Sandpile behaviour in discrete water-wave turbulence

Abstract

We construct a sandpile model for evolution of the energy spectrum of the water surface waves in finite basins. This model take into account loss of resonant wave interactions in discrete Fourier space and restoration of these interactions at larger nonlinearity levels. For weak forcing, the waveaction spectrum takes a critical ${\omega }^{-10}$ shape where the nonlinear resonance broadening is equal to the Fourier grid spacing. The energy cascade in this case takes form of rare weak avalanches on the critical slope background. For larger forcing, this regime is replaced by a continuous cascade and Zakharov-Filonenko ${\omega }^{-8}$ waveaction spectrum. For intermediate forcing levels, both scalings will be seen: ${\omega }^{-10}$ at small and ${\omega }^{-8}$ at large frequencies. The interval between these two scaling regions is characterised by strong avalanches.

7 pages

References in corpus (1)

• Freely decaying weak turbulence for sea surface gravity waves

Cited by in corpus (27)

• Gravity surface wave turbulence in a laboratory flume
• Experiments in Surface Gravity-Capillary Wave Turbulence
• One-Dimensional Optical Wave Turbulence: Experiment and Theory
• Discreteness and its effect on the water-wave turbulence
• Discrete and mesoscopic regimes of finite-size wave turbulence
• Kelvin-wave turbulence in superfluids
• Simultaneous numerical simulation of direct and inverse cascades in wave turbulence
• Energy flux measurement from the dissipated energy in capillary wave turbulence
• Role of the basin boundary conditions in gravity wave turbulence
• Sustained turbulence in the three-dimensional Gross-Pitaevskii model
• Numerical Verification of the Weak Turbulent Model for Swell Evolution
• Coexistence of Weak and Strong Wave Turbulence in a Swell Propagation
• Wave turbulence on the surface of a ferrofluid submitted to a magnetic field
• Resonant interactions of nonlinear water waves in a finite basin
• Wave condensation with weak disorder versus beam self-cleaning in multimode fibers
• Impact of dissipation on the energy spectrum of experimental turbulence of gravity surface waves
• Robust energy transfer mechanism via precession resonance in nonlinear turbulent wave systems
• Numerical investigation of turbulence of surface gravity waves
• The Effect of Discrete Resonant Manifold Structure on Discrete Wave Turbulence
• Inverse cascade of gravity waves in the presence of condensate: numerical simulation
• Influence of the condensate and inverse cascade on the direct cascade in wave turbulence
• Wave turbulence on the surface of a fluid in a high-gravity environment
• Percolation transition in the kinematics of nonlinear resonance broadening in Charney-Hasegawa-Mima model of Rossby wave turbulence
• Non-equilibrium Bose-Einstein Condensation
• Identification of weakly- to strongly-turbulent three-wave processes in a micro-scale system
• Direct numerical experiment on measuring of dispersion relation for gravity waves in the presence of condensate
• Generation of intermittent gravitocapillary waves via parametric forcing