Evolutionary isotropic radiation

1978 ◽  
Vol 364 (1717) ◽  
pp. 181-209 ◽  
Keyword(s):  
Group Velocity ◽  
Internal Gravity Waves ◽  
Source Distribution ◽  
Field Quantity ◽  
Long Run ◽  
Transient Energy ◽  
Invariant Group ◽  
Boussinesq Fluid ◽  
Group Velocities ◽  
Isotropic Radiation

A directionally dependent source distribution activates within a multi-dimensional isotropic dispersive medium. It then develops into a purely pulsatory state. The radiation problem is approached via a convolution principle. Certain basic postulates are imposed to help secure integral convergence at various stages. The Sommerfeld radiation principle holds through an applied initial condition. One field quantity results from stationary phase approximations and represents a superposition of slowly transient spherical wavemodes over a continuously evolving set of wavenumbers and frequencies that must avoid the source frequency. Their radial group velocities vary coincidentally with a positive reception velocity parameter; the associated dispersion is basically a function of the medium, but admits amplitudes with some dependence on source frequency. Another field quantity accumulates relevant residues which contribute to a superposition of quasisteady spherical wavemodes over an intermittently growing set. This depends not only on the medium, but also on the source frequency, imparted to all such wavemodes, as well as an observation criterion, namely that any specific wavemode is observed after its enclosing energy front crosses the observer, in particular, with an invariant group velocity exceeding that common to all slowly transient wavemodes; amplitudes quickly lose their source-induced time dependence. It is this last quantity that survives in the long run and progresses into a non-trivial purely pulsatory steady state consistent with Lighthill’s radiation principle. Its ultimate survival is accomplished through a permanent flow of source-generated non-transient energy, permanency of the energy supply being guaranteed by an indefinitely sustained source amplitude; moreover, both medium and source never conspire to cancel the supply. On an energy basis, the fading of slowly transient modes may be due to the decreasing group velocity of their energy arrival. Spherically symmetric and axisymmetric cases are briefly examined. Finally, arguments and results are applied, with some modifications, to (i) an unsteadily vibrating elastic plate problem, and (ii) radiation of certain internal gravity waves in a Boussinesq fluid.

Compressional‐wave velocities in attenuating media: A laboratory physical model study

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1162-1167 ◽  
Author(s):  
Joseph B. Molyneux ◽  
Douglas R. Schmitt
Keyword(s):  
Phase Velocity ◽  
Group Velocity ◽  
Wave Velocity ◽  
Propagation Distance ◽  
Compressional Wave ◽  
Arrival Times ◽  
Wave Velocities ◽  
Amplitude Maximum ◽  
Phase And Group Velocities ◽  
Group Velocities

Elastic‐wave velocities are often determined by picking the time of a certain feature of a propagating pulse, such as the first amplitude maximum. However, attenuation and dispersion conspire to change the shape of a propagating wave, making determination of a physically meaningful velocity problematic. As a consequence, the velocities so determined are not necessarily representative of the material’s intrinsic wave phase and group velocities. These phase and group velocities are found experimentally in a highly attenuating medium consisting of glycerol‐saturated, unconsolidated, random packs of glass beads and quartz sand. Our results show that the quality factor Q varies between 2 and 6 over the useful frequency band in these experiments from ∼200 to 600 kHz. The fundamental velocities are compared to more common and simple velocity estimates. In general, the simpler methods estimate the group velocity at the predominant frequency with a 3% discrepancy but are in poor agreement with the corresponding phase velocity. Wave velocities determined from the time at which the pulse is first detected (signal velocity) differ from the predominant group velocity by up to 12%. At best, the onset wave velocity arguably provides a lower bound for the high‐frequency limit of the phase velocity in a material where wave velocity increases with frequency. Each method of time picking, however, is self‐consistent, as indicated by the high quality of linear regressions of observed arrival times versus propagation distance.

On parametric instabilities of finite-amplitude internal gravity waves

1982 ◽  
Vol 119 ◽  
pp. 367-377 ◽  
Author(s):  
J. Klostermeyer
Keyword(s):  
Gravity Wave ◽  
Internal Gravity Wave ◽  
Maximum Growth ◽  
Numerical Approach ◽  
Internal Gravity Waves ◽  
Resonant Interaction ◽  
Finite Amplitude ◽  
Interaction Diagram ◽  
Parametric Instabilities ◽  
Boussinesq Fluid

The equations describing parametric instabilities of a finite-amplitude internal gravity wave in an inviscid Boussinesq fluid are studied numerically. By improving the numerical approach, discarding the concept of spurious roots and considering the whole range of directions of the Floquet vector, Mied's work is generalized to its full complexity. In the limit of large disturbance wavenumbers, the unstable disturbances propagate in the directions of the two infinite curve segments of the related resonant-interaction diagram. They can therefore be classified into two families which are characterized by special propagation directions. At high wavenumbers the maximum growth rates converge to limits which do not depend on the direction of the Floquet vector. The limits are different for both families; the disturbance waves propagating at the smaller angle to the basic gravity wave grow at the larger rate.

