On the laboratory generation of two-dimensional, progressive, surface waves of nearly permanent form on deep water

Henderson, D. M.; Patterson, Matthew; Segur, Harvey

doi:10.1017/s0022112006000103

Cited by 21 publications

(34 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As discussed by Henderson et al (2006), many issues may arise when generating periodic wave trains of permanent form in a basin. For two-sided segmented Li et al (2012) found that the propagation direction of waves is the key issue affecting the simulation quality.…”

Section: Summary Of Theoretical Frameworkmentioning

confidence: 99%

“…Short-crested waves, as probably the simplest waves of permanent form that are two-dimensional, have received growing interest in experimental (Hammack, Scheffner & Segur 1989;Hammack et al 1995;Kimmoun, Branger & Kharif 1999;Hammack, Henderson & Segur 2005;Henderson, Patterson & Segur 2006;Henderson, Segur & Carter 2010), analytical (Roberts 1983;Bryant 1985;, 2012 and numerical (Chen & Liu 1995;Craig & Nicholls 2002;Fuhrman, Madsen & Bingham 2006;Nicholls & Reitich 2006;Xu & Guyenne 2009) investigations in recent years.…”

mentioning

confidence: 99%

See 1 more Smart Citation

On the existence of steady-state resonant waves in experiments

Liu

et al. 2014

J. Fluid Mech.

View full text Add to dashboard Cite

This paper describes an experimental investigation of steady-state resonant waves. Several co-propagating short-crested wave trains are generated in a basin at the State Key Laboratory of Ocean Engineering (SKLOE) in Shanghai, and the wavefields are measured and analysed both along and normal to the direction of propagation. These steady-state resonant waves are first calculated theoretically under the exact resonance criterion with sufficiently high nonlinearity, and then are generated in the basin by means of the main wave components that contain at least 95 % of the wave energy. The steady-state wave spectra are quantitatively observed within the inherent system error of the basin and identified by means of a contrasting experiment. Both symmetrical and anti-symmetrical steady-state resonant waves are observed and the experimental and theoretical results show excellent agreement. These results offer the first experimental evidence of the existence of steady-state resonant waves with multiple solutions.

show abstract

Section: Summary Of Theoretical Frameworkmentioning

confidence: 99%

mentioning

confidence: 99%

On the existence of steady-state resonant waves in experiments

Liu

et al. 2014

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…These unsteady phenomena were found to be at least as significant as the well-known spurious features resulting from the neglect of second-harmonic terms. Their conclusions were experimentally confirmed by Henderson, Patterson & Segur (2006), even though the third-order boundary conditions for their paddle motion were only approximate and without any compensation for evanescent modes. and Henderson et al (2006) found that the third-order short-crested theory was useful for providing steady solutions even for grazing angles as small as 10 • and wave steepness as high as ka = 0.30.…”

Section: Third-order Theory For Multi-directional Irregular Wavesmentioning

confidence: 78%

“…Their conclusions were experimentally confirmed by Henderson, Patterson & Segur (2006), even though the third-order boundary conditions for their paddle motion were only approximate and without any compensation for evanescent modes. and Henderson et al (2006) found that the third-order short-crested theory was useful for providing steady solutions even for grazing angles as small as 10 • and wave steepness as high as ka = 0.30. The new theory presented in this paper provides a method for nonlinear analysis of a general sea state, and may also be useful for the generation of more complex wave trains involving several wave components of different frequencies and directions.…”

Section: Third-order Theory For Multi-directional Irregular Wavesmentioning

confidence: 78%

“…The reason is clearly that this case is of fundamental importance to the understanding of multidirectional irregular waves, and at the same time it has a relatively simple form and mathematical description even at high orders of nonlinearity. Experimentally, shortcrested waves have been studied by, for example, Hammack, Scheffner & Segur (1989), Kimmoun, Ioualalen & Kharif (1999), Hammack, Henderson & Segur (2005) and Henderson et al (2006). Analytical solutions have been provided by Chappelear (1961) and Hsu, Tsuchiya & Silvester (1979) to third order and by Ioualalen (1993) to fourth order.…”

