waves

The slow-drift phenomenon is important when the waves are irregular and the sea spectrum has a relatively narrow band. In this paper an expression is derived for the low-frequency force due to the second-order potential. This expression is the leading-order contribution in the wave spectrum bandwidth and can be exactly determined without computing the second-order potential. It is shown that this effect is of importance when the water depth is relatively shallow or the typical wave period relatively long.

scholarly journals First order normalization in the generalized photo gravitational non-planar restricted three body problems

2015 ◽  
Vol 3 (2) ◽  
pp. 46
Author(s):  
Nirbhay Kumar Sinha
Keyword(s):  
Oblate Spheroid ◽  
Second Order ◽  
Elliptic Motion ◽  
First Order ◽  
Short Period ◽  
Order Part ◽  
Three Body

<p>In this paper, we normalised the second-order part of the Hamiltonian of the problem. The problem is generalised in the sense that fewer massive primary is supposed to be an oblate spheroid. By photogravitational we mean that both primaries are radiating. With the help of Mathematica, H<sub>2</sub> is normalised to H<sub>2</sub> = a<sub>1</sub>b<sub>1</sub>w<sub>1</sub> + a<sub>2</sub>b<sub>2</sub>w<sub>2</sub>. The resulting motion is composed of elliptic motion with a short period (2p/w<sub>1</sub>), completed by an oscillation along the z-axis with a short period (2p/w<sub>2</sub>).</p>

STANDING‐WAVE PHENOMENA IN SHORT‐PERIOD SEISMIC NOISE

Geophysics ◽  
1965 ◽  
Vol 30 (6) ◽  
pp. 1179-1186 ◽  
Author(s):  
Indra N. Gupta
Keyword(s):  
Steady State ◽  
Standing Wave ◽  
Seismic Noise ◽  
P Wave ◽  
Stratified Medium ◽  
Alternative Theory ◽  
Compressional Waves ◽  
Short Period ◽  
Wave Phenomena ◽  
Phase Spectra

Short‐period vertical seismometers are used in deep holes at several sites to obtain the change with depth in amplitude and phase spectra of short‐period seismic noise. Although the observed spectra can be explained by an arbitrary combination of several Rayleigh modes, an alternative theory is suggested here. An attempt is made to explain both amplitude and phase spectra of observed microseisms of period less than 6 sec in terms of standing‐wave phenomena caused by steady‐state plane harmonic compressional waves propagating vertically through a horizontally stratified medium. At most sites, the observed data indicate satisfactory agreement with the expected results. A considerable fraction of the short‐period noise may, therefore, be regarded as P‐wave noise propagating vertically from below.

Studies of Extreme Energy Localizations With Smoothed Particle Hydrodynamics

2015 ◽  
Author(s):  
Ayan Moitra ◽  
Christopher Chabalko ◽  
Balakumar Balachandran
Keyword(s):  
Smoothed Particle Hydrodynamics ◽  
Ocean Waves ◽  
Breaking Wave ◽  
Wave Focusing ◽  
Wave Interference ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Wave Heights ◽  
The Waves ◽  
Wave Phenomena

Smoothed particle hydrodynamics (SPH) is used to simulate hydrodynamic waves and wave phenomena including focusing from wave interference. This Lagrangian based method can be used to naturally simulate hydrodynamic free surfaces, including the free surface of a breaking wave. A virtual wave tank is simulated where wave motions can be excited from either side. Wave focusing is observed at the tank center, where the waves interfere. As a measure of the interference, the wave heights that result from focusing are presented. Certain types of wave focusing are thought to lead to large ocean waves. The efficacy of SPH in modeling wave focusing is critical to further understanding and predicting extreme wave phenomena with SPH.

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