The effects of interplay between the rotation and shoaling for a solitary wave on variable topography

Stepanyants, Yury

doi:10.1111/sapm.12255

Cited by 13 publications

(16 citation statements)

References 32 publications

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“…The effect of Earth' rotation on the dynamics of nonlinear waves in the oceans has been extensively studied in previous decades (see, for example, Refs. [24,11,14,12,20,18,25,31] and references therein). As is well-know, wave propagation in big lakes can be also affected by the Earth's rotation [5,7,28,32,29].…”

Section: Introductionmentioning

confidence: 99%

“…In an inhomogeneous medium the dynamics of solitary waves is determined by synergetic effects of inhomogeneity and fluid rotation. In particular, at a certain relationship between these two factors, a Korteweg-de Vries (KdV) soliton propagating towards a coast with a gradually decreasing depth can preserve its shape and amplitude, whereas its width and velocity adiabatically change [31].…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of Internal Envelope Solitons in a Rotating Fluid of a Variable Depth

Stepanyants

2019

Fluids

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We consider the dynamics of internal envelope solitons in a two-layer rotating fluid with a linearly varying bottom. It is shown that the most probable frequency of a carrier wave which constitutes the solitary wave is the frequency where the growth rate of modulation instability is maximal. An envelope solitary wave of this frequency can be described by the conventional nonlinear Schrödinger equation. A soliton solution to this equation is presented for the time-like version of the nonlinear Schrödinger equation. When such envelope soliton enters a coastal zone where the bottom gradually linearly increases, then it experiences an adiabatical transfor-arXiv:1903.07817v2 [physics.flu-dyn] 22 Mar 2019mation. This leads to an increase of soliton amplitude, velocity, and period of a carrier wave, whereas its duration decreases. It is shown that the soliton becomes taller and narrower. At some distance it looks like a breather, a narrow nonstationary solitary wave. The dependences of soliton parameters on the distance when it moves towards the shoaling are found from the conservation laws and analysed graphically. Estimates for the real ocean are presented.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamics of Internal Envelope Solitons in a Rotating Fluid of a Variable Depth

Stepanyants

2019

Fluids

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“…Features of the separated wave dynamics within Ostrovsky's equation with variable coefficients relative to the surface and internal waves in the ocean with variable bottom topography were presented in [4]. For separated waves moving to a beach, attenuation effect can be suppressed by the effect of rotation.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Dependence of the internal wave energy flux on the parameters of a twolayer hydrodynamic system

Naradovyi

Hurtovyi

Авраменко

2020

EEJET

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The study was performed to analyze the flux of energy of internal gravitational-capillary waves in a two-layer hydrodynamic liquid system with finite layer thicknesses. The problem was considered for an ideal incompressible fluid in the field of gravity as well as taking into account the forces of surface tension. The problem was formulated in a dimensionless form for small values of the coefficient of nonlinearity. The dispersion of the gravitational-capillary progressive waves was studied in detail depending on the coefficient of surface tension and the ratio of layer densities. It was proved that with the increase in the wavenumber, the group velocity begins to pass ahead of the phase velocity and their equality occurs at the minimum of the phase velocity. Dependence of the total average energy flux on the wavenumber (wavelength) and thickness of the liquid layers was calculated and graphically analyzed for different values of physical quantities, in particular, density and the coefficient of surface tension. It follows from the analysis that the energy flux of gravitational internal waves increases to a certain maximum value with an increase in the thickness of the lower layer and then approaches a certain limit value. For capillary waves, the energy flux of internal waves is almost independent of the thickness of the lower layer. It was also shown that the average energy flux for gravitational waves at a stable amplitude is almost independent of the wavelength. On the contrary, for capillary waves, the energy flux increases sharply with an increase in the wavenumber. The results of the analysis of the energy flux of internal progressive waves make it possible to qualitatively assess physical characteristics in the development of environmental technologies that use internal undulatory motions in various aquatic environments as a source of energy

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“…Internal long wave nonlinear theory in a basin of variable depth is well developed in various approximations for both nonrotating fluid (see, e.g., Refs. ) 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%

“…6,8,13-18) and rotating fluid. 19,20 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). [21][22][23] Here, we consider nonlinear shallow-water theory taking into account that the thickness of the lower layer is very small.…”

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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The effects of interplay between the rotation and shoaling for a solitary wave on variable topography

Cited by 13 publications

References 32 publications

Dynamics of Internal Envelope Solitons in a Rotating Fluid of a Variable Depth

Dynamics of Internal Envelope Solitons in a Rotating Fluid of a Variable Depth

Dependence of the internal wave energy flux on the parameters of a twolayer hydrodynamic system

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

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The effects of interplay between the rotation and shoaling for a solitary wave on variable topography

Cited by 13 publications

References 32 publications

Dynamics of Internal Envelope Solitons in a Rotating Fluid of a Variable Depth

Dynamics of Internal Envelope Solitons in a Rotating Fluid of a Variable Depth

Dependence of the internal wave energy flux on the parameters of a two­layer hydrodynamic system

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

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Product

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Dependence of the internal wave energy flux on the parameters of a twolayer hydrodynamic system