scholarly journals The propagation of groups of waves in dispersive media, with application to waves on water produced by a travelling disturbance

1908 ◽  
Vol 81 (549) ◽  
pp. 398-430 ◽  
Keyword(s):  
Wave Train ◽  
Harmonic Wave ◽  
Simple Wave ◽  
Fourier Integral ◽  
Wave Pattern ◽  
Difficult Problem ◽  
Point Of View ◽  
Simple Groups ◽  
Dispersive Media ◽  
Single Element

The object of this paper is to illustrate the main features of wave propagation in dispersive media. In the case of surface waves on deep water it has been remarked that the earlier investigators considered the more difficult problem of the propagation of an arbitrary initial disturbance as expressed by a Fourier integral, ignoring the simpler theory developed subsequently by considering the propagation of a single element of their integrals, namely an unending train of simple harmonic waves. The point of view on which stress is laid here consists of a return to the Fourier integral, with the idea that the element of disturbance is not a simple harmonic wave-train, but a simple group, an aggregate of simple wave-trains clustering around a given central period. In many cases it is then possible to select from the integral die few simple groups that are important, and hence to isolate the chief regular features, if any, in the phenomena. In certain of the following sections well-known results appear; the aim has been to develop these from the present point of view, and so illustrate die dependence of the phenomena upon the character of the velocity function, In the other sections it is hoped that progress has been made in the theory if the propagation of an arbitrary initial group of waves, and also of the character of the wave pattern diverging from a point impulse travelling on die surface.

scholarly journals The wave pattern of a doublet in a stream

1928 ◽  
Vol 121 (788) ◽  
pp. 515-523 ◽  
Keyword(s):  
Surface Effect ◽  
Ideal Point ◽  
Finite Size ◽  
Wave Pattern ◽  
Wave Resistance ◽  
Point Of View ◽  
The Body ◽  
Surface Elevation ◽  
More Care ◽  
Forced Waves

The following paper is a study of the surface waves caused by a doublet in a uniform stream, and in particular the variation in the pattern with the velocity of the stream or the depth of the doublet. In most recent work on this subject attention has been directed more to the wave resistance, which can be evaluated with less difficulty than is involved in a detailed study of the waves; in fact, it would seem that it is not necessary for that purpose to know the surface elevation completely, but only certain significant terms at large distances from the disturbance. Recent experimental work has shown con­siderable agreement between theoretical expressions for wave resistance and results for ship models of simple form, and attempts have been made at a similar comparison for the surface elevation in the neighbourhood of the ship. In the latter respect it may be necessary to examine expressions for the surface elevation with more care, as they are not quite determinate; any suitable free disturbance may be superposed upon the forced waves. For instance, it is well known that in a frictionless liquid a possible solution is one which gives waves in advance as well as in the rear of the ship, and the practical solution is obtained by superposing free waves which annul those in advance, or by some equivalent artifice. This process is simple and definite for an ideal point disturbance, but for a body of finite size or a distributed disturbance the complete surface elevation in the neighbourhood of the body requires more careful specification as regards the local part due to each element. It had been intended to consider some expressions specially from this point of view, but as the matter stands at present it would entail a very great amount of numerical calculation, and the present paper is limited to a much simpler problem although also involving considerable computation. A horizontal doublet of given moment is at a depth f below the surface of a stream of velocity c ; the surface effect may be described as a local disturbance symmetrical fore and aft of the doublet together with waves to the rear. Two points are made in the following work.

