Eigenmodes in the water-wave problems for infinite pools with cone-shaped bottom

2016 ◽  
Vol 800 ◽  
pp. 645-665 ◽  
Author(s):  
Mikhail A. Lyalinov
Keyword(s):  
Water Waves ◽  
Mellin Transform ◽  
Point Spectrum ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Functional Difference ◽  
Infinite Domains ◽  
Linearized Theory ◽  
Functional Difference Equations ◽  
Wave Problems

In the framework of the assumptions of the linearized theory of small-amplitude water waves, the eigenfunctions of the point spectrum are studied for boundary-value problems in infinite domains. Special types of three-dimensional infinite water pools characterised by cone-shaped bottoms are considered. By means of an incomplete separation of variables and exploiting the Mellin transform, we reduce construction of the eigenmodes to the study and solution of the problems for some functional difference equations with meromorphic coefficients. The behaviour of the eigenmodes at a singular point of the boundary and the rate of their decay at infinity are also examined.

Numerical Calculation of the Wave Integrals in the Linearized Theory of Water Waves

1977 ◽  
Vol 21 (01) ◽  
pp. 1-10 ◽  
Author(s):  
Hung-Tao Shen ◽  
Cesar Farell
Keyword(s):  
Water Waves ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Three Dimensional Flow ◽  
Integral Term ◽  
Linearized Theory ◽  
Single Integral ◽  
Numerical Computing ◽  
Complex Exponential ◽  
Derivatives Of

A method for the numerical evaluation of the derivatives of the linearized velocity potential for three-dimensional flow past a unit source submerged in a uniform stream is presented together with a discussion of existing techniques. It is shown in particular that calculation of the double integral term in these functions can be efficiently accomplished in terms of a single integral with the integrand expressed in terms of the complex exponential integral, for which numerical computing techniques are available.

scholarly journals POLYNOMIAL APPROXIMATION AND WATER WAVES

1986 ◽  
Vol 1 (20) ◽  
pp. 15 ◽  
Author(s):  
John D. Fenton
Keyword(s):  
Polynomial Approximation ◽  
Water Waves ◽  
Three Dimensional ◽  
Wave Theory ◽  
General Nature ◽  
Linear Wave ◽  
Wave Refraction ◽  
Approximate Wave ◽  
Spatial Approximation ◽  
Wave Problems

A different approach to the solution of water wave problems is considered. Instead of using an approximate wave theory combined with highly accurate global spatial approximation methods, as for example in many applications of linear wave theory, a method is developed which uses local polynomial approximation combined with the full nonlinear equations. The method is applied to the problem of inferring wave properties from the record of a pressure transducer, and is found to be capable of high accuracy for waves which are not too short, even for large amplitude waves. The general approach of polynomial approximation is well suited to problems of a rather more general nature, especially where the geometry is at all complicated. It may prove useful in other areas, such as the nonlinear interaction of long waves, shoaling of waves, and in three dimensional problems, such as nonlinear wave refraction and diffraction.

THREE-DIMENSIONAL WAVE-FREE POTENTIALS IN THE THEORY OF WATER WAVES

2013 ◽  
Vol 55 (2) ◽  
pp. 175-195 ◽  
Author(s):  
HARPREET DHILLON ◽  
B. N. MANDAL
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Surface Condition ◽  
Three Dimensional ◽  
Wave Interaction ◽  
Finite Depth ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Thin Elastic Plate ◽  
Linearized Theory

AbstractProblems of wave interaction with a body with arbitrary shape floating or submerged in water are of immense importance in the literature on the linearized theory of water waves. Wave-free potentials are used to construct solutions to these problems involving bodies with circular geometry, such as a submerged or half-immersed long horizontal circular cylinder (in two dimensions) or sphere (in three dimensions). These are singular solutions of Laplace’s equation satisfying the free surface condition and decaying rapidly away from the point of singularity. Wave-free potentials in two and three dimensions for infinitely deep water as well as water of uniform finite depth with a free surface are known in the literature. The method of constructing wave-free potentials in three dimensions is presented here in a systematic manner, neglecting or taking into account the effect of surface tension at the free surface or for water with an ice cover modelled as a thin elastic plate floating on the water. The forms of the wave motion at the upper surface (free surface or ice-covered surface) related to these wave-free potentials are depicted graphically in a number of figures for all the cases considered.

Center of Mass Theorem and the Separation of Variables for Two-Body System on a Three-Dimensional Sphere

2020 ◽  
Vol 23 (3) ◽  
pp. 306-311
Author(s):  
Yu. Kurochkin ◽  
Dz. Shoukavy ◽  
I. Boyarina
Keyword(s):  
Constant Curvature ◽  
Jacobi Equation ◽  
Separation Of Variables ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Relative Distance ◽  
Dimensional Sphere ◽  
Body System ◽  
Spaces Of Constant Curvature ◽  
Hamilton Jacobi Equation

The immobility of the center of mass in spaces of constant curvature is postulated based on its definition obtained in [1]. The system of two particles which interact through a potential depending only on the distance between particles on a three-dimensional sphere is considered. The Hamilton-Jacobi equation is formulated and its solutions and trajectory equations are found. It was established that the reduced mass of the system depends on the relative distance.

3D simulation of emulsion flow using the boundary element method on the heterogeneous computational systems

2012 ◽  
Vol 9 (1) ◽  
pp. 142-146
Author(s):  
O.A. Solnyshkina
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Problem Size ◽  
Low Reynolds Numbers ◽  
Infinite Domains ◽  
The Matrix ◽  
Computational Systems ◽  
Element Method

In this work the 3D dynamics of two immiscible liquids in unbounded domain at low Reynolds numbers is considered. The numerical method is based on the boundary element method, which is very efficient for simulation of the three-dimensional problems in infinite domains. To accelerate calculations and increase the problem size, a heterogeneous approach to parallelization of the computations on the central (CPU) and graphics (GPU) processors is applied. To accelerate the iterative solver (GMRES) and overcome the limitations associated with the size of the memory of the computation system, the software component of the matrix-vector product

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