scholarly journals Non-linear water waves generated by impulsive motion of submerged obstacle

2013 ◽  
Vol 1 (6) ◽  
pp. 7647-7665
Author(s):  
N. I. Makarenko ◽  
V. K. Kostikov
Keyword(s):  
Water Waves ◽  
Elliptic Cylinder ◽  
Small Time ◽  
Leading Order ◽  
Constant Acceleration ◽  
Impulsive Motion ◽  
Wave Elevation ◽  
Fluid Velocities ◽  
Model Equations ◽  
Moving Obstacle

Abstract. Fully nonlinear problem on unsteady water waves generated by impulsively moving obstacle is studied analytically. Our method involves the reduction of Euler equations to the integral-differential system for the wave elevation together with normal and tangential fluid velocities at the free surface. Exact model equations are derived in explicit form in the case when the isolated obstacle is presented by totally submerged elliptic cylinder. Small-time asymptotic solution is constructed for the cylinder which starts with constant acceleration from rest. It is demonstrated that the leading-order solution terms describe several wave regimes such as the formation of non-stationary splash jets by vertical rising or vertical submersion of the obstacle, as well as the generation of diverging waves is observed.

scholarly journals Non-linear water waves generated by impulsive motion of submerged obstacles

2014 ◽  
Vol 14 (4) ◽  
pp. 751-756 ◽  
Author(s):  
N. I. Makarenko ◽  
V. K. Kostikov
Keyword(s):  
Water Waves ◽  
Linear Problem ◽  
Elliptic Cylinder ◽  
Small Time ◽  
Impulsive Motion ◽  
Wave Elevation ◽  
Fluid Velocities ◽  
Non Linear ◽  
Model Equations ◽  
Moving Obstacle

Abstract. A fully non-linear problem on unsteady water waves generated by an impulsively moving obstacle is studied analytically. Our method involves reduction of the Euler equations to the integral-differential system for the wave elevation together with normal and tangential fluid velocities at a free surface. Exact model equations are derived in explicit form in a case where an isolated obstacle is presented by a totally submerged elliptic cylinder. A small-time asymptotic solution is constructed for a cylinder which starts with constant acceleration from rest. It is demonstrated that the leading-order solution terms describe several wave regimes such as the formation of non-stationary splash jets by vertical rising or vertical submersion of the obstacle; the generation of diverging waves is also observed.

Nonlinear Water Waves in the Presence of Submerged Elliptic Cylinder

2004 ◽  
Author(s):  
Nikolai I. Makarenko
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Boundary Integral Equations ◽  
Fluid Velocity ◽  
Elliptic Cylinder ◽  
Small Time ◽  
Boundary Integral ◽  
Nonlinear Water Waves ◽  
Wave Elevation ◽  
Boundary Equations

The fully nonlinear problem on unsteady two-dimensional water waves generated by elliptic cylinder, that is horizontally submerged beneath a free surface, is considered. An analytical boundary integral equations method using a version of Milne-Thomson transformation is developed. Boundary equations (the BEq system) determine immediately exact wave elevation and fluid velocity at free surface. Small-time solution expansion is obtained in the case of accelerated cylinder starting from rest.

Free-surface flow due to impulsive motion of a submerged circular cylinder

1995 ◽  
Vol 286 ◽  
pp. 67-101 ◽  
Author(s):  
Peder A. Tyvand ◽  
Touvia Miloh
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Hydrodynamic Force ◽  
Free Surface Flow ◽  
Small Time ◽  
Surface Flow ◽  
Constant Acceleration ◽  
Impulsive Motion ◽  
Gravitational Effects ◽  
Bipolar Coordinates

The impulsively starting motion of a circular cylinder submerged horizontally below a free surface is studied analytically using a small-time expansion. The series expansion is taken as far as necessary to include the leading gravitational effects for two cases: constant velocity and constant acceleration, both commencing from rest. The hydrodynamic force on the cylinder and the surface elevation are calculated and expressed in terms of bipolar coordinates. Comparisons are also made with earlier theoretical and experimental work. The theory is valid for arbitrary value of submergence depth to cylinder radius.