Seismic phases and scaling associated with small high-explosive surface shots

1981 ◽  
Vol 71 (6) ◽  
pp. 1731-1741
Author(s):  
I. N. Gupta ◽  
R. A. Hartenberger
Keyword(s):  
Blast Wave ◽  
Rayleigh Waves ◽  
Wave Train ◽  
Simple Wave ◽  
P Wave ◽  
Peak Ground Velocity ◽  
Air Blast ◽  
Geological Conditions ◽  
Wide Range ◽  
First Arrival

Abstract An analysis of seismic field data from surface shots in two radically different geologic environments shows significantly different seismic phases at the two sites. At the first site, which has a layered sedimentary section, five distinct phases are observed: the P-wave first arrival; a complex wave train consisting of higher mode Rayleigh waves; a precursor to air-blast wave; the air blast wave; and the air-coupled Rayleigh waves. Records from the second site, overlying an unlayered mass of igneous rocks, show only three distinct seismic phases: the P-wave first arrival; a simple wave train of fundamental-mode Rayleigh and Love waves; and an air blast wave. Peak ground velocity, based on the average of the three largest amplitudes in the surface waves preceding the air blast wave, scales well with yield for both sites. Measurements of peak ground velocity may be used to estimate yields of explosive charges at either site within a factor of about 2 if the source distance is known. The scaling relationship appears to be valid over a wide range of yields and site geological conditions.

scholarly journals The fully nonlinear stratified geostrophic adjustment problem

2017 ◽  
Vol 24 (1) ◽  
pp. 61-75 ◽  
Author(s):  
Aaron Coutino ◽  
Marek Stastna
Keyword(s):  
Stokes Equations ◽  
Wave Train ◽  
Shallow Water Equation ◽  
Classical Problem ◽  
Point Of View ◽  
Rossby Number ◽  
Adjustment Problem ◽  
Inertial Oscillations ◽  
Dispersive Waves ◽  
Fully Nonlinear

Abstract. The study of the adjustment to equilibrium by a stratified fluid in a rotating reference frame is a classical problem in geophysical fluid dynamics. We consider the fully nonlinear, stratified adjustment problem from a numerical point of view. We present results of smoothed dam break simulations based on experiments in the published literature, with a focus on both the wave trains that propagate away from the nascent geostrophic state and the geostrophic state itself. We demonstrate that for Rossby numbers in excess of roughly 2 the wave train cannot be interpreted in terms of linear theory. This wave train consists of a leading solitary-like packet and a trailing tail of dispersive waves. However, it is found that the leading wave packet never completely separates from the trailing tail. Somewhat surprisingly, the inertial oscillations associated with the geostrophic state exhibit evidence of nonlinearity even when the Rossby number falls below 1. We vary the width of the initial disturbance and the rotation rate so as to keep the Rossby number fixed, and find that while the qualitative response remains consistent, the Froude number varies, and these variations are manifested in the form of the emanating wave train. For wider initial disturbances we find clear evidence of a wave train that initially propagates toward the near wall, reflects, and propagates away from the geostrophic state behind the leading wave train. We compare kinetic energy inside and outside of the geostrophic state, finding that for long times a Rossby number of around one-quarter yields an equal split between the two, with lower (higher) Rossby numbers yielding more energy in the geostrophic state (wave train). Finally we compare the energetics of the geostrophic state as the Rossby number varies, finding long-lived inertial oscillations in the majority of the cases and a general agreement with the past literature that employed either hydrostatic, shallow-water equation-based theory or stratified Navier–Stokes equations with a linear stratification.

scholarly journals BREAKWATER ARMOR DISPLACEMENT THRESHOLDS: A POSSIBLE CORRELATION WITH CUMULATIVE WAVE ENERGY

1984 ◽  
Vol 1 (19) ◽  
pp. 186
Author(s):  
Daniel L. Behnke ◽  
Frederic Raichlen
Keyword(s):  
Wave Energy ◽  
Wave Train ◽  
Wave Length ◽  
Simple Wave ◽  
Wave Theory ◽  
Irregular Waves ◽  
Reconstruction Technique ◽  
Regular Wave ◽  
Regular Waves ◽  
Three Dimensional Model

An extensive program of stability experiments in a highly detailed three-dimensional model has recently been completed to define a reconstruction technique for a damaged breakwater (Lillevang, Raichlen, Cox, and Behnke, 1984). Tests were conducted with both regular waves and irregular waves from various directions incident upon the breakwater. In comparison of the results of the regular wave tests to those of the irregular wave tests, a relation appeared to exist between breakwater damage and the accumulated energy to which the structure had been exposed. The energy delivered per wave is defined, as an approximation, as relating to the product of H2 and L, where H is the significant height of a train of irregular waves and L is the wave length at a selected depth, calculated according to small amplitude wave theory using a wave period corresponding to the peak energy of the spectrum. As applied in regular wave testing, H is the uniform wave height and L is that associated with the period of the simple wave train. The damage in the model due to regular waves and that caused by irregular waves has been related through the use of the cumulative wave energy contained in those waves which have an energy greater than a threshold value for the breakwater.

