Vertical oscillations in a viscous and thermally conducting isothermal atmosphere

Abstract

The presence of dissipation in an isothermal atmosphere may cause upwardpropagating small amplitude waves to be reflected downward. For an atmosphere with small dynamic viscosity μ this was demonstrated in Yanowitch (1967b); this will be referred to as case II. Here two problems will be investigated: (i) a thermally conducting atmosphere with small conductivity k (case III) and (ii) a viscous and thermally conducting atmosphere with small k and μ, and a small ratio μ/k, i.e. small Prandtl number (case IV). It will be shown that the validity of the model in case III is questionable. The solution for case IV is determined from the conditions that the average rate of energy dissipation and of entropy increase in a column of fluid be finite, but a radiation condition is required in case III. The solution for case III does not approximate the one for case IV uniformly, and the reflexion coefficient for case IV does not tend to the one for case III as the Prandtl number Pr → 0, but varies periodically with log Pr. Numerical results show that when the Prandtl number is not small the reflexion coefficient can be approximated by the asymptotic value obtained from case II.

Nonlinear MHD Waves and Turbulence

“…Here we describe relatively simple experiments based on the numerical solutions of the system (92), (93), (63) with simplifications (95) and (96). Of course, it is a model system based on the assumption of the smallness of parameter /x which is correct only for sufficiently broad beams.…”

“…In what follows this condition will be assumed to be met, so that it is necessary to consider neither slow and fast magneto-acoustic-gravity waves [149,105,100,135,115,3,4,128,126,136,151,152,153,31,32,36,37,38,41,42,54], nor acoustic-gravity waves [108,90,33]. The present paper will thus concentrate on Alfven waves, excluding dissipative effects either on incompressible [57,107,71,114,133,113,32,33,39,41,44,45] or compressible modes [148,95,34,29,2], which are relevant to the heating and other phenomena in the solar atmosphere [6,20,129,118,89,74,137,154,35,40,53].…”

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

“…Much more studies were developed with more new results reported in the following 25 years. 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]).…”

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

“…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]). …”