Studies on Magneto-Hydrodynamic Waves and other Anisotropic wave motions

1960 ◽  
Vol 252 (1014) ◽  
pp. 397-430 ◽  
Keyword(s):  
Elastic Waves ◽  
Radiation Condition ◽  
Wave Theory ◽  
Local Source ◽  
Hydrodynamic Waves ◽  
Energy Propagation ◽  
Constant Coefficients ◽  
Pass Through ◽  
Hydrodynamic Wave ◽  
The Waves

There are two separate but closely interwoven strands of argument in this paper; one mainly mathematical, and one mainly physical. The mathematical strand begins with a method of asymptotically evaluating Fourier integrals in many dimensions, for large values of their arguments. This is used to investigate partial differential equations in four variables, x, y, z and t , which are linear with constant coefficients, but which may be of any order and represent wave motions that are anisotropic or dispersive or both. It gives the asymptotic behaviour (at large distances) of solutions of these equations, representing waves generated by a source of finite or infinitesimal spatial extent. The paper concentrates particularly on sources of fixed frequency, and solutions satisfying the radiation condition; but an Appendix is devoted to waves generated by a source of finite duration in an initially quiescent medium, and to unstable systems. The mathematical results are given a partial physical interpretation by arguments determining the velocity of energy propagation in a plane wave traversing an anisotropic medium. These show, among other facts not generally realized, that even for non-dispersive (e.g. elastic) waves, the energy propagation velocity is not in general normal to the wave fronts, although its component normal to them is the phase velocity. The second, mainly physical, strand of argument starts from the important and striking property of magneto-hydrodynamic waves in an incompressible, inviscid and perfectly conducting medium, of propagation in one direction only—a given disturbance propagates only along the magnetic lines of force which pass through it, and therefore suffers no attenuation with distance. There are cases of astrophysical importance where densities are so low that attenuation due to collisional effects—for example, electrical resistivity—should be negligible over relevant length scales. We therefore ask how far the effects of a non-collisional nature which are neglected in the simple theory, particularly compressibility and Hall current, would alter the unidirectional, attenuation-less propagation of the waves. These effects have been included previously in magneto-hydrodynamic wave theory, but the directional distribution of waves from a local source was not obtained. This problem explains the need for the mathematical theory just described, and gives a comprehensive illustration of its application.

scholarly journals WAVE RECORDERS

2010 ◽  
Vol 1 (1) ◽  
pp. 7
Author(s):  
F. E. Snodgrass
Keyword(s):  
Data Analysis ◽  
Attenuation Factor ◽  
Wave Theory ◽  
Ocean Waves ◽  
Simple Method ◽  
Characteristic Wave ◽  
Analysis Techniques ◽  
Wave Heights ◽  
Hydrodynamic Wave ◽  
The Waves

Several satisfactory instruments are available for recording the height and period of ocean waves, and new improved gages for this purpose are being designed. The actual procurement of wave data is no longer a major problem, but the present theories interpreting these data and the methods of data analysis leave much to be desired. Definitions of characteristic wave height and wave period are vague, as no specific period of observation is designated for determining these measurements. Analysis techniques and results are inconsistent. Preliminary studies of the statistical distribution of wave heights are encouraging, but no simple method of describing the waves with regard to period has been developed. Current hydrodynamic wave theory is apparently in error, and reexamination of this basic theory in regard to the hydrodynamic attenuation factor should be made.

The electron as a wave

2018 ◽  
Author(s):  
L. Solymar ◽  
D. Walsh ◽  
R. R. A. Syms
Keyword(s):  
Fourier Transform ◽  
Electron Microscope ◽  
Simultaneous Determination ◽  
Pulse Length ◽  
Wave Theory ◽  
Spectral Width ◽  
Pass Through ◽  
The Fourier Transform ◽  
The Waves

Discusses the Davisson–Germer experiment in which electrons pass through a screen having one or two slits, and shows the necessity for a wave theory. The operation of an electron microscope is explained and some properties of the waves including the uncertainty between the simultaneous determination of position and momentum of the particle. Analogies with classical phenomena are discussed, namely the Fourier transform relationship between pulse length and spectral width, and the size of an aperture aerial and its relationship to the beamwidth.

