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.

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.

scholarly journals Acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere (part III: for arbitrary Prandtl number)

1997 ◽  
Vol 20 (2) ◽  
pp. 367-374 ◽  
Author(s):  
Hadi Yahya Alkahby
Keyword(s):  
Prandtl Number ◽  
Gravity Waves ◽  
Acoustic Waves ◽  
Thermal Conduction ◽  
Thermal Condition ◽  
Acoustic Gravity Waves ◽  
Representative Model ◽  
The Subject ◽  
Thermally Conducting ◽  
Isothermal Atmosphere

In this paper we will investigate the combined effect of Newtonian cooling, viscosity and thermal condition on upward propagating acoustic waves in an isothermal atmosphere. In part one of this series we considered the case of large Prandtl number, while in part two we investigated the case of small Prandtl number. In those parts we examined only the limiting cases, i.e. the cases of small and large Prandtl number, and it is more interesting to consider the case of arbitrary Prandtl number, which is the subject of this paper, because it is a better representative model. It is shown that if the Newtonian cooling coefficient is small compared to the frequency of the wave, the effect of the thermal conduction is dominated by that of the viscosity. Moreover, the solution can be written as a linear combination of an upward and a downward propagating wave with equal wavelengths and equal damping factors. On the other hand if Newtonian cooling is large compared to the frequency of the wave the effect of thermal conduction will be eliminated completely and the atmosphere will be transformed from the adiabatic form to an isothermal. In addition, all the linear relations among the perturbations quantities will be modified. It follows from the above conclusions and those of the first two parts, that when the effect of Newtonian cooling is negligible thermal conduction influences the propagation of the wave only in the case of small Prandtl number.

scholarly journals Spectra of Acoustic-Gravity Waves in the Atmosphere with a Quasi-Isothermal Upper Layer

Atmosphere ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 818
Author(s):  
Sergey P. Kshevetskii ◽  
Yuliya A. Kurdyaeva ◽  
Nikolai M. Gavrilov
Keyword(s):  
Gravity Waves ◽  
Evolution Operator ◽  
Mathematical Problem ◽  
Cutoff Frequency ◽  
Lower Boundary ◽  
Low Frequency ◽  
Acoustic Gravity Waves ◽  
Wide Range ◽  
Different Altitudes ◽  
Wave Modes

In this paper, we study, in theoretical terms, the structure of the spectrum of acoustic-gravity waves (AGWs) in the nonisothermal atmosphere having asymptotically constant temperature at high altitudes. A mathematical problem of wave propagation from arbitrary initial perturbations in the half-infinite nonisothermal atmosphere is formulated and analyzed for a system of linearized hydrodynamic equations for small-amplitude waves. Besides initial and lower boundary conditions at the ground, wave energy conservation requirements are applied. In this paper, we show that this mathematical problem belongs to the class of wave problems having self-adjoint evolution operators, which ensures the correctness and existence of solutions for a wide range of atmospheric temperature stratifications. A general solution of the problem can be built in the form of basic eigenfunction expansions of the evolution operator. The paper shows that wave frequencies considered as eigenvalues of the self-adjoint evolution operator are real and form two global branches corresponding to high- and low-frequency AGW modes. These two branches are separated since the Brunt–Vaisala frequency is smaller than the acoustic cutoff frequency at the upper boundary of the model. Wave modes belonging to the low-frequency global spectral branch have properties of internal gravity waves (IGWs) at all altitudes. Wave modes of the high-frequency spectral branch at different altitudes may have properties of IGWs or acoustic waves depending on local stratification. The results of simulations using a high-resolution nonlinear numerical model confirm possible changes of AGW properties at different altitudes in the nonisothermal atmosphere.

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.

The cooling of a low-heat-resistance sheet moving through a fluid

1974 ◽  
Vol 341 (1625) ◽  
pp. 233-252 ◽  
Keyword(s):  
Nusselt Number ◽  
Thermal Diffusivity ◽  
Viscous Fluid ◽  
Prandtl Number ◽  
Heat Resistance ◽  
Series Expansion ◽  
Kinematic Viscosity ◽  
Flat Sheet

In this paper we consider the cooling of a flat sheet moving through a semiinfinite expanse of viscous fluid. The heat resistance of the sheet is assumed to be so small that the temperature can be considered uniform across the sheet. Precise conditions for this assumption to be valid are derived. The problem is solved first by means of a coordinate expansion, which can be proved to converge for all values of the expansion variable. Since this series cannot be used numerically downstream, an alternative series expansion, which applies downstream, is also derived.Special sections are devoted to deriving solutions valid for small or large values of the Prandtl number. Finally, expressions are obtained for the Nusselt number and the cooling length. It is found that cooling is determined by the smaller of two diffusivities, namely, the kinematic viscosity and the thermal diffusivity.

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