427 research outputs found
Laminated Wave Turbulence: Generic Algorithms III
Model of laminated wave turbulence allows to study statistical and discrete
layers of turbulence in the frame of the same model. Statistical layer is
described by Zakharov-Kolmogorov energy spectra in the case of irrational
enough dispersion function. Discrete layer is covered by some system(s) of
Diophantine equations while their form is determined by wave dispersion
function. This presents a very special computational challenge - to solve
Diophantine equations in many variables, usually 6 to 8, in high degrees, say
16, in integers of order and more. Generic algorithms for solving
this problem in the case of
{\it irrational} dispersion function have been presented in our previous
papers. In this paper we present a new generic algorithm for the case of {\it
rational} dispersion functions. Special importance of this case is due to the
fact that in wave systems with rational dispersion the statistical layer does
not exist and the general energy transport is governed by the discrete layer
alone.Comment: submitted to IJMP
Cluster formation in mesoscopic systems
Graph-theoretical approach is used to study cluster formation in mesocsopic
systems. Appearance of these clusters are due to discrete resonances which are
presented in the form of a multigraph with labeled edges. This presentation
allows to construct all non-isomorphic clusters in a finite spectral domain and
generate corresponding dynamical systems automatically. Results of MATHEMATICA
implementation are given and two possible mechanisms of cluster destroying are
discussed
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 connections between
neighboring triads that determine the general dynamics of a cluster. Each
connection type corresponds to substantially different scenarios of energy flux
among the modes. The general approach can be applied directly to various
mesoscopic systems with 3-mode interactions, encountered in hydrodynamics,
astronomy, plasma physics, chemistry, medicine, etc.Comment: 6 pages, 3 figs, EPL, publishe
A Model of Intra-seasonal Oscillations in the Earth atmosphere
We suggest a way of rationalizing an intra-seasonal oscillations (IOs) of the
Earth atmospheric flow as four meteorological relevant triads of interacting
planetary waves, isolated from the system of all the rest planetary waves.
Our model is independent of the topography (mountains, etc.) and gives a
natural explanation of IOs both in the North and South Hemispheres. Spherical
planetary waves are an example of a wave mesoscopic system obeying discrete
resonances that also appears in other areas of physics.Comment: 4 pages, 2 figs, Submitted to PR
Nonlinear resonances of water waves
In the last fifteen years, a great progress has been made in the
understanding of the nonlinear resonance dynamics of water waves. Notions of
scale- and angle-resonances have been introduced, new type of energy cascade
due to nonlinear resonances in the gravity water waves have been discovered,
conception of a resonance cluster has been much and successful employed, a
novel model of laminated wave turbulence has been developed, etc. etc. Two
milestones in this area of research have to be mentioned: a) development of the
-class method which is effective for computing integer points on the
resonance manifolds, and b) construction of the marked planar graphs, instead
of classical resonance curves, representing simultaneously all resonance
clusters in a finite spectral domain, together with their dynamical systems.
Among them, new integrable dynamical systems have been found that can be used
for explaining numerical and laboratory results. The aim of this paper is to
give a brief overview of our current knowledge about nonlinear resonances among
water waves, and formulate three most important open problems at the end.Comment: 14 pages, 3 figures, to appear in DCDS, final version (small changes
in the text, type errors corrected, some additional bibliographic items
added
Time scales and structures of wave interaction
In this paper we give a general account of Wave Interaction Theory which by
now consists of two parts: kinetic wave turbulence theory (WTT), using a
statistical description of wave interactions, and the D-model recently
introduced in \emph{Kartashova, PRE \textbf{86}: 041129 (2012)} describing
interactions of distinct modes. Applying time scale analysis to weakly
nonlinear wave systems modeled by the focusing nonlinear Sch\"{o}dinger
equation, we give an overview of the structures appearing in Wave Interaction
Theory, their time scales and characteristic times. We demonstrate that kinetic
cascade and D-cascade are not competing processes but rather two processes
taking place at different time scales, at different characteristic levels of
nonlinearity and due to different physical mechanisms. Taking surface water
waves as an example we show that energy cascades in this system occur at much
faster characteristic times than those required by the kinetic WTT but can be
described as D-cascades. As D-model has no special pre-requisites, it may be
rewarding to re-evaluate existing experiments in other wave systems appearing
in hydrodynamics, nonlinear optics, electrodynamics, plasma, convection theory,
etc.
To appear in EP
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