Comparisons of Simulation Methods for Motions of a Moored Body in Waves

1985 ◽  
Vol 107 (1) ◽  
pp. 34-41
Author(s):  
M. Takagi ◽  
K. Saito ◽  
S. Nakamura
Keyword(s):  
Wave Theory ◽  
Simulation Methods ◽  
Convolution Integral ◽  
Linear Water Wave Theory ◽  
Initial Stage ◽  
Constant Coefficients ◽  
Exciting Forces ◽  
Linear Differential ◽  
Experimental Values ◽  
The Time Domain

Based on the linear water wave theory, numerical simulations are carried out for motions in waves of a body moored by a nonlinear-type mooring system. Numerical results obtained by using the equation of motion described in the time domain with a convolution integral (C.I. method) are compared with those of the second-order linear differential equation with constant coefficients (C. C. method). These results are also compared with experimental values measured from the initial stage when the action of exciting forces starts and the validity of C.I. method is discussed.

Linear and non-linear potential-flow calculations of free-surface waves with lift and induced drag

2000 ◽  
Vol 214 (6) ◽  
pp. 801-812
Author(s):  
C-E Janson
Keyword(s):  
Free Surface ◽  
Potential Flow ◽  
Lift Force ◽  
Radiation Condition ◽  
Linear Potential ◽  
Surface Boundary ◽  
Model Approximation ◽  
Non Linear ◽  
Lifting Surfaces ◽  
The Waves

A potential-flow panel method is used to compute the waves and the lift force from surface-piercing and submerged bodies. In particular the interaction between the waves and the lift produced close to the free surface is studied. Both linear and non-linear free-surface boundary conditions are considered. The potential-flow method is of Rankine-source type using raised source panels on the free surface and a four-point upwind operator to compute the velocity derivatives and to enforce the radiation condition. The lift force is introduced as a dipole distribution on the lifting surfaces and on the trailing wake, together with a flow tangency condition at the trailing edge of the lifting surface. Different approximations for the spanwise circulation distribution at the free surface were tested for a surface-piercing wing and it was concluded that a double-model approximation should be used for low speeds while a single-model, which allows for a vortex at the free surface, was preferred at higher speeds. The lift force and waves from three surface-piercing wings, a hydrofoil and a sailing yacht were computed and compared with measurements and good agreement was obtained.

Application of Ship-Wave Theory to the Hydrofoil of Finite Span

1957 ◽  
Vol 1 (02) ◽  
pp. 27-55
Author(s):  
John P. Breslin
Keyword(s):  
Wave Theory ◽  
Wave Pattern ◽  
Wave Drag ◽  
Test Results ◽  
Dimensional Theory ◽  
Ship Hydrodynamics ◽  
Finite Span ◽  
Induced Drag ◽  
Load Distributions ◽  
The Waves

It is demonstrated in this paper2 that the deepwater wave drag of a hydrofoil of finite span can be found directly from the theory developed largely for ship hydrodynamics by Havelock and others. The wave drag is then studied at high Froude numbers and from the observed behavior the induced drag of the hydrofoil can be deduced from existing aerodynamic formulas. Evaluation of the resulting formulas is effected for two arbitrary load distributions and a comparison with some model test results is made. A practical approximation which gives the influence of gravity over a range of high Froude numbers is found and from this one can deduce a Froude number beyond which the effects of gravity may be ignored. It is also shown that an expression for the waves at some distance aft of the hydrofoil can be deduced from the general formulas developed for ship hydrodynamics. A discussion of the wave pattern is given with particular emphasis on the centerline profile at high Froude numbers and a contrast is pointed out in regard to the results of the two-dimensional theory for the hydrofoil waves and wave resistance.

scholarly journals Climatology of planetary wave type oscillations with periods of 2–20 days derived from O<sub>2</sub> atmospheric and OH(6-2) airglow observations at mid-latitude with SATI

