Effect of weak nonlinearities on the plane waves in a plasma stream

1976 ◽  
Vol 54 (1) ◽  
pp. 39-47 ◽  
Author(s):  
S. R. Seshadri
Keyword(s):  
Plane Waves ◽  
Equation Of Motion ◽  
Wave Number ◽  
Plasma Stream ◽  
Electromagnetic Mode ◽  
Correct Equation ◽  
Long Time ◽  
Modulational Stability ◽  
The Waves ◽  
Slow Modulation

The effect of weak nonlinearities on the monochromatic plane waves in a cold infinite plasma stream is investigated for the case in which the waves are progressing parallel to the drift velocity. The fast and the slow space-charge waves undergo amplitude-dependent frequency and wave number shifts. There is a long time slow modulation of the amplitude of the electromagnetic mode which becomes unstable to this nonlinear wave modulation. The importance of using the relativistically correct equation of motion for predicting correctly the modulational stability of the electromagnetic mode is pointed out.

Evolution of solitary waves in a two-pycnocline system

2009 ◽  
Vol 642 ◽  
pp. 235-277 ◽  
Author(s):  
M. NITSCHE ◽  
P. D. WEIDMAN ◽  
R. GRIMSHAW ◽  
M. GHRIST ◽  
B. FORNBERG
Keyword(s):  
Solitary Waves ◽  
Initial Conditions ◽  
Oscillation Period ◽  
Resonance Phenomenon ◽  
Numerical Code ◽  
Asymptotic Model ◽  
Narrow Region ◽  
Near Resonance ◽  
Long Time ◽  
The Waves

Over two decades ago, some numerical studies and laboratory experiments identified the phenomenon of leapfrogging internal solitary waves located on separated pycnoclines. We revisit this problem to explore the behaviour of the near resonance phenomenon. We have developed a numerical code to follow the long-time inviscid evolution of isolated mode-two disturbances on two separated pycnoclines in a three-layer stratified fluid bounded by rigid horizontal top and bottom walls. We study the dependence of the solution on input system parameters, namely the three fluid densities and the two interface thicknesses, for fixed initial conditions describing isolated mode-two disturbances on each pycnocline. For most parameter values, the initial disturbances separate immediately and evolve into solitary waves, each with a distinct speed. However, in a narrow region of parameter space, the waves pair up and oscillate for some time in leapfrog fashion with a nearly equal average speed. The motion is only quasi-periodic, as each wave loses energy into its respective dispersive tail, which causes the spatial oscillation magnitude and period to increase until the waves eventually separate. We record the separation time, oscillation period and magnitude, and the final amplitudes and celerity of the separated waves as a function of the input parameters, and give evidence that no perfect periodic solutions occur. A simple asymptotic model is developed to aid in interpretation of the numerical results.

scholarly journals WAVE RECORDING ON THE IJSSELMEER

2011 ◽  
Vol 1 (7) ◽  
pp. 3
Author(s):  
P. W. Roest
Keyword(s):  
Average Period ◽  
Recording Time ◽  
Ice Drift ◽  
Recording Station ◽  
Long Time ◽  
Wave Heights ◽  
Wave Research ◽  
The Difference ◽  
Hydraulics Laboratory ◽  
The Waves

The dimensions of the dikes in the Ijsselmeer are mainly determined by wave-attack. The dimensions of the waves as a result of the design gale are calculated with the diagram of the Hydraulics Laboratory at Delft (ref« 1). This diagram is based on data of Sverdrup for deep water and principally on laboratory studies for shallow water. For a long time there has been a need of wave recordings on the lake in order to verify the calculated wave heights. A problem is the impossibility of maintaining a permanent recording station on the lake due to ice-drift in wintertime. Otherwise the Ijsselmeer lends itself admirably to wave-research, because there are vast regions with only small variations in waterdepth. Another advantage is that frequently more or less stationary conditions will occur under the influence of winds of constant force and direction. When Dr. Dorrestein of the Royal Dutch Meteorological Institute introduced his new floating waverecorder, it was possible to take observations in every place of the lake. Soon it appeared that this recorder has many advantages. The equipment consists of an accelerometer mounted on a little raft of one meter each way, that follows the movement of the water surface. The signal of the accelerometer is transmitted by an electric cable to the ship, where it is double integrated and then recorded (ref. 3). During the last winter several observations have been carried out with an instrument of this type* As a result of initial troubles with the electronic equipment the number of observations during gale-conditions has been limited. The usual duration of each recording is about 15 minutes. The average period of the waves lies between three and a half and five seconds, so each diagram consists of 180 to 250 waves. Wave height is measured as the difference in height between a trough and the next crest. The average period is determined by dividing the total recording time by half the number of zerocrossings.

