Nonlinear Interaction of Submerged Cylinder With Free Surface

2002 ◽  
Author(s):  
Nikolai I. Makarenko
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Fluid Velocity ◽  
Wave Form ◽  
Cylinder Axis ◽  
Moving Cylinder ◽  
Solution Estimate ◽  
Submerged Cylinder ◽  
Special Case ◽  
Majorant Method

The fully nonlinear problem on the unsteady water waves generated by submerged moving cylinder is considered. Using the analytic majorant method we prove local in time unique solvability of this problem. For the case when the dimensionless cylinder radius is small, the solution estimate obtained predicts rigorously dipole-like structure for the lowest order far field flow. The strength of dipole concentrated at the cylinder axis depends on the instantaneous wave form and fluid velocity at the free surface. Special case of the lifting accelerated cylinder starting from the rest is studied analytically in more detail.

Nonlinear Interaction of Submerged Cylinder With Free Surface

2003 ◽  
Vol 125 (1) ◽  
pp. 72-75 ◽  
Author(s):  
Nikolai I. Makarenko
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Fluid Velocity ◽  
Wave Form ◽  
Cylinder Axis ◽  
Moving Cylinder ◽  
Solution Estimate ◽  
Submerged Cylinder ◽  
Special Case ◽  
Majorant Method

The fully nonlinear problem on the unsteady water waves generated by submerged moving cylinder is considered. Using the analytic majorant method we prove local in time unique solvability of this problem. For the case when the dimensionless cylinder radius is small, the solution estimate obtained predicts rigorously dipole-like structure for the lowest order far field flow. The strength of dipole concentrated at the cylinder axis depends on the instantaneous wave form and fluid velocity at the free surface. A special case of the lifting accelerated cylinder starting from the rest is studied analytically in more detail.

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.

Development of the Inflow Boundary With a Free Surface to Apply the MPS Method to Tsunami Analysis on Coastal Areas

2012 ◽  
Author(s):  
Koichi Masuda ◽  
Tomoki Ikoma ◽  
Yasuhiro Aida ◽  
Junpei Takayama
Keyword(s):  
Free Surface ◽  
Fluid Velocity ◽  
Fluid Pressure ◽  
Particle Method ◽  
Wave Form ◽  
Mps Method ◽  
Wave Elevation ◽  
Wave Maker ◽  
Computationally Expensive ◽  
Run Up

The wave maker of MPS method, a kind of particle method, with free surface is developed in this study. This wave maker has the function of the inflow and outflow of particles. Compared to piston-type wave maker, this is possible to reduce the particle for calculation keeping wave form. As a result, this way is faster computation than that. This way controlled by fluid velocity and wave elevation is able to input propagating tsunami of actual phenomenon and data generated by the other result of MPS method and able to continue simulation. This means that it is possible to simulate in detail with 3D-MPS method after 2D-MPS method that is less computationally expensive. This approach is applied to the analysis to tsunami in coastal area. In this study, fluid pressure of run-up-tsunami affecting a building with MPS method is compared and with experiment. And applying MPS method to analysis of run-up-tsunami is considered.

Diffraction of water waves by a submerged vertical plate

1970 ◽  
Vol 40 (3) ◽  
pp. 433-451 ◽  
Author(s):  
D. V. Evans
Keyword(s):  
Free Surface ◽  
Boundary Value Problem ◽  
Incident Wave ◽  
Water Waves ◽  
Vertical Plate ◽  
Velocity Potential ◽  
Wave Train ◽  
Plane Waves ◽  
Two Dimensional ◽  
Special Case

A thin vertical plate makes small, simple harmonic rolling oscillations beneath the surface of an incompressible, irrotational liquid. The plate is assumed to be so wide that the resulting equations may be regarded as two-dimensional. In addition, a train of plane waves of frequency equal to the frequency of oscillation of the plate, is normally incident on the plate. The resulting linearized boundary-value problem is solved in closed form for the velocity potential everywhere in the fluid and on the plate. Expressions are derived for the first- and second-order forces and moments on the plate, and for the wave amplitudes at a large distance either side of the plate. Numerical results are obtained for the case of the plate held fixed in an incident wave-train. It is shown how these results, in the special case when the plate intersects the free surface, agree, with one exception, with results obtained by Ursell (1947) and Haskind (1959) for this problem.

scholarly journals A variational formulation for steady surface water waves on a Beltrami flow

2020 ◽  
Vol 476 (2234) ◽  
pp. 20190495
Author(s):  
M. D. Groves ◽  
J. Horn
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Water Wave Problem ◽  
Normal Fluid ◽  
Beltrami Flow ◽  
Spatial Coordinates ◽  
Surface Water Waves ◽  
Non Local

This paper considers steady surface waves ‘riding’ a Beltrami flow (a three-dimensional flow with parallel velocity and vorticity fields). It is demonstrated that the hydrodynamic problem can be formulated as two equations for two scalar functions of the horizontal spatial coordinates, namely the elevation η of the free surface and the potential Φ defining the gradient part (in the sense of the Hodge–Weyl decomposition) of the horizontal component of the tangential fluid velocity there. These equations are written in terms of a non-local operator H ( η ) mapping Φ to the normal fluid velocity at the free surface, and are shown to arise from a variational principle. In the irrotational limit, the equations reduce to the Zakharov–Craig–Sulem formulation of the classical three-dimensional steady water-wave problem, while H ( η ) reduces to the familiar Dirichlet–Neumann operator.

