Broadening of interfacial solitary waves

Turner, R. E.; Vanden‐Broeck, J.‐M.

doi:10.1063/1.866602

Cited by 87 publications

(60 citation statements)

References 9 publications

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“…The volume of the wave may become infinitely large in this limit (Turner & Vanden-Broeck 1988). The formulae for c max and a max derived by Amick & Turner read…”

Section: Interfacial Waves With Maximal Amplitudementioning

confidence: 98%

Properties of large-amplitude internal waves

et al. 1999

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Properties of solitary waves propagating in a two-layer fluid are investigated comparing experiments and theory. In the experiments the velocity field induced by the waves, the propagation speed and the wave shape are quite accurately measured using particle tracking velocimetry (PTV) and image analysis. The experiments are calibrated with a layer of fresh water above a layer of brine. The depth of the brine is 4.13 times the depth of the fresh water. Theoretical results are given for this depth ratio, and, in addition, in a few examples for larger ratios, up to 100:1. The wave amplitudes in the experiments range from a small value up to almost maximal amplitude. The thickness of the pycnocline is in the range of approximately 0.13-0.26 times the depth of the thinner layer. Solitary waves are generated by releasing a volume of fresh water trapped behind a gate. By careful adjustment of the length and depth of the initial volume we always generate a single solitary wave, even for very large volumes. The experiments are very repeatable and the recording technique is very accurate. The error in the measured velocities non-dimensionalized by the linear long wave speed is less than about 7-8% in all cases. The experiments are compared with a fully nonlinear interface model and weakly nonlinear Korteweg-de Vries (KdV) theory. The fully nonlinear model compares excellently with the experiments for all quantities measured. This is true for the whole amplitude range, even for a pycnocline which is not very sharp. The KdV theory is relevant for small wave amplitude but exhibit a systematic deviation from the experiments and the fully nonlinear theory for wave amplitudes exceeding about 0.4 times the depth of the thinner layer. In the experiments with the largest waves, rolls develop behind the maximal displacement of the wave due to the Kelvin-Helmholtz instability. The recordings enable evaluation of the local Richardson number due to the flow in the pycnocline. We find that stability or instability of the flow occurs in approximate agreement with the theorem of Miles and Howard.

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“…The volume of the wave may become infinitely large in this limit (Turner & Vanden-Broeck 1988). The formulae for c max and a max derived by Amick & Turner read…”

Section: Interfacial Waves With Maximal Amplitudementioning

confidence: 98%

Properties of large-amplitude internal waves

et al. 1999

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“…Two-layered systems have been considered in detail in numerous studies (e.g., Evans & Ford 1996, Funakoshi & Oikawa 1986, Grue et al 1999, Pullin & Grimshaw 1988, Turner & Vanden-Broeck 1988. Potential flow within each layer allows the full formulation to be reduced to boundary integral equations.…”

Section: Fully Nonlinear Wavesmentioning

confidence: 99%

Long Nonlinear Internal Waves

Helfrich

Melville

2006

Annu. Rev. Fluid Mech.

683

491

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Over the past four decades, the combination of in situ and remote sensing observations has demonstrated that long nonlinear internal solitary-like waves are ubiquitous features of coastal oceans. The following provides an overview of the properties of steady internal solitary waves and the transient processes of wave generation and evolution, primarily from the point of view of weakly nonlinear theory, of which the Korteweg-de Vries equation is the most frequently used example. However, the oceanographically important processes of wave instability and breaking, generally inaccessible with these models, are also discussed. Furthermore, observations often show strongly nonlinear waves whose properties can only be explained with fully nonlinear models.

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“…AsĒ a increases the wave amplitude asymptotes to a limiting value. This is indicative of the conjugate flow limit being reached at which waves flatten in the centre and broaden as the energy in the waves is increased (Tung et al, 1982;Turner and Vanden-Broeck, 1988;Lamb and Wan, 1998). When there is no background current the maximum ISW amplitude is −0.32 m (negative implying a wave of depression), slightly larger than the distance of the pycnocline from the mid-depth.…”

Section: Energetics Of Internal Solitary Waves Under the Boussinesq Amentioning

confidence: 99%

Energetics of internal solitary waves in a background sheared current

Lamb

2010

Nonlin. Processes Geophys.

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Abstract. The energetics of internal waves in the presence of a background sheared current is explored via numerical simulations for four different situations based on oceanographic conditions: the nonlinear interaction of two internal solitary waves; an internal solitary wave shoaling through a turning point; internal solitary wave reflection from a sloping boundary and a deep-water internal seiche trapped in a deep basin. In the simulations with variable water depth using the Boussinesq approximation the combination of a background sheared current, bathymetry and a rigid lid results in a change in the total energy of the system due to the work done by a pressure change that is established across the domain. A final simulation of the deep-water internal seiche in which the Boussinesq approximation is not invoked and a diffuse airwater interface is added to the system results in the energy remaining constant because the generation of surface waves prevents the establishment of a net pressure increase across the domain. The difference in the perturbation energy in the Boussinesq and non-Boussinesq simulations is accounted for by the surface waves.

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Broadening of interfacial solitary waves

Cited by 87 publications

References 9 publications

Properties of large-amplitude internal waves

Properties of large-amplitude internal waves

Long Nonlinear Internal Waves

Energetics of internal solitary waves in a background sheared current

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