The Effect of Discrete Resonant Manifold Structure on Discrete Wave Turbulence

Abstract

We consider the long-term dynamics of nonlinear dispersive waves in a finite periodic domain. The purpose of the work is to show 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 recent number theory results.

References in corpus (5)

• Gravity surface wave turbulence in a laboratory flume
• Fourier analysis of wave turbulence in a thin elastic plate
• The role of dissipation in flexural wave turbulence: from experimental spectrum to Kolmogorov-Zakharov spectrum
• Wave turbulence on the surface of a fluid in a high-gravity environment
• Observation of the resonance frequencies of a stable torus of fluid

Cited by in corpus (7)

• Experiments in Surface Gravity-Capillary Wave Turbulence
• Numerical investigation of turbulence of surface gravity waves
• On the Properties of Energy Flux in Wave Turbulence
• Energy cascade in the Garrett-Munk spectrum of internal gravity waves
• Experimental Dispersion Relation of Surface Waves Along a Torus of Fluid
• Energy transfer for solutions to the nonlinear Schrödinger equation on irrational tori
• Modified scattering for the cubic Schrödinger equation on Diophantine waveguides