On the spectral evolution of strongly interacting waves

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Abstract
Spectral evolution of small amplitude waves can be predicted by the resonant interaction (RI) formalism when the interaction is sufficiently weak in the sense that characteristic interaction times are much greater than wave periods. Often this is not the case, e.g. planetary waves, internal gravity waves and plasma waves which commonly are of large amplitude, interacting in times comparable to wave periods. At still larger amplitude, interaction will occur in times shorter than wave periods and the motion becomes a wave-modified kind of turbulence. By re-examining the RI assumptions, this paper describes a systematic extension to include stronger wave interactions, obtaining in the limit of large amplitude a spectral theory of turbulence. The present method has been used to calculate anisotropic evolution of barotropic planetary (Rossby) waves and of linear waves propagating in a, strongly randomly inhomogeneous medium, in both cases in agreement with resuIts of numericai-hydrodynamic simulations. Another criterion for appiicability of RI is obtained, namely that the interaction time must be greater than a “group period”, i.e. the time in which a wave group or packet travels over a packet length. Similar criteria are s e m to limit the effects of “distant” boundary conditions on “local” wave interactions and to establish requirements for valid numerical wave simulation in terms of an “information propagation length”. Unresolved questions concern possible existence of solitons and possible amplitude elfects on wave propagation frequencies.

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