The Effect of Discrete Resonant Manifold Structure on Discrete Wave Turbulence
arXiv:2003.10801 · doi:10.1103/PhysRevE.102.041101
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 (23)
- A weak turbulence theory for incompressible MHD
- Observation of gravity-capillary wave turbulence
- Gravity surface wave turbulence in a laboratory flume
- Statistical Description of Acoustic Turbulence
- Discreteness and its effect on the water-wave turbulence
- Statistics of surface gravity wave turbulence in the space and time domains
- Double scaling in the relaxation time in the -FPUT model
- Turbulence of Weak Gravitational Waves in the Early Universe
- Discrete and mesoscopic regimes of finite-size wave turbulence
- Sandpile behaviour in discrete water-wave turbulence
- Energy flux measurement from the dissipated energy in capillary wave turbulence
- Fourier analysis of wave turbulence in a thin elastic plate
- Role of the basin boundary conditions in gravity wave turbulence
- The role of dissipation in flexural wave turbulence: from experimental spectrum to Kolmogorov-Zakharov spectrum
- Nonlinear waves on the surface of a fluid covered by an elastic sheet
- Kinetic Wave Turbulence
- Nonlinear dynamics of flexural wave turbulence
- Weak versus strong wave turbulence in the MMT model
- Exact discrete resonances in the Fermi-Pasta-Ulam-Tsingou system
- Wave-Turbulence Theory of four-wave nonlinear interactions
- Wave turbulence on the surface of a fluid in a high-gravity environment
- Observation of the resonance frequencies of a stable torus of fluid
- Formal expansions in stochastic model for wave turbulence 1: kinetic limit
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