2009 ◽  
Vol 27 (9) ◽  
pp. 3645-3662 ◽  
Author(s):  
M. J. López-González ◽  
E. Rodríguez ◽  
M. García-Comas ◽  
V. Costa ◽  
M. G. Shepherd ◽  
...  
Keyword(s):  
Sierra Nevada ◽  
Planetary Wave ◽  
Lower Thermosphere ◽  
Maximum Activity ◽  
Energy Propagation ◽  
Wave Type ◽  
Winter Solstice ◽  
The Waves ◽  
Maximum Occurrence ◽  
Dissipation Processes

Abstract. The presence of planetary wave type oscillations at mid-latitudes in the mesosphere/lower thermosphere region has been investigated using airglow observations. The observations were taken with a Spectral Airglow Temperature Imager (SATI) installed at Sierra Nevada Observatory (37.06° N, 3.38° W) at 2900 m height. Airglow data of the column emission rate of the O2 Atmospheric (0-1) band and of the OH Meinel (6-2) band and deduced rotational temperatures from 1998 to 2007 have been used in this study. From these observations a climatology of planetary wave type oscillations at this location is inferred. It has been found that the planetary wave type oscillations of 5-day period is predominant in our data throughout the year, with activity greater than 50% during March/April and October/November months. The planetary wave type oscillations of 2-day period is predominant during both solstices, being predominant during winter solstice in O2 while a 10-day oscillation appears throughout the year with activity around 20% and with maximum activity during spring and autumn equinoxes. The 16-day oscillation has maximum occurrence during autumn-winter while its activity is almost disappeared during spring-summer. No clear seasonal dependence of the amplitude of the planetary wave type oscillations was observed in the cases considered in this study. The waves simultaneously detected in the rotational temperatures deduced from both OH and O2 emissions usually show an upward energy propagation and are affected by dissipation processes.

Electromagnetic damping of elastic waves: Experimental results

1968 ◽  
Vol 5 (4) ◽  
pp. 825-829 ◽  
Author(s):  
F. E. M. Lilley ◽  
C. M. Carmichael
Keyword(s):  
Magnetic Field ◽  
Elastic Wave ◽  
Applied Magnetic Field ◽  
Elastic Waves ◽  
Applied Field ◽  
Eddy Currents ◽  
Electrical Conductor ◽  
Electromagnetic Damping ◽  
The Waves ◽  
The Magnetic Field

The passage of an elastic wave causes straining and translation in the transmitting material. If a magnetic field is applied, and the medium is an electrical conductor, some of the energy of the wave is dissipated by the flow of electrical eddy currents. Usually the amount of energy lost is very small, but it may be greatly increased if the applied field is strongly non-uniform.Laboratory experiments are described which demonstrate this effect for standing elastic waves in a metal bar. The applied magnetic field changes from almost zero to its full strength over a distance which is short compared to the length of the standing wave. The result of this strong non-uniformity is that the energy lost due to the translation of the bar in the field greatly exceeds the energy lost due to the straining of the bar in the field.The dependence of the attenuation of the waves by the magnetic field is investigated for variation in frequency of vibration, bar thickness, and field gradient.

On kinematic waves I. Flood movement in long rivers

1955 ◽  
Vol 229 (1178) ◽  
pp. 281-316 ◽  
Keyword(s):  
Shock Waves ◽  
Equations Of Motion ◽  
Functional Relation ◽  
Wave Theory ◽  
Observation Point ◽  
Rate Of Change ◽  
Kinematic Wave ◽  
Unit Distance ◽  
Kinematic Waves ◽  
The Waves

