Toward a Unified Theory of Gravity Wave Stability

Abstract

Abstract This paper reveals relationships among linear instabilities of internal gravity waves often supposed to be independent. Using a Floquet analysis of a monochromatic wave propagating in a uniformly stratified background without shear, which accounts for finite wave amplitude, spatial and temporal periodicity, tilted phase planes, and 3D disturbances, it is demonstrated that the dominant instabilities of overturning waves are the large-wave-amplitude manifestations of resonant and slantwise instabilities of small amplitude waves, and that they possess no threshold 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 to Kelvin–Helmholtz instability and Benard convection in simpler backgrounds. At small amplitudes, resonant instabilities rely on horizontal or slantwise gradients of wave ...