Puritan Radicalism and the Enlightenment

1960 ◽  
Vol 29 (4) ◽  
pp. 424-439 ◽  
Author(s):  
George L. Mosse
Keyword(s):  
Eighteenth Century ◽  
World View ◽  
Difficult Problem ◽  
Point Of View ◽  
Religious Truth ◽  
The Enlightenment ◽  
The World ◽  
Christian Thought ◽  
The Many ◽  
The Relationship

The relationship between Christianity and the Enlightenment presents a subtle and difficult problem. No historian has as yet fully answered the important question of how the world view of the eighteenth century is related to that of traditional Christianity. It is certain, however, that the deism of that century rejected traditional Christianity as superstitious and denied Christianity a monopoly upon religious truth. The many formal parallels which can be drawn between Enlightenment and Christianity cannot obscure this fact. From the point of view of historical Christianity, both Protestant and Catholic, the faith of the Enlightenment was blasphemy. It did away with a personal God, it admitted no supernatural above the natural, it denied the relevance of Christ's redemptive task in this world. This essay attempts to discover whether traditional Christian thought itself did not make a contribution to the Enlightenment.

A Note on Matthew 6:33

1945 ◽  
Vol 38 (4) ◽  
pp. 270-272
Author(s):  
William H. P. Hatch
Keyword(s):  
New Testament ◽  
Difficult Problem ◽  
Point Of View ◽  
The New Testament ◽  
Textual Critic

The first half of Matthew 6: 33 presents a difficult problem to the textual critic, and the leading editors of the New Testament have solved it in different ways. The textual authorities offer several variant readings, but none of them is satisfactory from every point of view. However, it is possible by means of a highly plausible conjecture to obtain a text which makes excellent sense.

Random packing of an interval. II

1979 ◽  
Vol 11 (03) ◽  
pp. 591-602
Author(s):  
David Mannion
Keyword(s):  
Fine Particles ◽  
Random Variables ◽  
Random Variable ◽  
Difficult Problem ◽  
Random Packing ◽  
Point Of View ◽  
Initial Size ◽  
Moderate Size ◽  
The Individual

We showed in [2] that if an object of initial size x (x large) is subjected to a succession of random partitions, then the object is decomposed into a large number of terminal cells, each of relatively small size, where if Z(x, B) denotes the number of such cells whose sizes are points in the set B, then there exists c, (0 < ≦ 1), such that Z(x, B)x −c converges in probability, as x → ∞, to a random variable W. We show here that if a parent object of size x produces k offspring of sizes y 1, y 2, ···, y k and if for each k x - y 1 - y 2 - ··· - y k (the ‘waste’ or the ‘cover’, depending on the point of view) is relatively small, then for each n the nth cumulant, Ψ n (x, B), of Z(x, B) satisfies Ψ n (x, B)x -c → κ n (B), as x → ∞, for some κ n (B). Thus, writing N = x c , Z(x, B) has approximately the same distribution as the sum of N independent and identically distributed random variables (The determination of the distribution of the individual appears to be a difficult problem.) The theory also applies when an object of moderate size is broken down into very fine particles or granules.