scholarly journals An alternative approach to study irrotational periodic gravity water waves

2021 ◽  
Vol 72 (4) ◽  
Author(s):  
Biswajit Basu ◽  
Calin I. Martin
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Water Wave ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Stagnation Points ◽  
Alternative Approach ◽  
New Formulation ◽  
Bounded Below ◽  
Surface Dynamic

AbstractWe are concerned here with an analysis of the nonlinear irrotational gravity water wave problem with a free surface over a water flow bounded below by a flat bed. We employ a new formulation involving an expression (called flow force) which contains pressure terms, thus having the potential to handle intricate surface dynamic boundary conditions. The proposed formulation neither requires the graph assumption of the free surface nor does require the absence of stagnation points. By way of this alternative approach we prove the existence of a local curve of solutions to the water wave problem with fixed flow force and more relaxed assumptions.

scholarly journals Bound Coherent Structures Propagating on the Free Surface of Deep Water

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 115
Author(s):  
Dmitry Kachulin ◽  
Sergey Dremov ◽  
Alexander Dyachenko
Keyword(s):  
Free Surface ◽  
Deep Water ◽  
Coherent Structures ◽  
Water Waves ◽  
Nonlinear Models ◽  
Ideal Incompressible Fluid ◽  
Equation Model ◽  
System Of Nonlinear Equations ◽  
Potential Flows ◽  
Deep Water Waves

This article presents a study of bound periodically oscillating coherent structures arising on the free surface of deep water. Such structures resemble the well known bi-soliton solution of the nonlinear Schrödinger equation. The research was carried out in the super-compact Dyachenko-Zakharov equation model for unidirectional deep water waves and the full system of nonlinear equations for potential flows of an ideal incompressible fluid written in conformal variables. The special numerical algorithm that includes a damping procedure of radiation and velocity adjusting was used for obtaining such bound structures. The results showed that in both nonlinear models for deep water waves after the damping is turned off, a periodically oscillating bound structure remains on the fluid surface and propagates stably over hundreds of thousands of characteristic wave periods without losing energy.

scholarly journals New exact relations for steady irrotational two-dimensional gravity and capillary surface waves

2017 ◽  
Vol 376 (2111) ◽  
pp. 20170220 ◽  
Author(s):  
Didier Clamond
Keyword(s):  
Free Surface ◽  
Gravity Waves ◽  
Water Waves ◽  
Two Dimensional ◽  
Physical Plane ◽  
Theme Issue ◽  
Nonlinear Water Waves ◽  
Dimensional Gravity ◽  
Irrotational Motion ◽  
Exact Relations

Steady two-dimensional surface capillary–gravity waves in irrotational motion are considered on constant depth. By exploiting the holomorphic properties in the physical plane and introducing some transformations of the boundary conditions at the free surface, new exact relations and equations for the free surface only are derived. In particular, a physical plane counterpart of the Babenko equation is obtained. This article is part of the theme issue ‘Nonlinear water waves’.

scholarly journals Experiments on generation of surface waves by an underwater moving bottom

2015 ◽  
Vol 471 (2178) ◽  
pp. 20150069 ◽  
Author(s):  
Timothée Jamin ◽  
Leonardo Gordillo ◽  
Gerardo Ruiz-Chavarría ◽  
Michael Berhanu ◽  
Eric Falcon
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Surface Deformation ◽  
Fluid Layer ◽  
Fluid Velocity ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass ◽  
Spatio Temporal ◽  
Experimental Findings

We report laboratory experiments on surface waves generated in a uniform fluid layer whose bottom undergoes an upward motion. Simultaneous measurements of the free-surface deformation and the fluid velocity field are focused on the role of the bottom kinematics (i.e. its spatio-temporal features) in wave generation. We observe that the fluid layer transfers bottom motion to the free surface as a temporal high-pass filter coupled with a spatial low-pass filter. Both filter effects are often neglected in tsunami warning systems, particularly in real-time forecast. Our results display good agreement with a prevailing linear theory without any parameter fitting. Based on our experimental findings, we provide a simple theoretical approach for modelling the rapid kinematics limit that is applicable even for initially non-flat bottoms: this may be a key step for more realistic varying bathymetry in tsunami scenarios.

Free-surface breakdown in a rapidly rotating liquid

1978 ◽  
Vol 86 (3) ◽  
pp. 457-463 ◽  
Author(s):  
W. E. Scott
Keyword(s):  
Free Surface ◽  
Capillary Waves ◽  
Mode Frequency ◽  
Wave Form ◽  
Inertial Waves ◽  
Rotating Liquid ◽  
Surface Breakdown ◽  
Beat Phenomenon ◽  
Inertial Wave ◽  
Wave Modes

It is shown that the wavelets which appear on the inertial wave form of the inner free surface of a fully spun-up cylindrical mass of liquid contained in a vertical, rapidly rotating and gyrating gyrostat are capillary waves. It is further shown that the interaction between these capillary waves and the excited inertial waves is not the mechanism which effects an observed two-period collapse (‘breakdown’) and reappearance of the free-surface inertial wave form. Rather, the two-period breakdown can be explained by the conjecture that it is a beat phenomenon arising from the interaction of two differently structured inertial wave modes, which have the same frequency at small amplitudes of oscillation of the gyrostat but which, owing to the dependence of the inertial mode frequency on the amplitude of the gyrostatic motion, have slightly different frequencies at larger amplitudes of oscillation of the gyrostat.

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