Atmospheric Tidal Oscillations in Viscid Atmosphere

Abstract

Characteristics of atmospheric tidal oscillations in viscid atmosphere are discussed. When the effect of thermal conduction is included, the equations of the oscillations remain separable with the Hough function as in the classical theory. The vertical structure of the oscillation is given by a fourth-order differential equation. The equation has two kinds of solutions. The one is modified tidal mode and the other is thermal conductive mode. On the other hand, viscous term does not make the equations separable because of the horizontal dependence of the Coriolis force. Approximately, a constant Coriolis force model is used. The horizontal structure is given by the associated Legendre function. The vertical structure is given by a sixth-order differential equation. Two kinds of viscous modes emerge under the Coriolis effect. If the thermal conductive term is also included, an eighth-order differential equation is obtained. Characteristics of the modified vertically propagating tidal modes are that the vertical wavelengths become long and the damping factors become large with increasing kinematic viscosity. The viscous and thermal conductive effects on the nonpropagating tidal modes are to modify their rate of decay to be slightly smaller. The diurnal viscous and thermal conductive modes with negative equivalent heights become important above the height of 140km because the damping factors decrease with increasing kinematic viscosity, and especially the former mode has similar characteristics to those of the vertically propagating tidal modes. The effect of viscosity on diurnal thermospheric wind is also discussed to investigate the physical meaning of the viscous wave.