Effect of Interfacial Tension on Internal Waves Based on Boussinesq Equations in Two-Layer Fluids

Mohapatra, Soudamini; Gadelho, J.F.M.; Soares, C. Guedes

doi:10.2112/jcoastres-d-17-00186.1

Cited by 8 publications

(15 citation statements)

References 46 publications

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“…In Figure 21 mn decreases with increase in wave number values. Moreover, the observation is similar to [8]. Furthermore, it is seen that for higher wave period the variations of second-order sub-harmonic wave amplitude becomes negligible for fixed values of radius and for different wave number.…”

Section: Effect Of Design Parameters On Second-order Sub-harmonic Wavsupporting

confidence: 77%

“…where x = r cos θ and y = r sin θ. Substituting Equation 5into Equations 7and (10) equating the powers of µ in terms of the specific elevation at z = z α (−h ≤ z α ≤ 0) and related velocity potential Φ α , one can obtain (as in [8,27]).…”

Section: Bes For Exterior Region Based On Perturbation Techniquementioning

confidence: 99%

“…A comparison of wave forces and free surface elevations of a box-type floating structure between was performed between analytical Boussinesq solutions and CFD simulations [7]. Furthermore, a general BM was developed [8] associated with two-layer fluids with floating rigid plate based on BEs to investigate the effect of interfacial tension on internal waves. A new multi-layer Boussinesq-type model associated with highly non-linear and dispersive surface waves using a mild slope seabed was developed [9].…”

Section: Introductionmentioning

confidence: 99%

“…Following the analytic and comparative research on the working principle of current WECs, the floating point absorber is one of the best choices for the wave energy sector of ocean devices [21]. Recently, several comparative studies based on various methodologies, such as analytical Boussinesq, numerical CFD models, other numerical data, and experimental studies associated with wave interaction with floating structures, have been performed [2,7,8,13,23,24] to analyze the fidelity level of accuracy among them for benchmarking.…”

Section: Introductionmentioning

confidence: 99%

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Boussinesq Model and CFD Simulations of Non-Linear Wave Diffraction by a Floating Vertical Cylinder

Mohapatra

Islam

Soares

2020

JMSE

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A mathematical model for the problem of wave diffraction by a floating fixed truncated vertical cylinder is formulated based on Boussinesq equations (BEs). Using Bessel functions in the velocity potentials, the mathematical problem is solved for second-order wave amplitudes by applying a perturbation technique and matching conditions. On the other hand, computational fluid dynamics (CFD) simulation results of normalized free surface elevations and wave heights are compared against experimental fluid data (EFD) and numerical data available in the literature. In order to check the fidelity and accuracy of the Boussinesq model (BM), the results of the second-order super-harmonic wave amplitude around the vertical cylinder are compared with CFD results. The comparison shows a good level of agreement between Boussinesq, CFD, EFD, and numerical data. In addition, wave forces and moments acting on the cylinder and the pressure distribution around the vertical cylinder are analyzed from CFD simulations. Based on analytical solutions, the effects of radius, wave number, water depth, and depth parameters at specific elevations on the second-order sub-harmonic wave amplitudes are analyzed.

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Section: Effect Of Design Parameters On Second-order Sub-harmonic Wavsupporting

confidence: 77%

Section: Bes For Exterior Region Based On Perturbation Techniquementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Boussinesq Model and CFD Simulations of Non-Linear Wave Diffraction by a Floating Vertical Cylinder

Mohapatra

Islam

Soares

2020

JMSE

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“…An analytical model related to internal waves in the presence of a tension in a two-layer system bounded by a rigid floating plate and a rigid bottom was presented in [7] based on Businesque's equations. General equations and boundary conditions of motion of internal waves at interphase tension were described.…”

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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Traveling waves of a generalized sixth‐order Boussinesq equation

Esfahani,

Levandosky

2024

Math Methods in App Sciences

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We investigate the existence and stability of traveling waves for the sixth‐order Boussinesq equation, considering a broad class of nonlinearities adhering to power‐like scaling relations. Employing the Nehari manifold method, we establish the existence of traveling waves and derive variational criteria for assessing their stability or instability. Subsequently, we develop a numerical approach based on these variational principles to delineate regions of stability and instability. Finally, for homogeneous nonlinearities, we establish a sufficient condition for strong instability.

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Effect of Interfacial Tension on Internal Waves Based on Boussinesq Equations in Two-Layer Fluids

Cited by 8 publications

References 46 publications

Boussinesq Model and CFD Simulations of Non-Linear Wave Diffraction by a Floating Vertical Cylinder

Boussinesq Model and CFD Simulations of Non-Linear Wave Diffraction by a Floating Vertical Cylinder

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

Traveling waves of a generalized sixth‐order Boussinesq equation

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Effect of Interfacial Tension on Internal Waves Based on Boussinesq Equations in Two-Layer Fluids

Cited by 8 publications

References 46 publications

Boussinesq Model and CFD Simulations of Non-Linear Wave Diffraction by a Floating Vertical Cylinder

Boussinesq Model and CFD Simulations of Non-Linear Wave Diffraction by a Floating Vertical Cylinder

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

Traveling waves of a generalized sixth‐order Boussinesq equation

Contact Info

Product

Resources

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