A conservation law for internal gravity waves

1976 ◽  
Vol 78 (2) ◽  
pp. 209-216 ◽  
Author(s):  
Michael Milder
Keyword(s):  
Internal Wave ◽  
Group Velocity ◽  
Internal Waves ◽  
Gravity Waves ◽  
Conservation Law ◽  
Short Wavelength ◽  
Internal Gravity Waves ◽  
Volume Integral ◽  
Weak Density ◽  
Progressive Waves

The scaled vorticity Ω/N and strain ∇ ζ associated with internal waves in a weak density gradient of arbitrary depth dependence together comprise a quantity that is conserved in the usual linearized approximation. This quantity I is the volume integral of the dimensionless density DI = ½[Ω2/N2 + (∇ ζ)2]. For progressive waves the ‘kinetic’ and ‘potential’ parts are equal, and in the short-wavelength limit the density DI and flux FI are related by the ordinary group velocity: FI = DIcg. The properties of DI suggest that it may be a useful measure of local internal-wave saturation.

On resonant over-reflexion of internal gravity waves from a Helmholtz velocity profile

1979 ◽  
Vol 90 (1) ◽  
pp. 161-178 ◽  
Author(s):  
R. H. J. Grimshaw
Keyword(s):  
Velocity Profile ◽  
Gravity Waves ◽  
Second Harmonic ◽  
Phase Speed ◽  
Internal Gravity Waves ◽  
Finite Amplitude ◽  
Weakly Nonlinear ◽  
Velocity Discontinuity ◽  
Interface Displacement ◽  
Boussinesq Fluid

A Helmholtz velocity profile with velocity discontinuity 2U is embedded in an infinite continuously stratified Boussinesq fluid with constant Brunt—Väisälä frequency N. Linear theory shows that this system can support resonant over-reflexion, i.e. the existence of neutral modes consisting of outgoing internal gravity waves, whenever the horizontal wavenumber is less than N/2½U. This paper examines the weakly nonlinear theory of these modes. An equation governing the evolution of the amplitude of the interface displacement is derived. The time scale for this evolution is α−2, where α is a measure of the magnitude of the interface displacement, which is excited by an incident wave of magnitude O(α3). It is shown that the mode which is symmetrical with respect to the interface (and has a horizontal phase speed equal to the mean of the basic velocity discontinuity) remains neutral, with a finite amplitude wave on the interface. However, the other modes, which are not symmetrical with respect to the interface, become unstable owing to the self-interaction of the primary mode with its second harmonic. The interface displacement develops a singularity in a finite time.

scholarly journals Automated detection and association of surface waves

1994 ◽  
Vol 37 (3) ◽  
Author(s):  
R. G. North ◽  
C. R. D. Woodgold
Keyword(s):  
Surface Waves ◽  
Group Velocity ◽  
Rayleigh Waves ◽  
Arrival Time ◽  
Narrow Band ◽  
Broad Band ◽  
Detection Algorithm ◽  
Automated Detection ◽  
Short Period ◽  
Group Velocities

An algorithm for the automatic detection and association of surface waves has been developed and tested over an 18 month interval on broad band data from the Yellowknife array (YKA). The detection algorithm uses a conventional STA/LTA scheme on data that have been narrow band filtered at 20 s periods and a test is then applied to identify dispersion. An average of 9 surface waves are detected daily using this technique. Beamforming is applied to determine the arrival azimuth; at a nonarray station this could be provided by poIarization analysis. The detected surface waves are associated daily with the events located by the short period array at Yellowknife, and later with the events listed in the USGS NEIC Monthly Summaries. Association requires matching both arrival time and azimuth of the Rayleigh waves. Regional calibration of group velocity and azimuth is required. . Large variations in both group velocity and azimuth corrections were found, as an example, signals from events in Fiji Tonga arrive with apparent group velocities of 2.9 3.5 krn/s and azimuths from 5 to + 40 degrees clockwise from true (great circle) azimuth, whereas signals from Kuriles Kamchatka have velocities of 2.4 2.9 km/s and azimuths off by 35 to 0 degrees. After applying the regional corrections, surface waves are considered associated if the arrival time matches to within 0.25 km/s in apparent group velocity and the azimuth is within 30 degrees of the median expected. Over the 18 month period studied, 32% of the automatically detected surface waves were associated with events located by the Yellowknife short period array, and 34% (1591) with NEIC events; there is about 70% overlap between the two sets of events. Had the automatic detections been reported to the USGS, YKA would have ranked second (after LZH) in terms of numbers of associated surface waves for the study period of April 1991 to September 1992.

scholarly journals Method for Determining Neutral Wind Velocity Vectors Using Measurements of Internal Gravity Wave Group and Phase Velocities

Atmosphere ◽  
2019 ◽  
Vol 10 (9) ◽  
pp. 546 ◽  
Author(s):  
Andrey V. Medvedev ◽  
Konstantin G. Ratovsky ◽  
Maxim V. Tolstikov ◽  
Roman V. Vasilyev ◽  
Maxim F. Artamonov
Keyword(s):  
Group Velocity ◽  
Wind Velocity ◽  
Wave Vector ◽  
Velocity Vector ◽  
Internal Gravity Waves ◽  
Vertical Wind ◽  
New Method ◽  
Neutral Wind ◽  
Wind Velocities ◽  
Wind Measurements

