SCALAR DIFFRACTION BY A PROLATE SPHEROID AT LOW FREQUENCIES

1960 ◽  
Vol 38 (12) ◽  
pp. 1632-1641 ◽  
Author(s):  
T. B. A. Senior
Keyword(s):  
Exact Solution ◽  
Plane Wave ◽  
Oblate Spheroid ◽  
Prolate Spheroid ◽  
Wave Number ◽  
Scalar Problem ◽  
Low Frequencies ◽  
Scalar Diffraction

For the scalar problem of the diffraction of a plane wave by a prolate spheroid the exact solution is known, and by expanding this in ascending powers of ka, where k is the wave number and 2a is the interfocal distance, the Rayleigh series for both the "soft" and "hard" bodies are obtained up to and including terms in (ka)6. The corresponding results for an oblate spheroid can be deduced by a trivial change of parameters. Some particular cases are examined.

The low frequency scalar diffraction by an elliptic disc

1967 ◽  
Vol 63 (4) ◽  
pp. 1273-1280 ◽  
Author(s):  
B. D. Sleeman
Keyword(s):  
Plane Wave ◽  
Cross Section ◽  
Scattered Field ◽  
Low Frequency ◽  
Field Amplitude ◽  
Wave Number ◽  
Series Expansions ◽  
Far Field ◽  
Scalar Diffraction ◽  
Scattering Cross

SummaryThe problem of scalar Dirichlet diffraction of a plane wave by an elliptic disc is discussed. A scheme is given whereby the low frequency expansion of the scattered field may be readily obtained. Series expansions are obtained for the far-field amplitude up to and including the second order in the wave number. The first two terms of the scattering cross-section are also derived.

Low Wave Number Radar Image Energy Influence on Determining Current

2012 ◽  
Vol 433-440 ◽  
pp. 6054-6059
Author(s):  
Gan Nan Yuan ◽  
Rui Cai Jia ◽  
Yun Tao Dai ◽  
Ying Li
Keyword(s):  
Wave Spectrum ◽  
Surface Current ◽  
Sea Surface ◽  
Radar Image ◽  
Wave Number ◽  
Sea State ◽  
Low Frequencies ◽  
In Situ Data ◽  
Main Effects

In the radar imaging mechanism different phenomena are present, as a result the radar image is not a direct representation of the sea state. In analyzing radar image spectra, it can be realized that all of these phenomena produce distortions in the wave spectrum. The main effects are more energy for very low frequencies. This work investigates the structure of the sea clutter spectrum, and analysis the low wave number energy influence on determining sea surface current. Then the radar measure current is validated by experiments. By comparing with the in situ data, we know that the radar results reversed by image spectrum without low wave number spectrum have high precision. The low wave number energy influent determining current seriously.

Inverse Scattering from a Perfectly Conducting Prolate Spheroid in the Quasi-Static Domain

1973 ◽  
Vol 51 (2) ◽  
pp. 219-222
Author(s):  
D. A. Hill
Keyword(s):  
Magnetic Fields ◽  
Magnetic Dipole ◽  
Inverse Scattering ◽  
Oblate Spheroid ◽  
Prolate Spheroid ◽  
Dipole Source ◽  
Intermediate Step

The problem of inverse scattering from a perfectly conducting prolate spheroid in the quasistatic region of a magnetic dipole source is considered. From one observation of the radial and transverse scattered magnetic fields, the parameters which identify the spheroid (interfocal distance and eccentricity) are uniquely determined. The intermediate step requires the determination of the two magnetic polarizabilities. Similar results are also obtained for the oblate spheroid by a transformation.

scholarly journals Exact Solutions Superimposed with Nonlinear Plane Waves

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
B. S. Desale ◽  
Vivek Sharma
Keyword(s):  
Exact Solution ◽  
Plane Wave ◽  
Incompressible Fluid ◽  
Exact Solutions ◽  
Large Scale ◽  
Plane Waves ◽  
Boussinesq Equations ◽  
Integral Curves ◽  
Nonlinear Plane ◽  
Scale Motion

The flow of fluid in atmosphere and ocean is governed by rotating stratified Boussinesq equations. Through the literature, we found that many researchers are trying to find the solutions of rotating stratified Boussinesq equations. In this paper, we have obtained special exact solutions and nonlinear plane waves. Finally, we provide exact solutions to rotating stratified Boussinesq equations with large scale motion superimposed with the nonlinear plane waves. In support of our investigations, we provided two examples: one described the special exact solution and in second example, we have determined the special exact solution superimposed with nonlinear plane wave. Also, we depicted some integral curves that represent the flow of an incompressible fluid particle on the planex1+x2=L(constant)as the particular case.

