Related papers: Discrete Wave Turbulence
We perform numerical simulations of the dynamical equations for free water surface in finite basin in presence of gravity. Wave Turbulence (WT) is a theory derived for describing statistics of weakly nonlinear waves in the infinite basin…
Bounding volume results in discreteness of eigenmodes in wave systems. This leads to a depletion or complete loss of wave resonances (three-wave, four-wave, etc.), which has a strong effect on Wave Turbulence, (WT) i.e. on the statistical…
We study the discrete wave turbulent regime of capillary water waves with constant non-zero vorticity. The explicit Hamiltonian formulation and the corresponding coupling coefficient are obtained. We also present the construction and…
Two fundamental facts of the modern wave turbulence theory are 1) existence of power energy spectra in $k$-space, and 2) existence of "gaps" in this spectra corresponding to the resonance clustering. Accordingly, three wave turbulent…
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…
Finite-dimensional wave turbulence refers to the chaotic dynamics of interacting wave `clusters' consisting of finite number of connected wave triads with exact three-wave resonances. We examine this phenomenon using the example of…
We report numerical investigations of wave turbulence in a vibrating plate. The possibility to implement advanced measurement techniques and long time numerical simulations makes this system extremely valuable for wave turbulence studies.…
The concept of Nonlinear dispersion relation (NDR) is used in various fields of Physics (nonlinear optics, hydrodynamics, hydroelasticity, mechanics, quantum optics, plasma physics,...) to characterize fundamental phenomena induced by…
Dispersive shock waves (DSWs), which connect states of different amplitude via a modulated wave train, form generically in nonlinear dispersive media subjected to abrupt changes in state. The primary tool for the analytical study of DSWs is…
Analysis of resonance clustering in weakly nonlinear dispersive wave systems, also called discrete wave turbulent systems, is a new methodology successfully used in the last years for characterizing energy transport due to exact and…
The structure of discrete resonances in water-wave turbulence is studied. It is shown that the number of exact 4-wave resonances is huge (hundreds million) even in comparatively small spectral domain when both scale and angle energy…
Traditionally resonant interactions among short waves, with large real wave-numbers, were described statistically and only a small domain in spectral space with integer wave-numbers, discrete resonances, had to be studied separately in…
We present a detailed review of large-scale structure (LSS) study using the discrete wavelet transform (DWT). After describing how one constructs a wavelet decomposition we show how this bases can be used as a complete statistical…
We derive rigorously the non-linear macroscopic system associated to a microscopic system of coupled quintic Schr\"odinger equations in the framework of discrete wave turbulence under a particular scaling law that describes the limiting…
In this paper we review recent developments in the statistical theory of weakly nonlinear dispersive waves, the subject known as Wave Turbulence (WT). We revise WT theory using a generalisation of the random phase approximation (RPA). This…
The discrete wavelet packet transform (DWPT) and discrete wavelet transform (DWT) are used to extract and study the dynamics of coherent structures in a turbulent rotating fluid. Three-dimensional (3D) turbulence is generated by strong…
We report the quantitative experimental observation of the weak inertial-wave turbulence regime of rotating turbulence. We produce a statistically steady homogeneous turbulent flow that consists of nonlinearly interacting inertial waves,…
We study generic waves without rotational symmetry in (2+1) - dimensional noncommutative scalar field theory. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by…
Using weak wave turbulence theory analysis, we distinguish three main regimes for 2D stratified fluids in the dimensionless parameter space defined by the Froude number and the Reynolds number: discrete wave turbulence, weak wave…
Two-dimensional arrays of nonlinear electric oscillators are considered theoretically, where nearest neighbors are coupled by relatively small, constant, but non-equal capacitors. The dynamics is approximately reduced to a weakly…