scholarly journals The relativity theory of plane waves

1926 ◽  
Vol 111 (757) ◽  
pp. 95-104 ◽  
Keyword(s):  
Gravitational Field ◽  
Electromagnetic Waves ◽  
Small Amplitude ◽  
Plane Waves ◽  
Cumulative Effect ◽  
Relativity Theory ◽  
Transverse Waves ◽  
Propagation Of Light ◽  
Cumulative Change ◽  
The Waves

Weyl has shown that any gravitational wave of small amplitude may be regarded as the result of the superposition of waves of three types, viz.: (i) longitudinal-longitudinal; (ii) longitudinal-transverse; (iii) transverse-transverse. Eddington carried the matter much further by showing that waves of the first two types are spurious; they are “merely sinuosities in the co­ordinate system,” and they disappear on the adoption of an appropriate co-ordinate system. The only physically significant waves are transverse-transverse waves, and these are propagated with the velocity of light. He further considers electromagnetic waves and identifies light with a particular type of transverse-transverse wave. There is, however, a difficulty about the solution as left by Eddington. In its gravitational aspect light is not periodic. The gravitational potentials contain, in addition to periodic terms, an aperiodic term which increases without limit and which seems to indicate that light cannot be propagated indefinitely either in space or time. This is, of course, explained by noting that the propagation of light implies a transfer of energy, and that the consequent change in the distribution of energy will be reflected in a cumulative change in the gravitational field. But, if light cannot be propagated indefinitely, the fact itself is important, whatever be its explana­tion, for the propagation of light over very great distances is one of the primary facts which the relativity theory or any like theory must meet. In endeavouring to throw further light on this question, it seemed desirable to avoid the assumption that the amplitudes of the waves are small; terms neglected on this ground might well have a cumulative effect. All the solu­tions discussed in this paper are exact.

The generalized Burgers and Zabolotskaya-Khokhlov equations

1994 ◽  
Vol 447 (1930) ◽  
pp. 253-270 ◽  
Keyword(s):  
Exact Solution ◽  
Plane Waves ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Compressive Wave ◽  
Similarity Reduction ◽  
Weakly Nonlinear ◽  
Cylindrically Symmetric ◽  
Generalized Burgers Equation ◽  
Long Time

A point transformation between forms of the generalized Burgers equation (g b e) first given by Cates (1989) is investigated. Applications include generalizations of Scott’s (1981) classification of long-time behaviour for compressive wave solutions of the GBE and the equivalence of the exponential and cylindrical forms of the GBE, yielding an exact solution for the exponential GBE. Applications to nonlinear diffractive acoustics are considered by using a similarity reduction of the dissipative Zabolotskaya-Khokhlov (dzk) equation (describing the evolution of nearly plane waves in a weakly nonlinear medium with allowance for transverse variation effects) onto the GBE. The result is that waves from parabolic sources may be described by the cylindrical GBE in the case of two dimensions, and by the spherical GBE in the three-dimensional, cylindrically symmetric case. Furthermore, results on the formation of shocks and caustics in the context of the ZK equation are presented, along with an exact solution to the DZK equation. Exact solutions with caustic singularities are studied, along with a possible mechanism for their control. Finally, results on the evolution of a shock approaching a caustic are given through the identification of a series of parameter regimes dependent on the diffusivity.

IDENTIFICATION OF IMPACT FORCE ON THE GAS PIPE BASED ON ANALYSIS OF THE ACOUSTIC WAVE

2008 ◽  
Vol 22 (09n11) ◽  
pp. 1039-1044 ◽  
Author(s):  
MIN-SOO KIM ◽  
SANG-KWON LEE ◽  
SUNG-JONG KIM
Keyword(s):  
Acoustic Wave ◽  
Cavity Mode ◽  
Impact Force ◽  
Correlation Technique ◽  
Frequency Method ◽  
Time Frequency ◽  
Long Time ◽  
Mode Characteristics ◽  
The Impact ◽  
The Waves

An acoustic wave signal measured on the gas pipe due to impact force is transfer to the far distance through the medium inside of duct. This signal is very complex since it includes the acoustic wave and solid wave. Acoustic wave is affected by the cavity mode inside of duct. The analysis of this acoustic wave gives information about the impact force. For the analysis of this signal, the correlation technique has been used for a long time. This method has a limitation for the application since the waves have dispersive and cavity mode characteristics for the flexible wave. In this paper, we present the time-frequency method for the identification of impact force and the location of impact on the gas pipe. The results give the useful information for the impact force and are applied to the analysis of leakage location of the gas pipe.

