Forced oscillations in simple and binary gas atmospheric models - Viljoen, Michael David (Department of Mathematics and Applied Mathematics, 2016)
The presence of periodic oscillations in the earth's atmosphere has been confirmed in recent years by analysis of satellite drag data. The amplitudes of these oscillations vary with height and time in a complex manner with the underlying physical mechanism of this behaviour not fully understood. Classical studies have been limited to the lower levels of the atmosphere, but these have neglected to include the damping effects of heat conduction and viscosity. These also ignored the second order terms in the equations of motion which, in effect, treats an otherwise singular perturbation problem as regular. Upper atmosphere studies of the diurnal density oscillations were discussed by Nicolet, on the basis of the mutual diffusion of the components of a binary gas system, where he compared different equilibrium configurations. This statical treatment again ignores the damping effects on mass flow. D.G. Parkyn reduced the problem in idealised form to that of investigating the effect of a travelling temperature wave at the base of a viscous, heat conducting, diffusing gas atmosphere. This model excludes molecular dissociation and ionization in the upper regions and absorption of solar energy. Incorporation of all these properties would render the problem impossibly difficult . As a first step to the development of the analysis for the complex spherical atmosphere, Parkyn simplified the model to that of a cylindrical homogeneous atmosphere, and he considered the effect of forced oscillations about an isothermal equilibrium state. Parkyn showed that this idealised problem is capable of explicit solution and, contrary to the result of Wilkes, he found that the amplitudes of the forced osciliations decrease with height in the lower atmospheric regions. This implies the importance of heat conduction and viscosity as damping effects in these regions. It is proposed to extend the analysis of Parkyn by simplifying the geometry, treating one space dimension, so giving more flexibility to the assumed physical properties. Continuum equations of motion will be taken to hold throughout the range of investigation.