Attenuation of Acoustic-Gravity Waves in an Isothermal Atmosphere: Consideration with the Modified Navier-Stokes and Heat-Transfer Equations

2020 ◽  
Vol 36 (5) ◽  
pp. 212-221
Author(s):  
A. K. Fedorenko ◽  
E. I. Kryuchkov ◽  
O. K. Cheremnykh
Keyword(s):  
Heat Transfer ◽  
Gravity Waves ◽  
Navier Stokes ◽  
Acoustic Gravity Waves ◽  
Transfer Equations ◽  
Isothermal Atmosphere

scholarly journals Acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere

1995 ◽  
Vol 18 (2) ◽  
pp. 371-382 ◽  
Author(s):  
H. Y. Alkahby
Keyword(s):  
Gravity Waves ◽  
Attenuation Factor ◽  
Volume Effect ◽  
Temperature Perturbation ◽  
Oscillatory Process ◽  
Acoustic Gravity Waves ◽  
Perturbation Problem ◽  
The One ◽  
Thermally Conducting ◽  
Isothermal Atmosphere

In this paper we will investigate the effect of Newtonian cooling on the propagation of acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere for large Prandtl number and for an arbitrary values of Newtonian cooling coefficient. This problem leads to a singular perturbation problem which is solved by matching inner and outer approximations. It is shown that the viscosity creates an absorbing and reflecting layer. Below it the oscillatory process is adiabatic, for small Newtonian cooling coefficient, and above it the solution will decay to constant before it is influenced by the effect of the thermal conductivity. Newtonian cooling is a volume effect and influences mainly the lower adiabatic region, in which it causes attenuation in the amplitude of the wave. Finally it is shown that when Newtonian cooling coefficient goes to infinity it acts directly to eliminate the temperature perturbation associated with the wave and the attenuation factor in the amplitude of the wave. Accordingly the wavelength changes to the one consistent with the Newtonian sound speed. The reflection coefficient and the attenuation factor of the amplitude of the wave are derived for all values of Newtonian cooling coefficient.

Simultaneous flow of ions and heat to a plate electrode in the region of natural convection

1979 ◽  
Vol 44 (6) ◽  
pp. 1857-1868 ◽  
Author(s):  
Petr Novák ◽  
Ivo Roušar
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Natural Convection ◽  
Convective Diffusion ◽  
Navier Stokes ◽  
Exponential Polynomials ◽  
Plate Electrode ◽  
Transfer Equations ◽  
Boundary Layer Region ◽  
Layer Region

The Sherwood criterion was calculated for a flow of ions to the surface of a plate electrode during natural convection by solving the Navier-Stokes, convective diffusion, and convective heat transfer equations. The solution for the boundary layer region was performed by the collocation method using orthogonal exponential polynomials. Values of the Sh criterion were obtained for Sc ##m <500; 2 000>, Pr ##m <5; 20>, and GrT/GrM ##m <0.2; 8.0>. A comparison with literature data revealed the best agreement with average errors of +2.0 and -1.4%. Another equation with an error of only +0.5% is proposed.

scholarly journals Excitation of acoustic-gravity waves in an isothermal atmosphere

Tellus ◽  
1971 ◽  
Vol 23 (2) ◽  
pp. 150-163 ◽  
Author(s):  
C. H. Liu ◽  
K. C. Yeh
Keyword(s):  
Gravity Waves ◽  
Acoustic Gravity Waves ◽  
Isothermal Atmosphere

scholarly journals Two-frequency acoustic-gravitational waves, simulation of satellite measurements

2020 ◽  
Vol 36 (6) ◽  
pp. 22-36
Author(s):  
E.I. Kryuchkov ◽  
I.T. Zhuk ◽  
O.K. Cheremnykh
Keyword(s):  
Gravity Waves ◽  
Natural Frequencies ◽  
Initial Conditions ◽  
Spectral Characteristics ◽  
Single Frequency ◽  
Center Frequency ◽  
Dual Frequency ◽  
Satellite Measurements ◽  
Acoustic Gravity Waves ◽  
Isothermal Atmosphere