This study presents a new method for determining a neutral wind velocity vector. The basis of the method is measurement of the group velocities of internal gravity waves. Using the case of the Boussinesq dispersion relation, we demonstrated the ability to measure a neutral wind velocity vector using the group velocity and wave vector data. An algorithm for obtaining the group velocity vector from the wave vector spectrum is proposed. The new method was tested by comparing the obtained winter wind pattern with wind data from other sources. Testing the new method showed that it is in quantitative agreement with the Fabry–Pérot interferometer wind measurements for zonal and vertical wind velocities. The differences in meridional wind velocities are also discussed here. Of particular interest were the results related to the measurement of vertical wind velocities. We demonstrated that two independent methods gave the presence of vertical wind velocities with amplitude of ~20 m/s. Estimation of vertical wind contribution to plasma drift velocity indicated the importance of vertical wind measurements and the need to take them into account in physical and empirical models of the ionosphere and thermosphere.

ATMOSPHERIC WAVES FROM U.S.S.R. NUCLEAR TEST EXPLOSIONS IN 1962

1964 ◽  
Vol 42 (4) ◽  
pp. 632-637 ◽  
Author(s):  
Bhartendu ◽  
B. W. Currie
Keyword(s):  
Group Velocity ◽  
Dispersion Curves ◽  
Nuclear Test ◽  
Atmospheric Waves ◽  
Novaya Zemlya ◽  
Group Velocities

Photographic reproductions of the records of the A1 wave systems at Saskatoon (52.1 °N., 106.6 °W.) from five nuclear test explosions in Novaya Zemlya during the summer of 1962 are given. Notable differences exist between some of the records. These may be due to differences in the heights of the explosions. Dispersion curves of group velocity against period are shown. Waves ranged in period from 6.0 to 0.8 minutes; group velocities from 275 to 313 m/sec.

scholarly journals Optical wave-packet with nearly-programmable group velocities

2020 ◽  
Vol 3 (1) ◽  
Author(s):  
Zhaoyang Li ◽  
Junji Kawanaka
Keyword(s):  
Wave Packet ◽  
Group Velocity ◽  
Wave Packets ◽  
Bessel Beam ◽  
Propagation Path ◽  
Uniform Motion ◽  
Optical Wave ◽  
Straight Line ◽  
Line Trajectory ◽  
Group Velocities

AbstractDuring the process of Bessel beam generation in free space, spatiotemporal optical wave-packets with tunable group velocities and accelerations can be created by deforming pulse-fronts of injected pulsed beams. So far, only one determined motion form (superluminal or luminal or subluminal for the case of group velocity; and accelerating or uniform-motion or decelerating for the case of acceleration) could be achieved in a single propagation path. Here we show that deformed pulse-fronts with well-designed axisymmetric distributions (unlike conical and spherical pulse-fronts used in previous studies) allow us to obtain nearly-programmable group velocities with several different motion forms in a single propagation path. Our simulation shows that this unusual optical wave-packet can propagate at alternating superluminal and subluminal group velocities along a straight-line trajectory with corresponding instantaneous accelerations that vary periodically between positive (acceleration) and negative (deceleration) values, almost encompassing all motion forms of the group velocity in a single propagation path. Such unusual optical wave-packets with nearly-programmable group velocities may offer new opportunities for optical and physical applications.

The generation of internal waves by vibrating elliptic cylinders. Part 1. Inviscid solution

1997 ◽  
Vol 351 ◽  
pp. 105-118 ◽  
Author(s):  
D. G. HURLEY
Keyword(s):  
Gravity Waves ◽  
Elliptic Cylinder ◽  
Major Axis ◽  
Internal Gravity Waves ◽  
Angular Frequency ◽  
Important Paper ◽  
Fourier Decomposition ◽  
Boussinesq Fluid ◽  
Made In ◽  
Phase Differences

We consider the internal gravity waves that are produced in an inviscid Boussinesq fluid, whose Brunt–Väisälä frequency N is constant, by the small rectilinear vibrations of a horizontal elliptic cylinder whose major axis is inclined at an arbitrary angle to the horizontal. When the angular frequency ω is greater than N, no waves are produced and the governing elliptic equation is solved using conformal transformations. Analytic continuation in ω to values less than N, when waves are produced, is then used to determine the solution. It exhibits the surprising feature that, apart from certain phase differences, the form of the velocity distributions in each of the beams of waves that occur is the same for all values of the thickness ratio of the ellipse, the inclination of its major axis to the horizontal and the plane in which the vibrations are occurring. The Fourier decomposition of the velocity distribution is found and is used in a sequel, Part 2, to investigate the effects of viscous dissipation.In an important paper Makarov et al. (1990) have given an approximate solution for a vibrating circular cylinder in a viscous fluid. We show that the limit of this solution as the viscosity tends to zero is not the exact inviscid solution discussed herein. Further comparison of their work and ours will be made in Part 2.

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