The radiation and scattering of surface waves by a vertical circular cylinder in a channel

1992 ◽  
Vol 338 (1650) ◽  
pp. 325-357 ◽  
Keyword(s):  
Circular Cylinder ◽  
Gravity Waves ◽  
The Body ◽  
Far Field ◽  
Algebraic Equations ◽  
Surface Gravity Waves ◽  
Infinite Systems ◽  
Linear Algebraic Equations ◽  
Correct Form ◽  
Body Boundary

In this paper we consider the problems of the radiation and scattering of surface gravity waves by a vertical circular cylinder placed on the centreline of a channel of width 2 d and depth H , and either extending from the bottom through the free surface or truncated so as to fill only part of the depth. These problems are solved, for arbitrary incident wavenumber k , by constructing appropriate multipoles for cylinders placed symmetrically in channels and then using the body boundary condition to derive a set of infinite systems of linear algebraic equations. For the general problems considered here, this method is superior to the more usual approach of using a set of image cylinders to model the channel walls, in particular the occurrence of modes other than the fundamental when kd > is accurately modelled and the correct form predicted for the far-field.

Surface Gravity Waves

2017 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Gravity Waves ◽  
Water Waves ◽  
Water Surface ◽  
Wave Pattern ◽  
The Body ◽  
Surface Gravity ◽  
Shallow Water Waves ◽  
Ship Waves ◽  
Surface Gravity Waves ◽  
Basic Fluid

This chapter deals with the underlying mathematics of surface gravity waves, defined as gravity waves observed on an air–sea interface of the ocean. Surface gravity waves, or surface waves, differ from internal waves, gravity waves that occur within the body of the water (such as between parts of different densities). Examples of gravity waves are wind-generated waves on the water surface, as well tsunamis and ocean tides. Wind-generated gravity waves on the free surface of the Earth's seas, oceans, ponds, and lakes have a period of between 0.3 and 30 seconds. The chapter first describes the basic fluid equations before discussing the dispersion relations, with a particular focus on deep water waves, shallow water waves, and wavepackets. It also considers ship waves and how dispersion affects the wave pattern produced by a moving object, along with long and short waves.

scholarly journals Excitation of anisotropic impedance metasurface in the form of elliptical cylinder.

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
A.I. Semenikhin ◽  
◽  
D.V. Semenikhin ◽  
Keyword(s):  
Elliptical Cylinder ◽  
Impedance Tensor ◽  
Reflection Coefficients ◽  
Algebraic Equations ◽  
Partial Reflection ◽  
Infinite Systems ◽  
Linear Algebraic Equations ◽  
External Sources ◽  
Surface Impedance Tensor ◽  
Special Case

The problem of arbitrary excitation of waves by a system of external sources near an anisotropic metasurface in the form of an elliptical cylinder with a surface homogenized impedance tensor of general form is solved. The solution to the problem is written as a superposition of E- and H-waves in elliptical coordinates. The partial reflection coefficients of waves were found from the boundary conditions using the orthogonality of the Mathieu angular functions. For these coefficients, four coupled infinite systems of linear algebraic equations of the second kind are obtained. The conditions under which the solution of the excitation problem by the method of eigenfunctions is obtained in an explicit form are found and analyzed. It is shown that for this, the surface impedance tensor of a uniform metasurface must belong to a class of deviators (have zero diagonal elements). In the particular case of a mutual (most easily realized) metasurface, its impedance tensor should only be reactance. In another special case, the impedance tensor of a set of deviators describes a class of anisotropic nonreciprocal metasurfaces with the so-called perfect electromagnetic conductivity (PEMC).

scholarly journals Quasihomogeneous Infinite Systems of Linear Algebraic Equations

2018 ◽  
Vol 1141 ◽  
pp. 012105
Author(s):  
F. M. Fedorov ◽  
N. N. Pavlov ◽  
O. F. Ivanova ◽  
S. V. Potapova
Keyword(s):  
Algebraic Equations ◽  
Infinite Systems ◽  
Linear Algebraic Equations

Calculation of Nonlifting Potential Flow About Arbitrary Three-Dimensional Bodies

1964 ◽  
Vol 8 (04) ◽  
pp. 22-44 ◽  
Author(s):  
John L. Hess ◽  
A. M. O. Smith
Keyword(s):  
Body Surface ◽  
Potential Flow ◽  
Fluid Velocity ◽  
Normal Component ◽  
Three Dimensional ◽  
Analytic Solutions ◽  
The Body ◽  
Algebraic Equations ◽  
Source Density ◽  
Linear Algebraic Equations

A general method is described for calculating, with the aid of an electronic computer, the incompressible potential flow about arbitrary, nonlifting, three-dimensional bodies. The method utilizes a source density distribution on the surface of the body and solves for the distribution necessary to make the normal component of fluid velocity zero on the boundary. Plane quadrilateral surface elements are used to approximate the body surface, and the integral equation for the source density is replaced by a set of linear algebraic equations for the values of the source density on the quadrilateral elements. When this set of equations has been solved, the flow velocity both on and off the body surface is calculated. After the basic ideas and equations have been derived end discussed, the accuracy of the method is exhibited by means of comparisons with analytic solutions, and its usefulness is shown by comparing calculated pressure distributions with experimental data. Some of the design problems to which the method has been applied are also presented, to indicate the variety of flow situations that can be calculated by this approach.