The theory of acoustic gravity waves (AGW) considers free disturbances of the atmosphere within the framework of a single-frequency approach. In this case, the theory implies the existence of two separate types of waves with different natural frequencies - acoustic and gravitational. In the single-frequency approach, wave fluctuations of density, temperature, and velocity are related to each other through the spectral characteristics of the wave, and these relationships are unchanged. However, satellite observations of AGW parameters cannot always be explained within the framework of a single-frequency approach. This paper presents a two-frequency approach to the study of AGWs using the model of two coupled oscillators. It is shown that the perturbed movements of the elementary volume of the medium occur simultaneously at two natural frequencies. In this case, the connections between the wave fluctuations of the parameters are determined by the initial conditions, which can be arbitrary. Solutions in real functions for an isothermal atmosphere are obtained. The conditions under which single-frequency AGWs are obtained from the general two-frequency solution are investigated. The AGW waveforms measured from the satellite for velocities and displacements in single-frequency and dual-frequency modes are numerically simulated. The results of simulating two-frequency AGWs agree with the data of satellite measurements. Two-frequency AGWs are not always implemented at two different frequencies. It is shown that when the frequencies approach each other, the beat effect occurs and two closely related modes become indistinguishable. At the same wavelength, they have one center frequency and one phase velocity. The main feature of the two-frequency approach to the study of AGW is the expansion of the relationships between the wave parameters of the medium. This makes it possible to achieve satisfactory agreement of the model waveforms with the data of satellite measurements. Thus, the use of a two-frequency AGW treatment opens up new possibilities in the interpretation of experimental data.

scholarly journals Acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere (part II: For small Prandtl number)

1995 ◽  
Vol 18 (3) ◽  
pp. 579-590 ◽  
Author(s):  
Hadi Y. Alkahby
Keyword(s):  
Thermal Diffusivity ◽  
Prandtl Number ◽  
Gravity Waves ◽  
Kinematic Viscosity ◽  
Cutoff Frequency ◽  
Temperature Perturbation ◽  
Solar Photosphere ◽  
Acoustic Gravity Waves ◽  
Exponential Increase ◽  
Isothermal Atmosphere

In part one of these series we investigated the effect of Newtonian cooling on acoustic-gravity waves in an isothermal atmosphere for large Prandtl number. It was shown that the atmosphere can be divided into two regions connected by an absorbing and reflecting layer, created by the exponential increase of the kinematic viscosity with height, and if Newtonian cooling coefficient goes to infinity the temperature perturbation associated with the wave will be eliminated. In addition all linear relations among the perturbation quantities will be modified. In this paper we will consider the effect of Newtonian cooling on acoustic-gravity waves for small Prandtl number in an isothermal atmosphere. It is shown that if the Newtonian cooling coefficient is small compared to the adiabatic cutoff frequency the atmosphere may be divided into three distinct regions. In the lower region the motion is adiabatic and the effect of the kinematic viscosity and thermal diffusivity are negligible, while the effect of these diffusivities is more pronounced in the upper region. In the middle region the effect of the thermal diffusivity is large, while that of the kinematic viscosity is still negligible. The two lower regions are connected by a semitransparent reflecting layer as a result of the exponential increase of the thermal diffusivity with height. The two upper regions are joined by an absorbing and reflecting barrier created but the exponential increase of the kinematic viscosity. If the Newtonian cooling coefficient is large compared to the adiabatic cutoff frequency, the wavelengths below and above the lower reflecting layer will be equalized. Consequently the reflection produced by the thermal conduction is eliminated completely. This indicates that in the solar photosphere the temperature fluctuations may be smoothed by the transfer of radiation between any two regions with different temperatures. Also the heat transfer by radiation is more dominant than the conduction process.

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