Section: Third-order Theory For Multi-directional Irregular Wavesmentioning

confidence: 99%

See 1 more Smart Citation

Third-order theory for multi-directional irregular waves

Madsen

Fuhrman

2012

J. Fluid Mech.

View full text Add to dashboard Cite

A new third-order solution for multi-directional irregular water waves in finite water depth is presented. The solution includes explicit expressions for the surface elevation, the amplitude dispersion and the vertical variation of the velocity potential. Expressions for the velocity potential at the free surface are also provided, and the formulation incorporates the effect of an ambient current with the option of specifying zero net volume flux. Harmonic resonance may occur at third order for certain combinations of frequencies and wavenumber vectors, and in this situation the perturbation theory breaks down due to singularities in the transfer functions. We analyse harmonic resonance for the case of a monochromatic short-crested wave interacting with a plane wave having a different frequency, and make long-term simulations with a high-order Boussinesq formulation in order to study the evolution of wave trains exposed to harmonic resonance.Key words: surface gravity waves, waves/free-surface flows IntroductionNonlinear irregular multi-directional water waves are commonly described to second order using the formulation by Sharma & Dean (1981). This is based on a double summation over all possible pairs of wave components, utilizing a second-order solution for bi-directional bichromatic waves as the kernel in the summation. In this work, we present a third-order analytical solution for trichromatic tri-directional waves, which is then used as the kernel in a triple summation over all triplets, plus a double summation over the relevant doublets. The outcome of this work is thus a third-order theory for multi-directional irregular waves in finite water depth, including the effect of ambient or wave-induced currents. The formulation is an extension of the work by Zhang & Chen (1999) from deep water to arbitrary depth, and from collinear interactions to multi-directional interactions. It is also an extension of the work by from third-order bi-directional bichromatic waves to multi-directional irregular waves. demonstrated the importance of accounting for third-order effects in boundary conditions for monochromatic short-crested waves in connection with numerical or laboratory experiments. They made numerical simulations using a high-order Boussinesq-type formulation and performed an analysis

show abstract

The role of dissipation in the evolution of ocean swell

Henderson

Segur

2013

J. Geophys. Res. Oceans

Self Cite

View full text Add to dashboard Cite

[1] Dissipation of ocean swell, inferred from published oceanographic data, is investigated to determine if laboratory results on the dissipative stabilization of narrow-banded wave trains are applicable to ocean swell. Three issues are addressed. (i) Dimensional decay rates of ocean swell are about a million times smaller than typical decay rates of laboratory waves. Nevertheless, when decay rates are nondimensionalized using scales of dispersive and nonlinear effects, the dimensionless decay rates of ocean swell are comparable to those of laboratory waves, indicating that dissipation and nonlinear effects can influence ocean swell on the same time scale. (ii) The stability of ocean swell to small perturbations is examined within the theoretical framework of nonlinear Schrödinger-type models that either do or do not include dissipation. As in laboratory experiments, for swell with small enough nonlinearity, dissipation can inhibit and eventually stop the growth of small perturbations before nonlinearity becomes important. And as in laboratory experiments, we document herein an example of ocean swell with stronger nonlinearity that exhibits frequency downshifting, which is not predicted by any nonlinear Schrödinger-type model, including higher-order models, with or without dissipation. (iii) Given that dissipation can influence the evolution of ocean swell, we compare the predicted decay rates of four (published) dissipative models with observed decay rates, both in the ocean and in a laboratory wave tank. The model that presupposes an inextensible film on the free surface agrees best with measured rates of dissipation of ocean swell. Statement of the Problem[2] Ocean ''swell'' refers to slowly varying wave trains of surface water waves, which are typically generated by an oceanic storm, and which are observed to propagate over thousands of km without additional forcing [Snodgrass et al., 1966]. The standard mathematical model of the dynamics of surface water waves, first posed by Stokes [1847], is an energy-conserving system, with no dissipation. But water and air are both viscous fluids, so the energy of ocean swell must dissipate as the swell propagates. The dissipation rate of ocean swell is measurable [cf. Collard et al., 2009] but weak enough that Snodgrass et al. [1966] pronounced it ''negligible'' in their landmark paper. It appears that they meant that dissipation is negligible in the sense that ocean swell can propagate the entire length of the Pacific Ocean, more than 1/3 of the distance around the world, while still maintaining measurable wave amplitudes and significant coherence.[3] At about the same time as the important work of Snodgrass et al. [1966], several scientists around the world discovered what is now called either the ''modulational instability'' or the ''Benjamin-Feir instability'' [Lighthill, 1965;Benjamin and Feir, 1967; Benney and Newell, 1967;Ostrovsky, 1967;Whitham, 1967;Zakharov, 1967Zakharov, , 1968. The instability occurs in energy-conserving systems with dispersive waves ...

show abstract

On the laboratory generation of two-dimensional, progressive, surface waves of nearly permanent form on deep water

Cited by 21 publications

References 42 publications

On the existence of steady-state resonant waves in experiments

On the existence of steady-state resonant waves in experiments

Third-order theory for multi-directional irregular waves

The role of dissipation in the evolution of ocean swell

Contact Info

Product

Resources

About