6,245 research outputs found
Multiscales and cascade in isotropic turbulence
The central problem of fully developed turbulence is the energy cascading
process. It has revisited all attempts at a full physical understanding or
mathematical formulation. The main reason for this failure are related to the
large hierarchy of scales involved, the highly nonlinear character inherent in
the Navier-Stokes equations, and the spatial intermittency of the dynamically
active regions. Richardson has described the interplay between large and small
scales and the phenomena so described are known as the Richardson cascade. This
local interplay also forms the basis of a theory by Kolmogorov. In this letter,
we use the explicit map method to analyze the nonlinear dynamical behavior for
cascade in isotropic turbulence. This deductive scale analysis is shown to
provide the first visual evidence of the celebrated Richardson cascade, and
reveals in particular its multiscale character. The results also indicate that
the energy cascading process has remarkable similarities with the deterministic
construction rules of the logistic map. Cascade of period-doubling bifurcations
have been seen in this isotropic turbulent systems that exhibit chaotic
behavior. The `cascade' appears as an infinite sequence of period-doubling
bifurcations.Comment: 7 pages,1 figur
Large scale dynamics in two-dimensional turbulence
We consider freely decaying two-dimensional isotropic turbulence. It is
usually assumed that, in such turbulence, the energy spectrum at small wave
number, takes the form, where is the two-dimensional version of Loitsyansky's
integral. In this paper, we developed a simple model for large scale dynamics
of free decay two-dimensional turbulence based on the statistical solution of
Navier-Stokes equation. We provide one possible explanation for the large scale
dynamics in two-dimensional turbulence.Comment: 5 pages, 0 figures, 1 tabl
Integrability and Hamiltonian system in isotropic turbulence
We present developments of the Hamiltonian approach to problems of the freely
decay of isotropic turbulence, and also consider specific applications of the
modified Prelle-Singer procedure to isotropic turbulence. It demonstrates that
a nonlinear second order ordinary differential equation is intimately related
to the self-preserving solution of Karman-Howarth equation, admitting
time-dependent first integrals and also proving the nonstandard Hamiltonian
structure, as well as the Liouville sense of integrability.Comment: 7 pages;0 figure
Nonlinear dynamical systems and linearly forced isotropic turbulence
In this paper, we present an extensive study of linearly forced isotropic
turbulence. By using an analytical method, we identified two parametric choices
that are new to our knowledge. We proved that the underlying nonlinear
dynamical system for linearly forced isotropic turbulence is the general case
of a cubic Lienard equation with linear damping (Dumortier and Rousseau 1990).Comment: 6 pages, 0 figure
A new class of exact solution of two-dimensional incompressible vortex motion
At present in the fluid mechanics, mostly one like to use the vortex as a
basic physical quantity, such that some exact solutions is based on the
vorticity evolution equation. For the vortex flow problem with axisymmetry, it
is well known that there exists in the circulation as a mechanical system of
basic physical quantities. In this paper, from the basic dynamic equation of
the mechanical system, the self-similar solution, eigenvalue system into a
self- consistent, new exact solutions of the two-dimensional circular symmetric
vortex flow are obtained, and some further comparison are made with the known
exact solutions. Key words: vortex motion, exact solution, eigenvalue systemComment: 6 pages, 0 figur
Logistic map and micro-structure of isotropic turbulent flow
ONE of the main goals in the development of theory of chaotic dynamical
system has been to make progress in understanding of turbulence. The attempts
to related turbulence to chaotic motion got strong impetus from the celebrated
paper by Ruelle and Takens . Considerable success has been achieved mainly in
the area: the onset of turbulence. For fully developed turbulence, many
questions remain unanswered. The aim of this letter is to show that there are
dynamical systems that are much simpler than the Navier-Stokes equations but
that can still have turbulent states and for which many concepts developed in
the theory of dynamical systems can be successfully applied. In this connection
we advocate a broader use of the universal properties of a wide range of
isotropic turbulence phenomena. Even for the case of fully developed
turbulence, which contains an extreme range of relevant length scales, it is
possible, by using the present model, to reproduce a surprising variety of
relevant features, such as multifractal cascade, intermittency. This letter
reverts to possible applications of the Navier-Stokes equations to studies of
the nature of turbulence.Comment: 8 pages, 7 figures, 1 tabl
Entropy and weak solutions in the LBGK model
In this paper, we derive entropy functions whose local equilibria are
suitable to recover the Euler-like equations in the framework of the Lattice
Boltzmann method. Numerical examples are also given, which are consistent with
the above theoretical arguments.Comment: 13pages,2 figure
Nonlinear dynamical systems and bistability in linearly forced isotropic turbulence
In this letter, we present an extensive study of the linearly forced
isotropic turbulence. By using analytical method, we identify two parametric
choices, of which they seem to be new as far as our knowledge goes. We prove
that the underlying nonlinear dynamical system for linearly forced isotropic
turbulence is the general case of a cubic Lienard equation with linear damping.
We also discuss a Fokker-Planck approach to this new dynamical system,which is
bistable and exhibits two asymmetric and asymptotically stable stationary
probability densities.Comment: 7 pages, 1 figur
Review and Update of the Compactified M/string Theory Prediction of the Higgs Boson Mass and Properties
The August 2011 Higgs mass prediction was based on an ongoing six year
project studying M-theory compactified on a manifold of G2 holonomy, with
significant contributions from Jing Shao, Eric Kuflik, and others, and
particularly co-led by Bobby Acharya and Piyush Kumar. The M-theory results
include: stabilization of all moduli in a de Sitter vacuum; gauge coupling
unification; derivation of TeV scale physics (solving the hierarchy problem);
the derivation that generically scalar masses are equal to the gravitino mass
which is larger than about 30 TeV; derivation of the Higgs mechanism via
radiative electroweak symmetry breaking; absence of the flavor and CP problems,
and the accommodation of string axions. tan beta and the mu parameter are part
of the theory and are approximately calculated; as a result, the little
hierarchy problem is greatly reduced. This paper summarizes the results
relevant to the Higgs mass prediction. A recent review describes the program
more broadly. Some of the results such as the scalar masses being equal to the
gravitino mass and larger than about 30 TeV, derived early in the program, hold
generically for compactified string theories as well as for compactified
M-theory, while some other results may or may not. If the world is described by
M-theory compactified on a G2 manifold and has a Higgs mechanism (so it could
be our world) then the Higgs mass was predicted to be 126 +/- 2 GeV before the
measurement. The derivation has some assumptions not related to the Higgs mass,
but involves no free parameters.Comment: 10 pages, 4 figures, Invited review for the International Journal of
Modern Physics
Probability Distribution of a Passive Scalar in Isotropic Turbulence
In this letter, we present developments of the Hamiltonian approach to
problems of the probability distribution for a passive scalar in isotropic
turbulence, and also considers specific applications of the modified
Prelle-Singer procedure to turbulence models. The following key questions are
discussed and solved: what is the general dynamical structure of the resulting
scale equation permitted by passive scalar turbulence models? What are the
general requirements of the relations between canonical variables and the
canonical variabes representation for turbulence by using canonical variables?
It is shown that the existence of the Haniltonian representation in turbulence
is a privilege of only turbulence systems for which the variational principle
of least action is impossible The master equation of the probability
distribution of a passive scalar in isotropic turbulence can also be deduced
explicitly.Comment: 7pages,0figure
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