Internal solitary waves

Pelinovsky, Efim; Polukhina, O. E.; Slunyaev, Alexey; Talipova, Tatiana

doi:10.2495/978-1-84564-157-3/04

Cited by 41 publications

(19 citation statements)

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“…4b) as a function of the initial angle between the ISW vector and the bathymetry in the deepest part of the sand-wave field (Supplementary Information). Numerical, theoretical and current-meter data82028 support our initial hypothesis that the topographically-induced ISW refraction generates the deflected sand-waves pattern (Fig. 3).…”

Section: Resultssupporting

confidence: 63%

“…This ISW refraction is described by using a non-linear ray method that leads to a ray equation of linear long wave theory of the type of Snell’s law2831…”

Section: Resultsmentioning

confidence: 99%

“…In particular, Grimshaw et al [refs 24 and 25] model ISWs behavior near the coast by using the Korteweg- de Vries equations with variable coefficients (i.e., the vKdV and the Gardner e-vKdV equations), which describe the shoaling and deformation of ISWs over the continental shelf. We here use a ray method that allows us to take into account the second horizontal dimension and thus to investigate wave refraction while, along a ray, the generalized KdV equation remains valid for a slowly varying depth28.…”

Section: Refracting Internal Solitary Waves For Sand-waves Generationmentioning

confidence: 99%

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The role of Internal Solitary Waves on deep-water sedimentary processes: the case of up-slope migrating sediment waves off the Messina Strait

Droghei

Falcini

Casalbore

et al. 2016

Sci Rep

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Subaqueous, asymmetric sand waves are typically observed in marine channel/canyon systems, tidal environments, and continental slopes exposed to strong currents, where they are formed by current shear resulting from a dominant unidirectional flow. However, sand-wave fields may be readily observed in marine environments where no such current exists; the physical processes driving their formation are enigmatic or not well understood. We propose that internal solitary waves (ISWs) induced by tides can produce an effective, unidirectional boundary “current” that forms asymmetric sand waves. We test this idea by examining a sand-wave field off the Messina Strait, where we hypothesize that ISWs formed at the interface between intermediate and surface waters are refracted by topography. Hence, we argue that the deflected pattern (i.e., the depth-dependent orientation) of the sand-wave field is due to refraction of such ISWs. Combining field observations and numerical modelling, we show that ISWs can account for three key features: ISWs produce fluid velocities capable of mobilizing bottom sediments; the predicted refraction pattern resulting from the interaction of ISWs with bottom topography matches the observed deflection of the sand waves; and predicted migration rates of sand waves match empirical estimates. This work shows how ISWs may contribute to sculpting the structure of continental margins and it represents a promising link between the geological and oceanographic communities.

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Section: Resultssupporting

confidence: 63%

“…This ISW refraction is described by using a non-linear ray method that leads to a ray equation of linear long wave theory of the type of Snell’s law2831…”

Section: Resultsmentioning

confidence: 99%

Section: Refracting Internal Solitary Waves For Sand-waves Generationmentioning

confidence: 99%

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The role of Internal Solitary Waves on deep-water sedimentary processes: the case of up-slope migrating sediment waves off the Messina Strait

Droghei

Falcini

Casalbore

et al. 2016

Sci Rep

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“…Similarly, the typical value of the coefficient at the cubic non-linear term is α 1 = 0.0005 m −1 s −1 and the magnitude of this term is α 1 A 2 = 0.2 m s −1 . The case when both non-linear terms are small is discussed in detail by Pelinovsky et al (2007) and Kurkina et al (2015). The typical magnitude of the phase speed of linear long internal waves of the second mode is c ∼ 0.4 m s −1 .…”

Section: Applicability Of the Asymptotic Model For Long Internal Wavementioning

confidence: 99%

Kinematic parameters of internal waves of the second mode in the South China Sea

Kurkina

Talipova

Soomere

et al. 2017

Nonlin. Processes Geophys.

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Abstract. Spatial distributions of the main properties of the mode function and kinematic and non-linear parameters of internal waves of the second mode are derived for the South China Sea for typical summer conditions in July. The calculations are based on the Generalized Digital Environmental Model (GDEM) climatology of hydrological variables, from which the local stratification is evaluated. The focus is on the phase speed of long internal waves and the coefficients at the dispersive, quadratic and cubic terms of the weakly nonlinear Gardner model. Spatial distributions of these parameters, except for the coefficient at the cubic term, are qualitatively similar for waves of both modes. The dispersive term of Gardner's equation and phase speed for internal waves of the second mode are about a quarter and half, respectively, of those for waves of the first mode. Similarly to the waves of the first mode, the coefficients at the quadratic and cubic terms of Gardner's equation are practically independent of water depth. In contrast to the waves of the first mode, for waves of the second mode the quadratic term is mostly negative. The results can serve as a basis for expressing estimates of the expected parameters of internal waves for the South China Sea.

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“…The analytical one-soliton solution of the Gardner equation is well known (Helfrich and Melville, 2006;Pelinovsky et al, 2007):…”

Section: Gardner Equations For Interfacial Displacementsmentioning

confidence: 99%

Propagation regimes of interfacial solitary waves in a three-layer fluid

Kurkina¹,

Kurkin²,

Rouvinskaya³

et al. 2015

Nonlin. Processes Geophys.

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Abstract. Long weakly nonlinear finite-amplitude internal waves in a fluid consisting of three inviscid layers of arbitrary thickness and constant densities (stable configuration, Boussinesq approximation) bounded by a horizontal rigid bottom from below and by a rigid lid at the surface are described up to the second order of perturbation theory in small parameters of nonlinearity and dispersion. First, a pair of alternatives of appropriate KdV-type equations with the coefficients depending on the parameters of the fluid (layer positions and thickness, density jumps) are derived for the displacements of both modes of internal waves and for each interface between the layers. These equations are integrable for a very limited set of coefficients and do not allow for proper description of several near-critical cases when certain coefficients vanish. A more specific equation allowing for a variety of solitonic solutions and capable of resolving most near-critical situations is derived by means of the introduction of another small parameter that describes the properties of the medium and rescaling of the ratio of small parameters. This procedure leads to a pair of implicitly interrelated alternatives of Gardner equations (KdV-type equations with combined nonlinearity) for the two interfaces. We present a detailed analysis of the relationships for the solutions for the disturbances at both interfaces and various regimes of the appearance and propagation properties of soliton solutions to these equations depending on the combinations of the parameters of the fluid. It is shown that both the quadratic and the cubic nonlinear terms vanish for several realistic configurations of such a fluid.

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Internal solitary waves

Cited by 41 publications

References 0 publications

The role of Internal Solitary Waves on deep-water sedimentary processes: the case of up-slope migrating sediment waves off the Messina Strait

The role of Internal Solitary Waves on deep-water sedimentary processes: the case of up-slope migrating sediment waves off the Messina Strait

Kinematic parameters of internal waves of the second mode in the South China Sea

Propagation regimes of interfacial solitary waves in a three-layer fluid

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