Reflection of vertically propagating waves in a thermally conducting isothermal atmosphere with a horizontal magnetic field

Alkahby, Hadi Y.; Yanowitch, Michael

doi:10.1080/03091929108219519

Cited by 13 publications

(8 citation statements)

References 8 publications

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“…It was verified that viscosity and conductivity influence the reflecting properties of an isothermal, small Prandtl number atmosphere, which can be divided into three distinct regions: an adiabatic lower layer with negligible viscosity and conductivity, an upper layer with considerable effects of the two terms, and the middle one with negligible viscosity (e.g., [27][28][29]). At the same time, some similar studies took into consideration a horizontal magnetic field (e.g., [30][31][32]). Particularly, in a series of work on the combined effect of Newtonian cooling, viscosity and thermal conduction, Alkahby [33][34][35] demonstrated that, for an arbitrary value of the Newtonian cooling coefficient, on the one hand, a large Prandtl number divides an atmosphere into two distinct regions between which there is an absorbing and reflecting layer produced by the exponential increase of the kinematic viscosity; on the other hand, a small Prandtl number divides the atmosphere into three distinct regions when the Newtonian cooling coefficient is small, while the two lower regions merge into one if the Newtonian cooling coefficient is large.…”

Section: Introductionmentioning

confidence: 99%

Atmospheric Layers in Response to the Propagation of Gravity Waves under Nonisothermal, Wind-shear, and Dissipative Conditions

John

2016

JMSE

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We study the atmospheric structure in response to the propagation of gravity waves under nonisothermal (nonzero vertical temperature gradient), wind-shear (nonzero vertical zonal/meridional wind speed gradients), and dissipative (nonzero molecular viscosity and thermal conduction) conditions. As an alternative to the "complex wave-frequency" model proposed by Vadas and Fritts, we employ the traditional "complex vertical wave-number" approach to solving an eighth-order complex polynomial dispersion equation. The empirical neutral atmospheric models of NRLMSISE-00 and HWM93 are employed to provide mean-field properties. In response to the propagation of gravity waves, the atmosphere is driven into three sandwich-like layers: the adiabatic layer (0-130 km), the dissipation layer (130-230 km) and the pseudo-adiabatic layer (above 230 km). In the lower layer, (extended-)Hines' mode or ordinary dissipative wave modes exist, whereas viscous dissipation and thermal conduction fail to exert perceptible influences; in the middle layer, Hines' mode ceases to exist, and both ordinary and extraordinary dissipative wave modes flourish; in the top layer, only extraordinary wave modes survive, and dissipations affect the real part of the vertical wavenumber (m r) substantially; however, they contribute little to the imaginary part, which is the vertical growth rate (m i). We also analyze the transition of Hines' classical mode to ordinary dissipative wave modes, describe both the upward and downward modes of gravity waves and illustrate nonisothermal and wind-shear effects on the propagation of gravity waves of different modes.

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Section: Introductionmentioning

confidence: 99%

Atmospheric Layers in Response to the Propagation of Gravity Waves under Nonisothermal, Wind-shear, and Dissipative Conditions

John

2016

JMSE

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“…Also the results of this section are needed for the results and the analysis of section (4). For this case, the differential equation can be obtained by setting where cl and c2 are constants and they will be determined from the boundary condition To examine the effect ofNewtonian cooling on the wave propagation and dissipation, let (V/1 TO')/2 -4-(--d(q,w) + i)).…”

Section: The Effect Of Newtonian Cooling Alonementioning

confidence: 99%

“…The exponential increase of the thermal diffusivity with height creates a semitransparent layer allowing part of the energy to propagate upward As a result, the reflecting layer separates two distinct regions with different sound speeds, because the signals propagate with Newtonian sound speed in the isothermal region. Consequently, the wavelengths in the two regions are different and this will account for the reflection (Alkahby [7], Alkahby and Yanowitch [3,4], Lyons and Yanowitch [18]). …”

Section: Introductionmentioning

confidence: 99%

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

Alkahby

1995

International Journal of Mathematics and Mathematical Sciences

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ABSTRACT. 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 seres 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, 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 ofNewtonian cooling is negligible thermal conduction influences the propagation of the wave only in the case of small Prandtl number.

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“…Three ranges for the frequency are identified, above the adiabatic cutoff frequency, below the isothermal cutoff frequency and in between. The results of section (3) are used in section (4). Finally These are, respectively, the equation for the change in the vertical momentum, the mass conservation equation, the equation for the rate change of the x-component of the magnetic field, the heat flow equation and the gas law.…”

Section: Introductionmentioning

confidence: 99%

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

Alkahby

1995

International Journal of Mathematics and Mathematical Sciences

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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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Reflection of vertically propagating waves in a thermally conducting isothermal atmosphere with a horizontal magnetic field

Cited by 13 publications

References 8 publications

Atmospheric Layers in Response to the Propagation of Gravity Waves under Nonisothermal, Wind-shear, and Dissipative Conditions

Atmospheric Layers in Response to the Propagation of Gravity Waves under Nonisothermal, Wind-shear, and Dissipative Conditions

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

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

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