Wave turbulence: the case of capillary waves (a review)
arXiv:2001.10270 · doi:10.1080/03091929.2020.1715966
Abstract
Capillary waves are perhaps the simplest example to consider for an introduction to wave turbulence. Since the first paper by Zakharov and Filonenko (1967), capillary wave turbulence has been the subject of many studies but a didactic derivation of the kinetic equation is still lacking. It is the objective of this paper to present such a derivation in absence of gravity and in the approximation of deep water. We use the Eulerian method and a Taylor expansion around the equilibrium elevation for the velocity potential to derive the kinetic equation. The use of directional polarities for three-wave interactions leads to a compact form for this equation which is fully compatible with previous work. The exact solutions are derived with the so-called Zakharov transformation applied to wavenumbers and the nature of these solutions is discussed. Experimental and numerical works done in recent decades are also reviewed.
arXiv comment17 pages, 3 figures, to be published in Geophys. & Astrophys. Fluid Dyn
References in corpus (27)
- A weak turbulence theory for incompressible MHD
- Observation of gravity-capillary wave turbulence
- Wave turbulence in incompressible Hall MHD
- Observation of wave turbulence in vibrating plates
- One-Dimensional Optical Wave Turbulence: Experiment and Theory
- Direct Evidence of the Transition from Weak to Strong MHD Turbulence
- Capillary wave turbulence on a spherical fluid surface in low gravity
- Energy cascades and spectra in turbulent Bose-Einstein condensates
- Turbulence of Weak Gravitational Waves in the Early Universe
- Nonlocal resonances in weak turbulence of gravity-capillary waves
- Direct numerical simulations of capillary wave turbulence
- Quasi-Adiabatic Decay of Capillary Turbulence on the Charged Surface of Liquid Hydrogen
- Wave turbulence in Bose-Einstein condensates
- Decay of capillary wave turbulence
- Sustained turbulence in the three-dimensional Gross-Pitaevskii model
- Space-Time Resolved Capillary Wave Turbulence
- Investigation of resonances in gravity-capillary wave turbulence
- Weak and strong wave turbulence spectra for elastic thin plate
- Imbalanced kinetic Alfvén wave turbulence: from weak turbulence theory to nonlinear diffusion models for the strong regime
- Weak turbulence theory for rotating magnetohydrodynamics and planetary dynamos
- Elastic wave-turbulence and intermittency
- Nonlinear Diffusion Models for Gravitational Wave Turbulence
- Turbulence of capillary waves forced by steep gravity waves
- Elastic Weak Turbulence: from the vibrating plate to the drum
- Wave turbulence on the surface of a fluid in a high-gravity environment
- Forced three-wave interactions of capillary-gravity surface waves
- Inverse cascade of hybrid helicity in -MHD turbulence