Propagation and reflexion of Alfvén-acoustic-gravity waves in an isothermal compressible fluid

1977 ◽  
Vol 80 (2) ◽  
pp. 223-236 ◽  
Author(s):  
N. Rudraiah ◽  
M. Venkatachalappa ◽  
P. Kandaswamy
Keyword(s):  
Magnetic Fields ◽  
Phase Velocity ◽  
Group Velocity ◽  
Gravity Waves ◽  
Vertical Component ◽  
Wave Number ◽  
Horizontal Magnetic Field ◽  
Acoustic Gravity Waves ◽  
Mach Numbers ◽  
Propagation Of Waves

The propagation of internal Alfvén-ácoustic-gravity waves in a compressible, stratified, inviscid, perfectly conducting, isothermal atmosphere in the presence of a horizontal magnetic field is investigated by considering both the horizontal and the vertical component of the group velocity. The vertical component of the group velocity is important because it determines the speed at which energy travels upwards and becomes available for heating the upper regions. The regions of propagation and no propagation of waves are delineated for different magnetic Mach numbers, in a refractive-index domain. The horizontal and vertical group velocities are compared with the corresponding phase velocity of the wave motion. It is found that the horizontal group velocity of the internal waves is always less than the horizontal phase velocity for small magnetic fields and vice versa for large magnetic fields, whereas the vertical group velocity is always opposite in direction to the vertical phase velocity for small magnetic fields and vice versa for large magnetic fields. We have also drawn the reflexion condition in a wave-number-frequency domain for different Mach numbers.

Refraction of gravity waves by weak current gradients

2001 ◽  
Vol 442 ◽  
pp. 157-159 ◽  
Author(s):  
KRISTIAN B. DYSTHE
Keyword(s):  
Surface Waves ◽  
Group Velocity ◽  
Gravity Waves ◽  
Deep Water ◽  
Current Velocity ◽  
Water Surface ◽  
Simple Formula ◽  
Vertical Component ◽  
Weak Current ◽  
The Waves

When deep water surface waves cross an area with variable current, refraction takes place. If the group velocity of the waves is much larger than the current velocity we show that the curvature of a ray, χ, is given by the simple formula χ = ζ/vg. Here ζ is the vertical component of the current vorticity and vg is the group velocity.

Supercritical Group Velocity for Dissipative Waves in Shallow Water

2012 ◽  
Author(s):  
Tae-Hwa Jung ◽  
Changhoon Lee
Keyword(s):  
Energy Dissipation ◽  
Phase Velocity ◽  
Shallow Water ◽  
Group Velocity ◽  
Water Depth ◽  
Numerical Experiments ◽  
Angular Frequency ◽  
Wave Number ◽  
Geometric Optics ◽  
Complex Valued

The group velocity for waves with energy dissipation in shallow water was investigated. In the Eulerian viewpoint, the geometric optics approach was used to get, at the first order, complex-valued wave numbers from given real-valued angular frequency, water depth, and damping coefficient. The phase velocity was obtained as the ratio of angular frequency to realvalued wave number. Then, at the second order, we obtained the energy transport equation which gives the group velocity. We also used the Lagrangian geometric optics approach which gives complex-valued angular frequencies from real-valued wave number, water depth, and damping coefficient. A noticeable thing was found that the group velocity is always greater than the phase velocity (i.e., supercritical group velocity) in the presence of energy dissipation which is opposite to the conventional theory for non-dissipative waves. The theory was proved through numerical experiments for dissipative bichromatic waves which propagate on a horizontal bed. Both the wave length and wave energy decrease for waves with energy dissipation. As a result, wave transformation such as shoaling, refraction, and diffraction are all affected by the energy dissipation. This implies that the shoaling, refraction, and diffraction coefficients for dissipative waves are different from the corresponding coefficients for non-dissipative waves. The theory was proved through numerical experiments for dissipative monochromatic waves which propagate normally or obliquely on a planar slope.