In this paper and in part II, we give the theory of a distinctive type of wave motion, which arises in any one-dimensional flow problem when there is an approximate functional relation at each point between the flow q (quantity passing a given point in unit time) and concentration k (quantity per unit distance). The wave property then follows directly from the equation of continuity satisfied by q and k . In view of this, these waves are described as ‘kinematic’, as distinct from the classical wave motions, which depend also on Newton’s second law of motion and are therefore called ‘dynamic’. Kinematic waves travel with the velocity dq/dk , and the flow q remains constant on each kinematic wave. Since the velocity of propagation of each wave depends upon the value of q carried by it, successive waves may coalesce to form ‘kinematic shock waves ’. From the point of view of kinematic wave theory, there is a discontinuous increase in q at a shock, but in reality a shock wave is a relatively narrow region in which (owing to the rapid increase of q ) terms neglected by the flow concentration relation become important. The general properties of kinematic waves and shock waves are discussed in detail in §1. One example included in §1 is the interpretation of the group-velocity phenomenon in a dispersive medium as a particular case of the kinematic wave phenomenon. The remainder of part I is devoted to a detailed treatment of flood movement in long rivers, a problem in which kinematic waves play the leading role although dynamic waves (in this case, the long gravity waves) also appear. First (§2), we consider the variety of factors which can influence the approximate flow-concentration relation, and survey the various formulae which have been used in attempts to describe it. Then follows a more mathematical section (§3) in which the role of the dynamic waves is clarified. From the full equations of motion for an idealized problem it is shown that at the ‘Froude numbers’ appropriate to flood waves, the dynamic waves are rapidly attenuated and the main disturbance is carried downstream by the kinematic waves; some account is then given of the behaviour of the flow at higher Froude numbers. Also in §3, the full equations of motion are used to investigate the structure of the kinematic shock; for this problem, the shock is the ‘monoclinal flood wave’ which is well known in the literature of this subject. The final sections (§§4 and 5) contain the application of the theory of kinematic waves to the determination of flood movement. In §4 it is shown how the waves (including shock waves) travelling downstream from an observation point may be deduced from a knowledge of the variation with time of the flow at the observation point; this section then concludes with a brief account of the effect on the waves of tributaries and run-off. In §5, the modifications (similar to diffusion effects) which arise due to the slight dependence of the flow-concentration curve on the rate of change of flow or concentration, are described and methods for their inclusion in the theory are given.

Study on Measurement Method of Dynamic Linearity for High G Micro Accelerometer

2014 ◽  
Vol 609-610 ◽  
pp. 908-913
Author(s):  
Yun Bo Shi ◽  
Sheng Fei Dong ◽  
Zhi Jun Zhou
Keyword(s):  
Finite Element ◽  
Elastic Waves ◽  
Measurement Method ◽  
Wave Theory ◽  
Hopkinson Bar ◽  
Element Model ◽  
One Dimension ◽  
Calibration System ◽  
Operation Process ◽  
Micro Accelerometer

Linearity, dynamic linearity particularly, is an important parameter in measuring the performance of an accelerometer. The Hopkinson bar has been widely used in calibration of high g accelerometer and other high overloading conditions. Based on one-dimension stress wave theory and superposition theory of elastic waves, designed a Dual Warhead Hopkinson bar to demarcate the dynamic linear parameters of high g micro accelerometer accurately. A finite element model for Hopkinson bar calibration system was created, ANSYS/LS-DYNA was employed to simulate the operation process of Hopkinson bar, and the effects of the projectile's materials, adjustment pads materials and thickness on the acceleration waveform were found.

Wave Scattering From Multiple Horizontal Plates as a Breakwater

2009 ◽  
Author(s):  
Guoyu Wang ◽  
Yongxue Wang
Keyword(s):  
Water Depth ◽  
Plate Thickness ◽  
Wave Theory ◽  
Linear Potential ◽  
Antisymmetric Part ◽  
Transmission Coefficients ◽  
Present Solution ◽  
Relative Water ◽  
Constant Coefficients ◽  
Finite Water Depth

The multiple horizontal plates breakwater is proposed in this article, which mainly consists of several horizontal plates. The regular wave test results demonstrate that it has good performance of dissipating waves. Based on the linear potential wave theory, the scattering of waves normally incident on the multiple horizontal plates in a channel of finite water depth is investigated. The velocity potential is split to the symmetric and antisymmetric part, and the method of eigenfunction expansions is used to obtain the unknown constant coefficients determined from the matching conditions. The thickness of the plates is considered in the theoretical analysis. The present solution is compared with the existing theoretical, numerical and experimental results with good agreements. The parameters such as the relative water depth, relative plate width, relative plate thickness and number of plates, those identified with the performance of the breakwater are investigated and discussed. The variation of reflection and transmission coefficients alone with the above mentioned parameters are also presented.

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