Electromagnetic field of the circular magnetic source in biconical section

2020 ◽  
Vol 2020 (48) ◽  
pp. 5-10
Author(s):  
O.M. Sharabura ◽  
◽  
D.B. Kuryliak ◽  
Keyword(s):  
Field Pattern ◽  
Geometrical Parameters ◽  
Algebraic Equations ◽  
Axially Symmetric ◽  
Reduction Procedure ◽  
Infinite Systems ◽  
Linear Algebraic Equations ◽  
Regularization Techniques ◽  
Far Field Pattern ◽  
Analytical Regularization

The problem of axially-symmetric electromagnetic wave diffraction from the perfectly conducting biconical scatterer formed by the finite cone placed in the semi-infinite conical region is solved rigorously using the mode-matching and analytical regularization techniques. The problem is reduced to the infinite systems of linear algebraic equations (ISLAE) of the second kind. The obtained equations admit the reduction procedure and can be solved with a given accuracy for any geometrical parameters and frequency. The numerical examples of the solution are presented. The analysis of the source location influences on the far-field pattern for different geometrical parameters of the bicone is carried out.

Internal gravity waves generated by oscillations of a sphere

1987 ◽  
Vol 183 ◽  
pp. 439-450 ◽  
Author(s):  
J. C. Appleby ◽  
D. G. Crighton
Keyword(s):  
Gravity Waves ◽  
Separation Of Variables ◽  
Near Field ◽  
Wave Structure ◽  
Internal Gravity Waves ◽  
Spherical Body ◽  
The Body ◽  
Wave Radiation ◽  
Far Field ◽  
Field Solution

We consider the radiation of internal gravity waves from a spherical body oscillating vertically in a stratified incompressible fluid. A near-field solution (under the Boussinesq approximation) is obtained by separation of variables in an elliptic problem, followed by analytic continuation to the frequencies ω < N of internal wave radiation. Matched expansions are used to relate this solution to a far-field solution in which non-Boussinesq terms are retained. In the outer near field there are parallel conical wavefronts between characteristic cones tangent to the body, but with a wavelength found to be shorter than that for oscillations of a circular cylinder. It is also found that there are caustic pressure singularities above and below the body where the characteristics intersect. Far from the source, non-Boussinesq effects cause a diffraction of energy out of the cones. The far-field wave-fronts are hyperboloidal, with horizontal axes. The case of horizontal oscillations of the sphere is also examined and is shown to give rise to the same basic wave structure.The related problem of a pulsating sphere is then considered, and it is concluded that certain features of the wave pattern, including the caustic singularities near the source, are common to a more general class of oscillating sources.

The motion of a rigid body in viscous fluid bounded by a plane wall

1989 ◽  
Vol 207 ◽  
pp. 29-72 ◽  
Author(s):  
Richard Hsu ◽  
Peter Ganatos
Keyword(s):  
Aspect Ratio ◽  
Stokes Equations ◽  
Hydrodynamic Force ◽  
Orientation Angle ◽  
Boundary Integral ◽  
The Body ◽  
Boundary Integral Method ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Planar Wall

The boundary-integral method is used to calculate the hydrodynamic force and torque on an arbitrary body of revolution whose axis of symmetry is oriented at an arbitrary angle relative to a planar wall in the zero-Reynolds-number limit. The singular solution of the Stokes equations in the presence of a planar wall is used to formulate the integral equations, which are then reduced to a system of linear algebraic equations by satisfying the no-slip boundary conditions on the body surface using the boundary collocation method or weighted residual technique.Numerical tests for the special case of a sphere moving parallel or perpendicular to a planar wall show that the present theory is accurate to at least three significant figures when compared with the exact solutions for gap widths as small as only one-tenth of the particle radius. Higher accuracy can be achieved and solutions can be obtained for smaller gap widths at the expense of more computation time and larger storage requirements.The hydrodynamic force and torque on a spheroid with varying aspect ratio and orientation angle relative to the planar wall are obtained. The theory is also applied to study the motion of a toroidal particle or biconcave shaped disc adjacent to a planar wall. The coincidence of the drag and torque of a biconcave-shaped body and a torus having an aspect ratio b/a = 2 with the same surface area shows that in this case the hole of a torus has little influence on the flow field. On the other hand, for an aspect ratio b/a = 10, the effect of the hole is significant. It is also shown that when the body is not very close to the wall, an oblate spheroid can be used as a good approximation of a biconcave-shaped disc.