THE SCATTERING OF A PLANE WAVE BY A ROW OF SMALL CYLINDERS

1960 ◽  
Vol 38 (2) ◽  
pp. 272-289 ◽  
Author(s):  
R. F. Millar
Keyword(s):  
Boundary Condition ◽  
Plane Wave ◽  
Integral Equations ◽  
Cross Sections ◽  
Simultaneous Equations ◽  
Wave Number ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Higher Order Terms ◽  
Scattering Cross Sections

Consideration is given to the scattering of a plane wave by N cylinders equispaced in a row. The problems associated with scatterers, both "soft" and "hard" in the acoustical sense, are treated. An application of Green's theorem together with the appropriate boundary condition on the cylinders leads to a set of simultaneous integral equations in the unknown function on the cylinders.Solutions in the form of series in powers of a small parameter δ (essentially the ratio of cylinder dimension to wavelength) are assumed. In the case of elliptic cylinders, the integral equations are reduced to sets of linear algebraic equations. Only for the first term in the solution for "soft" cylinders is it necessary to solve N simultaneous equations in N unknowns; all other equations involve essentially only one unknown. Far-fields and scattering cross sections are calculated. The case of two "soft" cylinders is given particular attention.Conditions for justification of the neglect of higher-order terms are discussed. It is found that all terms but the first (in either problem) may be neglected if [Formula: see text] and (N–1)/(ka) is sufficiently small. (Here a is the spacing between centers of adjacent cylinders, and k is the wave number.) For this reason these solutions are most useful when the number of cylinders is small.

Flow in Narrow Curved Channels

1980 ◽  
Vol 47 (1) ◽  
pp. 7-10 ◽  
Author(s):  
C.-Y. Wang
Keyword(s):  
Exact Solution ◽  
Pressure Gradient ◽  
Wave Number ◽  
Perturbation Scheme ◽  
Arc Length ◽  
Flow Rates ◽  
Circular Arc ◽  
Curved Channels ◽  
Flow Through ◽  
Small Periodic

The flow through narrow, arbitrarily curved channels is formulated using intrinsic coordinates. An exact solution exists for constant curvature or circular arc boundaries. A perturbation scheme is used for the case of small, periodic curvature. The velocities and flow rates depend on both the curvature amplitude and the wave number. It is found that for a given pressure gradient per arc length, the flow may be larger for periodically curved channels than that of straight channels.

The motion of an ellipsoid in tube flow at low Reynolds numbers

1996 ◽  
Vol 324 ◽  
pp. 287-308 ◽  
Author(s):  
Masako Sugihara-Seki
Keyword(s):  
Initial Conditions ◽  
Flow Direction ◽  
Major Axis ◽  
Oblate Spheroid ◽  
Reynolds Numbers ◽  
Prolate Spheroid ◽  
Stable Configuration ◽  
Axis Ratio ◽  
Low Reynolds Numbers ◽  
Freely Suspended

The motion of a rigid ellipsoidal particle freely suspended in a Poiseuille flow of an incompressible Newtonian fluid through a narrow tube is studied numerically in the zero-Reynolds-number limit. It is assumed that the effect of inertia forces on the motion of the particle and the fluid can be neglected and that no forces or torques act on the particle. The Stokes equation is solved by a finite element method for various positions and orientations of the particle to yield the instantaneous velocity of the particle as well as the flow field around it, and the particle trajectories are determined for different initial configurations. A prolate spheroid is found to either tumble or oscillate in rotation, depending on the particle–tube size ratio, the axis ratio of the particle, and the initial conditions. A large oblate spheroid may approach asymptotically a steady, stable configuration, at which it is located close to the tube centreline, with its major axis slightly tilted from the undisturbed flow direction. The motion of non-axisymmetric ellipsoids is also illustrated and discussed with emphasis on the effect of the particle shape and size.

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