The Stability of Internal Gravity Waves of Finite Width

Internal gravity waves propagate in a form of 'beam' from a wave source in the atmosphere and the ocean. The corresponding solution is an exact solution of the Euler equations. In the present study, we consider 'triad resonance' (3-wave interaction) among one beam and two plane waves. The triad resonance among three plane waves is well-known to occur, but their dynamics when one of them is a beam has not been elucidated so far. According to recent studies, occurrence of instability depends not only on their amplitudes but also on 'width' of the beam. We demonstrate this fact by numerical simulation of the Euler equations and clarify the effect of width on the stability of wave beam.