Propagation of Solitary Internal Waves in Two-Layer Ocean of Variable Depth

Talipova, T. G.; Kurkina, O. E.; Rouvinskaya, Ekaterina; Pelinovsky, Efim

doi:10.7868/s0002351515010101

Cited by 6 publications

(16 citation statements)

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“…This conjecture is consistent with the practice of the use of such asymptotic models. This level of deviations of the estimates from the true values is commonly acceptable (Liu et al, 2004;Talipova et al, 2014Talipova et al, , 2015. As errors of this kind rapidly increase with increasing wave amplitude, the use of such models for smaller-amplitude waves is associated with much lower levels of errors.…”

Section: Applicability Of the Asymptotic Model For Long Internal Wavementioning

confidence: 98%

“…In particular, Gardner's equation is commonly used as the classic model of internal waves of the first mode (Holloway et al, 1999;Grimshaw et al, 2004;Talipova et al, 2014Talipova et al, , 2015. This model has been applied inter alia to explain and replicate a polarity switch of internal solitons propagating along the north-eastern continental shelf in the South China Sea (Liu et al, 1998;Orr and Mignerey, 2003;Grimshaw et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Applicability Of the Asymptotic Model For Long Internal Wavementioning

confidence: 98%

Section: Introductionmentioning

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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“…) and rotating fluid . In the case of interfacial waves in a two‐layer fluid of variable depth, an important effect is the change of polarity of solitary waves (solitons) …”

Section: Wave Reflection From the Bifurcation Pointmentioning

confidence: 99%

Interfacial long traveling waves in a two‐layer fluid with variable depth

et al. 2018

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Long wave propagation in a two‐layer fluid with variable depth is studied for specific bottom configurations, which allow waves to propagate over large distances. Such configurations are found within the linear shallow‐water theory and determined by a family of solutions of the second‐order ordinary differential equation (ODE) with three arbitrary constants. These solutions can be used to approximate the true bottom bathymetry. All such solutions represent smooth bottom profiles between two different singular points. The first singular point corresponds to the point where the two‐layer flow transforms into a uniform one. In the vicinity of this point nonlinear shallow‐water theory is used and the wave breaking criterion, which corresponds to the gradient catastrophe is found. The second bifurcation point corresponds to an infinite increase in water depth, which contradicts the shallow‐water assumption. This point is eliminated by matching the “nonreflecting” bottom profile with a flat bottom. The wave transformation at the matching point is described by the second‐order Fredholm equation and its approximated solution is then obtained. The results extend the theory of internal waves in inhomogeneous stratified fluids actively developed by Prof. Roger Grimshaw, to the new solutions types.

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“…This model, however, did not consider any uneven topography and the consequent refracting effects of the ISWs. Further generalizations of the KdV model allow for a description of ISWs over a slowly varying topography24252627. 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.…”

Section: Refracting Internal Solitary Waves For Sand-waves Generationmentioning

confidence: 99%

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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Propagation of Solitary Internal Waves in Two-Layer Ocean of Variable Depth

Cited by 6 publications

References 0 publications

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

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

Interfacial long traveling waves in a two‐layer fluid with variable depth

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

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