The decline of Myriophyllum spicatum in a eutrophic Wisconsin lake

1980 ◽  
Vol 58 (5) ◽  
pp. 527-535 ◽  
Author(s):  
Stephen R. Carpenter
Keyword(s):  
Exotic Species ◽  
Myriophyllum Spicatum ◽  
Simple Wave ◽  
Wave Pattern ◽  
Single Factor ◽  
Submersed Macrophyte ◽  
Macrophyte Communities ◽  
Biomass Dynamics

The recent changes in the submersed macrophyte communities of Lake Wingra, Wisconsin, have been dominated by the dynamics of one exotic species. After a decade of abundance, Myriophyllum spicatum has undergone a sustained decline in the Madison lakes. A pattern of explosive growth followed by declining abundance may describe most M. spicatum invasions.No simple single-factor explanation can adequately account for the biomass dynamics of M. spicatum in Lake Wingra. The decline in M. spicatum biomass appears to be the result of a complex of synergistically interacting factors, perhaps including nutrients, epiphytes, competitors, and parasites or pathogens.Invasions of lake districts by M. spicatum are hypothesized to follow a wave pattern. When interlake distances are accounted for, departure from a simple wave is hypothesized to result from lags in infestation of lakes which are not susceptible to colonization by M. spicatum. Several testable hypotheses are suggested by this view of M. spicatum invasions.

scholarly journals Distribution of minor metallic elements within waste incineration bottom ashes defined by WDX/EDX spectrometry

2018 ◽  
Vol 45 ◽  
pp. 259-265 ◽  
Author(s):  
Piotr R. Kowalski ◽  
Monika Kasina ◽  
Marek Michalik
Keyword(s):  
Bottom Ash ◽  
Waste Incineration ◽  
Point Of View ◽  
Glassy Matrix ◽  
Single Element ◽  
Metallic Elements ◽  
X Ray ◽  
Metallic Inclusions ◽  
Incineration Residues ◽  
Incineration Residue

Abstract. A number of metallic elements are inherited from waste during thermal treatment and concentrated in the incineration residues. Because the major part of the incineration residue mass are bottom ashes (BAs), their study is of great importance from the point of view of their environmental impact or resource potential. The general focus of this study was on the minor metallic elements present in BAs. They co-occurred with main phases and often determined the inherited potential of the material. The analysed residues were produced from municipal and industrial waste. The BAs were studied using spectroscopic methods of chemical microanalysis: energy dispersive X-ray spectrometry (EDX) and wavelength dispersive X-ray spectrometry (WDX). Both the main and minor metallic elements were concentrated in metallic components. They were typically present as separate grains and metallic inclusions (commonly in the glass matrix of the grains) ranging in size from several to hundreds of micrometres. Despite Fe-, Al- and Cu-rich occurrences, metallic elements rarely occurred in fragments composed of a single element. Their main forms of occurrence were alloy grains, admixtures in polymetallic occurrences and micro-inclusions in glassy matrix. The content of particular elements in those forms was investigated and described in greater detail. Even though two types of bottom ash were formed from different types of waste and differences in used technologies were present, the obtained materials contained metallic components having similar attributes. Elevated concentrations of not only Fe and Al, but also Ti, Cu and Zn, allow us to consider bottom ash as a promising material from the point of view of metallic elements' recovery (e.g. by the physical concentration of elements through gravity or magnetic methods).

scholarly journals Numerical Analysis of the Ability of a Floating Vehicle to Overcome a Water Obstacle

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Krzysztof Kosiuczenko ◽  
◽  
Robert Sosnowicz ◽  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Computational Model ◽  
Difficult Problem ◽  
Point Of View ◽  
Vehicle Safety ◽  
Extreme Conditions ◽  
The Finite Element Method ◽  
Element Method

The paper presents the results of simulation tests of the entry of a floating transporter to a water obstacle. The simulation tests were performed with the use of LS Dyna program, based on the finite element method (FEM). The computational model was developed and used in the simulation of the manoeuvre of entering the water obstacle for the extreme conditions, which are described by NATO standards. For a model, as an example vehicle, the floating transporter PTS-M was used. The results of the application of the elaborated model confirmed the possibility to utilise the method to verify the behaviour of a vehicle in a very important and difficult problem from the point of view of vehicle safety conditions.

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