Longitudinal Waves in a Submerged Cylindrical Rod 1

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
G. Iosilevskii
Keyword(s):  
Boundary Layer ◽  
Wave Number ◽  
Analytical Relation ◽  
Velocity Of Sound ◽  
Longitudinal Displacement ◽  
Wave Propagation Velocity ◽  
Longitudinal Waves ◽  
Short Waves ◽  
The Waves ◽  
Surrounding Fluid

This study is concerned with longitudinal displacement waves propagating in an elastic cylindrical rod submerged in a viscous fluid. Provided that the wave propagation velocity in the rod is small compared with the velocity of sound in the surrounding fluid and the wavelength is large compared with the thickness of the boundary layer around the rod, an analytical relation is obtained between the wave number and the frequency. The presence of the fluid makes the waves disperse—the short waves become faster than the long ones.

Non-linear transverse waves in a Vlasov plasma

1969 ◽  
Vol 3 (4) ◽  
pp. 577-592 ◽  
Author(s):  
S. Peter Gary
Keyword(s):  
Perturbation Expansion ◽  
Second Order ◽  
Electron Cyclotron ◽  
Wave Number ◽  
Linear Dispersion ◽  
Transverse Waves ◽  
Non Linear ◽  
Long Time ◽  
Linear Damping ◽  
Electron Cyclotron Waves

Non-linear transverse waves in a classical non-relativistic collisionless, Maxwellian electron gas with external magnetic field B0 are considered. There is assumed a small, sinusoidal variation in the initial electric and magnetic fields, corresponding to excitation of a discrete wave-number mode. The non-linear Vlasov equation is solved to second order in the long time limit via the Montgomery—Gorman perturbation expansion, and the time-independent, spatially homogeneous part of the second-order distribution function is used to modify the linear dispersion relation. For frequencies near the electron cyclotron frequency a non-linear damping decrement results such that, for many values of the parameters, the damping is less than the linear rate. Thus at sufficiently long times, the rate of damping of transverse electron cyclotron waves should decrease, a result similar to that for non-linear damping of longitudinal electron plasma waves.

Reflection Coefficient for Plane Waves in a Fluid Incident on a Layered Elastic Half-Space

1983 ◽  
Vol 50 (2) ◽  
pp. 405-414 ◽  
Author(s):  
D. B. Bogy ◽  
S. M. Gracewski
Keyword(s):  
Reflection Coefficient ◽  
Half Space ◽  
Plane Waves ◽  
Elastic Half Space ◽  
Wave Number ◽  
Solid Boundary ◽  
Inviscid Fluid ◽  
Interface Waves ◽  
Plate Models ◽  
Layered Solid

The reflection coefficient is derived for an isotropic, homogeneous elastic layer of arbitrary thickness that is perfectly bonded to such an elastic half-space of a different material for the case when plane waves are incident from an inviscid fluid onto the layered solid. The derived function is studied analytically by considering several limiting cases of geometry and materials to recover previously known results. Approximate reflection coefficents are then derived using various plate models for the layer to obtain simpler expressions that are useful for small values of σd, where σ is the wave number and d is the layer thickness. Numerical results based on all the models for the propagation of interface waves localized near the fluid-solid boundary are obtained and compared. These results are also compared with some previously published experimental measurements.

scholarly journals Near-Inertial Mixing in the Central Arctic Ocean

2014 ◽  
Vol 44 (8) ◽  
pp. 2031-2049 ◽  
Author(s):  
Ilker Fer
Keyword(s):  
Arctic Ocean ◽  
Vertical Mixing ◽  
The Arctic ◽  
Storm Event ◽  
Central Arctic Ocean ◽  
Long Time ◽  
Wave Induced ◽  
The Waves ◽  
Inertial Energy ◽  
Made In

Abstract Observations were made in April 2007 of horizontal currents, hydrography, and shear microstructure in the upper 500 m from a drifting ice camp in the central Arctic Ocean. An approximately 4-day-long time series, collected about 10 days after a storm event, shows enhanced near-inertial oscillations in the first half of the measurement period with comparable upward- and downward-propagating energy. Rough estimates of wind work and near-inertial flux imply that the waves were likely generated by the previous storm. The near-inertial frequency band is associated with dominant clockwise rotation in time of the horizontal currents and enhanced dissipation rates of turbulent kinetic energy. The vertical profile of dissipation rate shows elevated values in the pycnocline between the relatively turbulent underice boundary layer and the deeper quiescent water column. Dissipation averaged in the pycnocline is near-inertially modulated, and its magnitude decays approximately at a rate implied by the reduction of energy over time. Observations suggest that near-inertial energy and internal wave–induced mixing play a significant role in vertical mixing in the Arctic Ocean.

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