An Efficient Numerical Model of Hyperbolic Mild-Slope Equation

2007 ◽  
Author(s):  
Zhiyao Song ◽  
Honggui Zhang ◽  
Jun Kong ◽  
Ruijie Li ◽  
Wei Zhang
Keyword(s):  
Wave Propagation ◽  
Numerical Model ◽  
Water Waves ◽  
Computational Time ◽  
Transient Wave ◽  
Flat Bottom ◽  
The Real ◽  
Wave Elevation ◽  
Mild Slope Equation ◽  
Effective Wave

Introduction of an effective wave elevation function, the simplest time-dependent hyperbolic mild-slope equation has been presented and an effective numerical model for the water wave propagation has been established combined with different boundary conditions in this paper. Through computing the effective wave elevation and transforming into the real transient wave motion, then related wave heights are computed. Because the truncation errors of the presented model only induced by the dissipation terms, but those of Lin’s model (2004) contributed by the convection terms, dissipation terms and source terms, the error analysis shows that calculation stability of this model is enhanced obviously compared with Lin’s one. The tests show that this model succeeds to the merit in Lin’s one and the computer program simpler, computational time shorter because of calculation stability enhanced efficiently and computer memory decreased obviously. The presented model has the capability of simulating exactly the location of transient wave front by the speed of wave propagation in the first test, which is important for the real-time prediction of the arrival time of water waves generated in the deep sea. The model is validated against experimental data for combined wave refraction and diffraction over submerged circular shoal on a flat bottom in the second test. Good agreements are gained. The model can be applied to the theory research and engineering applications about the wave propagation in the coastal waters.

A multiple exp-function method for the three model equations of shallow water waves

2017 ◽  
Vol 89 (3) ◽  
pp. 2291-2297 ◽  
Author(s):  
Yakup Yildirim ◽  
Emrullah Yasar ◽  
Abdullahi Rashid Adem
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Function Method ◽  
Shallow Water Waves ◽  
Model Equations

scholarly journals Stable model equations for long water waves

1976 ◽  
Vol 32 (6) ◽  
pp. 619-636 ◽  
Author(s):  
L. J. F. Broer ◽  
E. W. C. Groesen ◽  
J. M. W. Timmers
Keyword(s):  
Water Waves ◽  
Stable Model ◽  
Model Equations

Accurate refraction–diffraction equations for water waves on a variable-depth rough bottom

2001 ◽  
Vol 449 ◽  
pp. 301-311 ◽  
Author(s):  
YEHUDA AGNON ◽  
EFIM PELINOVSKY
Keyword(s):  
Water Waves ◽  
Mean Field ◽  
Variable Coefficients ◽  
Test Case ◽  
Random Roughness ◽  
Operator Calculus ◽  
Mild Slope Equation ◽  
The Mean ◽  
Model Equations ◽  
Systematic Derivation

The extended mild-slope equation and the modified mild-slope equation have been used successfully to study refraction–diffraction of linear water waves by steep bottom roughness. Their consistency has been questioned. A systematic derivation of these model equations exposes and illuminates their rationale. Their good performance stems from an accurate representation of (Class I) Bragg resonance. As a benchmark test case, we consider scattering by a sloping bottom with random roughness. The rates of scattering found for the mean field in both of the approximate models agree exactly with the full theory for scattering by small roughness. This greatly improves the limited agreement which was found for the mild-slope equation, and establishes the validity of the above model equations. The study involves operator calculus, a powerful method for simplifying problems with variable coefficients. The augmented mild-slope equation serves to consistently derive accurate model equations.

scholarly journals Model Equations for Three-Dimensional Nonlinear Water Waves under Tangential Electric Field

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Bo Tao
Keyword(s):  
Electric Field ◽  
Water Waves ◽  
Three Dimensional ◽  
Liquid Sheet ◽  
Capillary Waves ◽  
Uniform Electric Field ◽  
Nonlinear Water Waves ◽  
Petviashvili Equation ◽  
Model Equations ◽  
Layer Problem

We are concerned with gravity-capillary waves propagating on the surface of a three-dimensional electrified liquid sheet under a uniform electric field parallel to the undisturbed free surface. For simplicity, we make an assumption that the permittivity of the fluid is much larger than that of the upper-layer gas; hence, this two-layer problem is reduced to be a one-layer problem. In this paper, we propose model equations in the shallow-water regime based on the analysis of the Dirichlet-Neumann operator. The modified Benney-Luke equation and Kadomtsev-Petviashvili equation will be derived, and the truly three-dimensional fully localized traveling waves, which are known as “lumps” in the literature, are numerically computed in the Benney-Luke equation.

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