CHAOTIC PROPERTIES OF INTERNAL WAVE TRIAD INTERACTIONS

We discuss the stochasticities of two-triad interactions that occur in two-degree-of-freedom autonomous Hamiltonian systems. The system we s tudy is a two-triad test-wave system consisting of a single internal w ave mode (test-wave) interacting with a spectrum of ambient internal w ave modes; the ambient modes, however, do not interact among themselve s except through a three-wave interaction which includes the test-wave . The present study concerns the effect of nonlinearities on the ocean internal wave field. Our numerical results using the physical paramet ers appropriate for the deep ocean confirm that the test-wave system i s non-integrable. Moreover, there exists a certain separatrix net that fills the phase space and is covered by a thin stochastic layer for a two-triad pure resonant interaction. The stochastic web implies the e xistence of diffusion of the Arnold type for the minimal dimension of a non-integrable autonomous system. For the non-resonant case, tile st ochastic layer is formed where the separatrix from KAM theory is disru pted. However, the stochasticity does not increase monotonically with increasing energy. (C) 1997 American Institute of Physics.