scholarly journals Comparison of Linear Vortex Panel Method and Finite Volume Method for Calculation of Generated Lift in Potential Flow Over Two-Dimensional Car Bodies

2020 ◽  
Author(s):  
Saeid Moammaei ◽  
Mehran Khaki Jamei ◽  
Morteza Abbasi
Keyword(s):  
Pressure Distribution ◽  
Lift Coefficient ◽  
Control Point ◽  
Panel Method ◽  
The Body ◽  
Aerodynamic Load ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
The Impact

Abstract This paper describes one of the aspects of the panel method to analyze the aerodynamic characteristics of a sedan. The linear vortex panel method has been developed to simulate the ideal flow over a two-dimensional arbitrary car and, it also calculates the aerodynamic load on the body. By satisfying the boundary conditions on each control point, our linear algebraic equations are obtained. The results are sensitive to the distribution of the panels over the body thus the body is broken up equally into very small panels. After solving the set of equations, the vortices strength is obtained and the pressure distribution for the upper and the lower surface of the body is calculated. The impact of the angle of attack on the aerodynamic behavior of the intended car is investigated and it is found that the lift coefficient increases with the free stream angle from -4 to 4. The accuracy of the results has been determined by checking them against the standard CFD data. The pressure distribution trend is found very much in confirmation with the CFD results, however, a discrepancy at the rear end is observed. Therefore, it can be concluded that this method does not seem practical for geometries with steep slopes in the rear part of the car. Finally, both methods are applied to the other modified geometries with lower slopes at the rear section and the results compare well with the fluent.

scholarly journals TSUNAMI GENERATION BY EARTHQUAKES: SEABED TOPOGRAPHY AND INERTIAL EFFECTS

2018 ◽  
pp. 58
Author(s):  
Robert A. Dalrymple ◽  
Morteza Derakhti
Keyword(s):  
Gravity Waves ◽  
Acoustic Waves ◽  
Smooth Particle Hydrodynamic ◽  
Far Field ◽  
Relative Importance ◽  
Inertial Effects ◽  
Tsunami Generation ◽  
Moving Bed ◽  
Surface Gravity Waves ◽  
Seabed Topography

In this presentation, we examine the effects of the shape and height of a moving bed on the generated surface gravity waves using the 3-D Smooth Particle Hydrodynamic model, GPUSPH (Hérault et al., 2010). Further, we investigate the relative importance of the inertial effects on the general characteristics of the generated Tsunami in the near- and far-field for various rates of the bed displacement, ranging from creeping to impulsive regimes. The sensitivity of the inertial effects on the shape of the moving bed is also discussed. Finally, the characteristics of the acoustic waves generated during the various bed displacement scenarios are examined.

scholarly journals Wave-Slope Soaring of the Brown Pelican

2021 ◽  
Author(s):  
Ian Stokes ◽  
Andrew Lucas
Keyword(s):  
Gravity Waves ◽  
Ground Effect ◽  
Ocean Surface ◽  
The Body ◽  
Surface Gravity ◽  
Cost Of Transport ◽  
Surface Gravity Waves ◽  
Wave Slope ◽  
Ocean Conditions ◽  
Wave Induced

Abstract Background: From the laboratory at Scripps Institution of Oceanography, it is common to see the brown pelican (Pelecanus occidentalis) traveling along the crests of ocean waves just offshore of the surf zone. When flying in this manner, the birds can travel long distances without flapping, centimeters above the ocean's surface. Here we derive a theoretical framework for assessing the energetic savings related to this behavior, `wave-slope soaring,' in which an organism in flight takes advantage of localized updrafts caused by traveling ocean surface gravity waves. Methods: The energy cost of steady, constant altitude flight in and out of ground effect are analyzed as controls. Potential flow theory is used to quantify the ocean wave-induced wind associated with near-shoaling, weakly nonlinear, shallow water ocean surface gravity waves moving through an atmosphere initially at rest. Using perturbation theory and the Green's function for Laplace's equation in 2D with Dirichlet boundary conditions, we obtain integrals for the horizontal and vertical components of the wave-induced wind in a frame of reference moving with the wave. Wave-slope soaring flight is then analyzed using an energetics-based approach for waves under a range of ocean conditions and the body plan of P. occidentalis . Results: For ground effect flight, we calculate a ~ 15 - 25% reduction in cost of transport as compared with steady, level flight out of ground effect. When wave-slope soaring is employed at flight heights ≤ 2m in typical ocean conditions (2m wave height, 15s period), we calculate 60-70% reduction in cost of transport as compared with flight in ground effect. A relatively small increase in swell amplitude or decrease in flight height allows up to 100% of the cost of transport to be offset by wave-slope soaring behavior. Conclusions: The theoretical development presented here suggests there are energy savings associated with wave-slope soaring. Individual brown pelicans may significantly decrease their cost of transport utilizing this mode of flight under typical ocean conditions. Thus wave-slope soaring may provide fitness benefit to these highly mobile organisms that depend on patchy prey distribution over large home ranges.

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