Water-Waves Scattering by Permeable Bottom in Two-Layer Fluid in the Presence of Surface Tension

Panda, Srikumar; Martha, S. C.

doi:10.3846/13926292.2017.1386239

Cited by 11 publications

(2 citation statements)

References 25 publications

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“…To validate the results, we have calculated all the results by assuming U = 0 (in the absence of current) and S 2 = 0 (without interfacial tension) in relations (C.14 -C.21). It has been observed that the present results exactly match with the results of Panda and Martha [26] (when G=0). In addition, if we take S 1 = 0 in relations (C.14 -C.21), then all the results exactly match with the results of Mohapatra and Bora [21] (when θ = 0 in the absence of ice sheet) and Panda and Martha [27] (when G=0 and θ = 0).…”

Section: Appendix-c: Analytical Resultssupporting

confidence: 91%

Wave blocking and Bragg resonance in two-layer fluid with current and surface tension.

Aggarwal

Mohanty

Martha

2023

Preprint

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In the present work, the scattering of water waves by undulating bottom in a two-layer fluid system is investigated by the inclusion of current, surface tension and interfacial tension to better understand the phenomenon of wave blocking. The perturbation technique followed by the Fourier transform method is applied to solve the coupled boundary value problem. The associated velocity potentials, Bragg reflection coefficients, and Bragg transmission coefficients are obtained in integral forms. A particular case of the undulating bottom, namely sinusoidal bottom undulation, has been taken into consideration for showing the effects of current speed and surface tension. A shift in the Bragg resonant frequency is observed with a change in the current speed. Further, the combined effects of Bragg resonance and wave blocking are investigated. For some values of opposing current, the group velocity vanishes at two distinct points in the frequency space; the maxima is known as the primary blocking point and the minima is called as the secondary blocking point. For each frequency, there exist three propagating modes between these two blocking points. Certain abnormalities and a sharp increase in the Bragg reflection and transmission coefficients are caused by the superposition of various propagating wave modes and triad interaction within the blocking points as well as a change in the incident wave mode. Mathematics Subject Classification: 76B15, 42A38, 35Q35.

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Section: Appendix-c: Analytical Resultssupporting

confidence: 91%

Wave blocking and Bragg resonance in two-layer fluid with current and surface tension.

Aggarwal

Mohanty

Martha

2023

Preprint

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“…У праці [13] вивчено двошарову систему, що вкрита кригою, для якої проаналізовано явище відбиття і передачі водяних хвиль у ній. Дно нижнього шару хвилеподібне і проникне, а верхній шар покритий крижаним листом.…”

Section: швидкості і траєкторії хвильового руху у двошаровій гідродинunclassified

Velocities and Trajectories of Wave Motion in a Two-Layer Hydrodynamic System

Hurtovyi

Kuharenko

2020

BNUKMM

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The paper deals with studying trajectories of motion of individual liquid particles in a two-layer hydrodynamic system with a finite layer thickness as well as analyzing phase and group velocities of internal waves in the system. The problem is modeled for an inviscid incompressible fluid under action of the gravity and surface tension forces in a dimensionless form. Solutions of the problem are sought in the form of progressive waves using the multi-scale method. The solutions are expanded in terms of the nonlinearity coefficient. Dependence of the dispersion ratio of the wavenumber is investigated for different values of the surface tension coefficient and the ratio of the layer densities. Formulas are obtained for the group and phase velocities for internal gravity-capillary waves as well as in the limiting case for capillary waves. A comparison of the values of the phase and group velocities of internal waves for different values of the wave number is carried out. It is proved that with an increase in the wave number, the group velocity begins to outstrip the phase velocity, and their equality occurs at the minimum phase velocity. It is shown that the trajectories are ellipses in which the horizontal semi axes are larger than the vertical ones. Formulas are obtained for the semi axes of elliptic trajectories for each of the layers. The character of the change in the semi axes of elliptical trajectories is analyzed depending on the distance from the interface between two liquid layers as well as on the values of the wave number. It is proved that the semi axes of ellipses decrease unevenly with increasing distance from the boundary. The asymmetry of the particle trajectories of each of the layers is shown for the case when the thickness of the lower layer differs from the thickness of the lower layer. The study of the kinematic characteristics of the particle motion makes it possible to simulate real physical wave processes in the World Ocean. The results are also relevant for creating a theoretical basis for experiments.

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Topographical and barrier influences on hydroelastic response of an elastic plate floating in a two-layer fluid

Prasad

2023

Z. Angew. Math. Phys.

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Water-Waves Scattering by Permeable Bottom in Two-Layer Fluid in the Presence of Surface Tension

Cited by 11 publications

References 25 publications

Wave blocking and Bragg resonance in two-layer fluid with current and surface tension.

Wave blocking and Bragg resonance in two-layer fluid with current and surface tension.

Velocities and Trajectories of Wave Motion in a Two-Layer Hydrodynamic System

Topographical and barrier influences on hydroelastic response of an elastic plate floating in a two-layer fluid

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