Finite-dimensional turbulence of planetary waves.

  title={Finite-dimensional turbulence of planetary waves.},
  author={Victor S. L’vov and Anna Pomyalov and Itamar Procaccia and Oleksii Rudenko},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={80 6 Pt 2},
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 atmospheric planetary (Rossby) waves. It is shown that the dynamics of the clusters is determined by the types of connections between neighboring triads within a cluster; these correspond to substantially different scenarios of energy flux between different triads… 
Discrete and mesoscopic regimes of finite-size wave turbulence.
It is argued that in mesoscopic systems the wave spectrum experiences a sandpile behavior and the mesoscopic regime is realized for a broad range of wave amplitudes which typically spans over several orders on magnitude, and not just for a particular intermediate level.
Resonance clustering in wave turbulent regimes: Integrable dynamics
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.
Time scales and structures of wave interaction exemplified with water waves
Presently two models for computing energy spectra in weakly nonlinear dispersive media are known: kinetic wave turbulence theory, using a statistical description of an energy cascade over a
Discrete exact and quasi-resonances of Rossby/drift waves on $\b$-plane with periodic boundary conditions
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
Stationary multi-wave resonant ensembles in a microtubule
Percolation transition in the kinematics of nonlinear resonance broadening in Charney-Hasegawa-Mima model of Rossby wave turbulence
We study the kinematics of nonlinear resonance broadening of interacting Rossby waves as modelled by the Charney–Hasegawa–Mima equation on a biperiodic domain. We focus on the set of wave modes which
Correlation Between Three-dimensional Sine Sweep Dynamics Vibration Testing and Resonantly Interacting Internal Gravity Wave Field
The main goal is to report a similarity in qualitative dynamics of (1) wave amplitudes within resonantly interactive internal gravity waves in the deep ocean and the sine sweep of three-dimensional


Noisy spectra, long correlations, and intermittency in wave turbulence.
  • Y. Lvov, S. Nazarenko
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2004
A minimal model based on the random phase approximation (RPA) is used and it is shown that any initial non-Gaussianity at small amplitudes propagates without change toward the high amplitudes at each fixed wave number, however, the probability distribution function becomes Gaussian at large time.
On the dynamics of unsteady gravity waves of finite amplitude Part 1. The elementary interactions
  • O. Phillips
  • Geology, Physics
    Journal of Fluid Mechanics
  • 1960
This paper is concerned with the non-linear interactions between pairs of intersecting gravity wave trains of arbitrary wavelength and direction on the surface of water whose depth is large compared
2D enslaving of MHD turbulence
At odds with its name, the classical weak turbulence theory only works for turbulence which is strong enough. Namely, the nonlinear resonance broadening has to be greater than the Fourier mode
Cluster dynamics of planetary waves
The dynamics of nonlinear atmospheric planetary waves is determined by a small number of independent wave clusters consisting of a few connected resonant triads. We classified the different types of
Gravity wave turbulence in a laboratory flume.
It is argued that at low wave amplitudes the wave statistics is affected by the flume finite size, and at high amplitude the wave breaking effect dominates.
On the Role of Resonant Interactions in the Short-Term Evolution of Deep-Water Ocean Spectra
Abstract The temporal evolution of the energy spectrum of a field of random surface gravity waves in deep water is investigated by means of direct numerical simulations of the deterministic primitive
Mesoscopic wave turbulence
We report results of simulation of wave turbulence. Both inverse and direct cascades are observed. The definition of “mesoscopic turbulence” is given. This is a regime when the number of modes in a