scholarly journals A Boussinesq-Type Model for Nonlinear Wave-Heaving Cylinder Interaction

Energies ◽  
2022 ◽  
Vol 15 (2) ◽  
pp. 469
Author(s):  
Theofanis Karambas ◽  
Eva Loukogeorgaki
Keyword(s):  
Numerical Model ◽  
Nonlinear Wave ◽  
Wave Model ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Floating Body ◽  
Type Model ◽  
Weakly Nonlinear ◽  
Exciting Forces ◽  
Heave Motion

In the present work, a Boussinesq-type numerical model is developed for the simulation of nonlinear wave-heaving cylinder interaction. The wave model is able to describe the propagation of fully dispersive and weakly nonlinear waves over any finite water depth. The wave-cylinder interaction is taken into account by solving simultaneously an elliptic equation that determines the pressure exerted by the fluid on the floating body. The heave motion for the partially immersed floating cylinder under the action of waves is obtained by solving numerically the body’s equation of motion in the z direction based on Newton’s law. The developed model is applied for the case of a fixed and a free-floating circular cylinder under the action of regular waves, as well as for a free-floating cylinder undergoing a forced motion in heave. Results (heave and surge exciting forces, heave motions, and wave elevation) are compared with those obtained using a frequency domain numerical model, which is based on the boundary integral equation method.

Influence of Draft Variation on Heave Added-Mass and Hydrodynamic Damping Coefficients of Floating Bodies

1990 ◽  
Vol 34 (03) ◽  
pp. 172-178
Author(s):  
Marc Vantorre
Keyword(s):  
Numerical Data ◽  
Integral Equation Method ◽  
Added Mass ◽  
Boundary Integral ◽  
Hydrodynamic Coefficients ◽  
Floating Bodies ◽  
Damping Coefficients ◽  
Hydrodynamic Damping ◽  
Harmonic Components ◽  
Heave Motion

A general nonlinear theory for solving the radiation problem for floating or immersed bodies in a periodic heave motion, composed of a number of harmonic components, is applied for calculating the influence of draft variations on the linear hydrodynamic coefficients for heave. It is shown that a calculation method for added-mass and damping coefficients of axisymmetric bodies based on a boundary integral equation method can easily be modified to obtain numerical values of the first and second derivatives with respect to draft of the hydrodynamic coefficients as well. The method is illustrated by experimental and numerical data for a floating cone.

scholarly journals Capillary-gravity waves on the interface of two dielectric fluid layers under normal electric fields

2020 ◽  
Vol 73 (3) ◽  
pp. 231-250
Author(s):  
A Doak ◽  
T Gao ◽  
J -M Vanden-Broeck ◽  
J J S Kandola
Keyword(s):  
Electric Fields ◽  
Solitary Waves ◽  
Gravity Waves ◽  
Integral Equation Method ◽  
Travelling Wave ◽  
Boundary Integral ◽  
Dielectric Fluid ◽  
Weakly Nonlinear ◽  
Dielectric Fluids ◽  
Fluid Layers

Summary In this article, we consider capillary-gravity waves propagating on the interface of two dielectric fluids under the influence of normal electric fields. The density of the upper fluid is assumed to be much smaller than the lower one. Linear and weakly nonlinear theories are studied. The connection to the results in other limit configurations is discussed. Fully nonlinear computations for travelling wave solutions are achieved via a boundary integral equation method. Periodic waves, solitary waves and generalised solitary waves are presented. The bifurcation of generalised solitary waves is discussed in detail.

Influence of varying magnetic field on nonlinear wave excitations in collisional quantum plasmas

2020 ◽  
Vol 75 (11) ◽  
pp. 913-919
Author(s):  
Debasish Roy ◽  
Biswajit Sahu
Keyword(s):  
Magnetic Field ◽  
Nonlinear Wave ◽  
Numerical Solutions ◽  
Soliton Solutions ◽  
Quantum Plasma ◽  
Type Model ◽  
Weakly Nonlinear ◽  
Quantum Hydrodynamic Model ◽  
Frame Work ◽  
Spatially Varying

AbstractThe nonlinear wave excitations arising from the spatially varying magnetic field in the quantum plasma environment are investigated in the frame work of quantum hydrodynamic model. In the weakly nonlinear, dispersive and dissipative limit it is shown that the varying magnetic field and collision-induced excitations can be described by a modified form of Korteweg-de Vries–Burgers’ type model equation. It is found that the dissipation terms (Burgers’ and collisional term) arise due to spatially varying magnetic field and the ion-neutral collisions. The numerical solutions of this equation predict that the localized soliton solutions decay algebraically due to the combined effect of varying magnetic field and collision by radiating oscillatory pulses behind the propagating soliton.

scholarly journals On satisfying the radiation condition in free-surface flows

2009 ◽  
Vol 624 ◽  
pp. 179-189 ◽  
Author(s):  
B. J. BINDER ◽  
J.-M. VANDEN-BROECK ◽  
F. DIAS
Keyword(s):  
Radiation Condition ◽  
Integral Equation Method ◽  
Free Surface Flows ◽  
Boundary Integral ◽  
Steady Flows ◽  
Surface Flows ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Analysis ◽  
Critical Solutions ◽  
Nonlinear Solutions

Binder & Vanden-Broeck (2005) showed there are no subcritical or critical solutions satisfying the radiation condition for steady flows past a flat plate. By using a weakly nonlinear analysis, it is shown that such flows exist for a curved plate. Fully nonlinear solutions are computed by a boundary integral equation method, and new nonlinear solutions for supercritical and generalized critical flows past a curved plate are presented.

scholarly journals Null modes effect in Rossby wave model

2004 ◽  
Vol 11 (3) ◽  
pp. 281-293
Author(s):  
V. Goncharov ◽  
V. Pavlov
Keyword(s):  
Nonlinear Wave ◽  
Rossby Wave ◽  
Wave Model ◽  
Wave Fields

Abstract. The problem of the null-modes existence and some particularities of their interaction with nonlinear vortex-wave-like structures is discussed. We show that the null-modes are fundamental elements of nonlinear wave fields. The conditions under which null-modes can manifest themselves are elucidated. The Rossby-Hasegawa-Mima (RHM) model is used for the illustration of features of null-modes-waves interactions.

The inverse elastic scattering by an impenetrable obstacle and a crack

2020 ◽  
Author(s):  
Jianli Xiang ◽  
Guozheng Yan
Keyword(s):  
Mixed Type ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Field Operator ◽  
Integral Equation Method ◽  
Factorization Method ◽  
Boundary Integral ◽  
Far Field ◽  
Direct Scattering ◽  
Time Harmonic

Abstract This paper is concerned with the inverse scattering problem of time-harmonic elastic waves by a mixed-type scatterer, which is given as the union of an impenetrable obstacle and a crack. We develop the modified factorization method to determine the shape of the mixed-type scatterer from the far field data. However, the factorization of the far field operator $F$ is related to the boundary integral matrix operator $A$, which is obtained in the study of the direct scattering problem. So, in the first part, we show the well posedness of the direct scattering problem by the boundary integral equation method. Some numerical examples are presented at the end of the paper to demonstrate the feasibility and effectiveness of the inverse algorithm.

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