TOWARD A UNIFIED THEORY OF GRAVITY-WAVE STABILITY

This paper reveals relationships among linear instabilities of interna l gravity waves often supposed to be independent. Using a Floquet anal ysis of a monochromatic wave propagating in a uniformly stratified bac kground without shear, which accounts for finite wave amplitude, spati al and temporal periodicity, tilted phase planes, and 3D disturbances, it is demonstrated that the dominant instabilities of overturning wav es are the large-wave-amplitude manifestations of resonant and slantwi se instabilities of small amplitude waves, and that they possess no th reshold amplitudes. An energy budget analysis examines the relation of parametric instabilities at large wave amplitude to vertical dynamic and static instabilities; however, the instability characteristics for propagating waves are very different from those inferred by analogy t o Kelvin-Helmholtz instability and Benard convection in simpler backgr ounds. At small amplitudes, resonant instabilities rely on horizontal or slantwise gradients of wave properties; in particular, parametric s ubharmonic instability is related to slantwise static instability. Thr ee-dimensional instabilities with a preferred oblique orientation are found: these are related to wave-shear-aligned instabilities at large amplitude and to higher-order resonances at small wave amplitude. A si mplified classification of gravity wave instability is proposed.