The interaction trapping of internal gravity waves

1968 ◽  
Vol 34 (2) ◽  
pp. 407-416 ◽  
Author(s):  
O. M. Phillips
Keyword(s):  
Density Gradient ◽  
Gravity Waves ◽  
Wave Motion ◽  
Vertical Component ◽  
Finite Depth ◽  
Internal Gravity Waves ◽  
Wave Number ◽  
Steady Current ◽  
Linear Interactions ◽  
Unbounded Fluid

It is shown that as a result of their non-linear interactions, internal gravity waves in an unbounded fluid can be trapped to a layer of finite depth by periodic small variations in either the density gradient or in a weak horizontal steady current. This trapping occurs when the vertical component of the wave-number is half that of the density gradient or of the current variations. The energy density of the wave motion trapped near the ocean surface decreases exponentially with depth over a distance that is inversely proportional to the magnitude of the variations in density gradient or in horizontal current speed.

scholarly journals Studies of gravity wave propagation in the mesosphere observed by MU radar

2013 ◽  
Vol 31 (5) ◽  
pp. 845-858 ◽  
Author(s):  
H. Y. Lue ◽  
F. S. Kuo ◽  
S. Fukao ◽  
T. Nakamura
Keyword(s):  
Wave Packet ◽  
Phase Velocity ◽  
Group Velocity ◽  
Gravity Waves ◽  
Wave Packets ◽  
Wave Period ◽  
Parameter Analysis ◽  
Mu Radar ◽  
Horizontal Wavelength ◽  
Group Velocities

Abstract. Mesospheric data were analyzed by a composite method combining phase and group velocity tracing technique and the spectra method of Stokes parameter analysis to obtain the propagation parameters of atmospheric gravity waves (AGW) in the height ranges between 63.6 and 99.3 km, observed using the MU radar at Shigaraki in Japan in the months of November and July in the years 1986, 1988 and 1989. The data of waves with downward phase velocity and the data of waves with upward phase velocity were independently treated. First, the vertical phase velocity and vertical group velocity as well as the characteristic wave period for each wave packet were obtained by phase and group velocity tracing technique. Then its horizontal wavelength, intrinsic wave period and horizontal group velocity were obtained by the dispersion relation. The intrinsic frequency and azimuth of wave vector of each wave packet were checked by Stokes parameters analysis. The results showed that the waves with intrinsic periods in the range 30 min–4.5 h had horizontal wavelength ranging from 25 to 240 km, vertical wavelength from 2.5 to 12 km, and horizontal group velocities from 15 to 60 m s−1. Both upward moving wave packets and downward moving wave packets had horizontal group velocities mostly directed in the sector between directions NNE (north-north-east) and SEE in the month of November, and mostly in the sector between directions NW and SWS in the month of July. Comparing with mean wind directions, the gravity waves appeared to be more likely to propagate along with mean wind than against it. This apparent prevalence for downstream wave packets was found to be caused by a systematic filtering effect existing in the process of phase and group velocity tracing analysis: A significant portion of upstream wave packets might have been Doppler shifted out of the vertical range in phase and group velocity tracing analysis.

Acoustic-Gravity Waves in Whirling Polar Thermosphere

2015 ◽  
Vol 47 (9) ◽  
pp. 10-22 ◽  
Author(s):  
Yuriy P. Ladikov-Roev ◽  
Oleg K. Cheremnykh ◽  
Alla K. Fedorenko ◽  
Vladimir E. Nabivach
Keyword(s):  
Gravity Waves ◽  
Acoustic Gravity Waves

scholarly journals Acoustic–gravity waves from multi-fault rupture

2021 ◽  
Vol 915 ◽  
Author(s):  
Byron Williams ◽  
Usama Kadri ◽  
Ali Abdolali
Keyword(s):  
Gravity Waves ◽  
Fault Rupture ◽  
Acoustic Gravity Waves

Abstract

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.

Investigation of acoustic gravity waves in the upper atmosphere by the artificial periodic inhomogeneities method at Nizhny Novgorod

1996 ◽  
Vol 39 (3) ◽  
pp. 224-228
Author(s):  
N. V. Bakhmet'eva ◽  
V. V. Belikovich ◽  
E. A. Benediktov ◽  
V. N. Bubukina ◽  
N. P. Goncharov ◽  
...  
Keyword(s):  
Gravity Waves ◽  
Upper Atmosphere ◽  
Acoustic Gravity Waves ◽  
Periodic Inhomogeneities
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