Lamb waves in the presence of realistic distributions of temperature and dissipation

Lamb waves are the fundamental free oscillations of a dissipationless, compressible, isothermal atmosphere. They can exist at all periods (less than a pendulum day) and though their energy is confined to within a few scale heights of the surface, their amplitudes increase exponentially with height. When realistic temperature distributions or dissipation or both are included then for periods in excess of about 15 min truly free oscillations no longer exist. However, there do exist oscillations analogous to Lamb waves that yield a highly magnified response to forcing and that should therefore dominate the atmospheric response to various lower atmosphere excitations. The lifetime (or equivalently the magnification) is shown to depend primarily on surface friction. The amplitudes of such waves grow with altitude until limited by a combination of molecular diffusion and ion drag. The detailed vertical structure of such waves is described.