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BIRS Workshop Lecture Videos

Wave Turbulence in Finite Domain â Role of Discrete Resonant Manifold Pan, Yulin


We consider the long-term dynamics of nonlinear dispersive waves in a finite periodic domain. The purpose of the work is to show, for the first time, that the statistical properties of the wave field rely critically on the structure of the discrete resonant manifold (DRM). To demonstrate this, we simulate the two-dimensional MMT equation on rational and irrational tori, resulting in remarkably different power-law spectra and energy cascades at low nonlinearity levels. The difference is explained in terms of different structures of the DRM, which makes use of the recent number theory results. The role of DRM will also be discussed in the context of physical wave systems and demonstrated for the case of capillary waves. Finally, we will discuss the implications of the findings to finite-domain wave turbulence in general.

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