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The detailed dynamics of the JuneâAugust Hadley Cell
The seminal theory for the Hadley Cells has demonstrated that their existence is necessary for the reduction of tropical temperature gradients to a value such that the implied zonal winds are realisable. At the heart of the theory is the notion of angular momentum conservation in the upper branch of the Hadley Cells. Eddy mixing associated with extraâtropical systems is invoked to give continuity at the edge of the Hadley Cell and to reduce the subtropical jet by a factor of 3 or more to those observed. In this paper a detailed view is presented of the dynamics of the JuneâAugust Hadley Cell, as given by ERA data for the period 1981â2010, with an emphasis on the dynamics of the upper branch. The steady and transient northward fluxes of angular momentum have a very similar structure, both having a maximum on the equator and a reversal in sign near 12°S, with the transient flux merging into that associated with eddies on the winter subâtropical jet. In the northward absolute vorticity flux, the Coriolis torque is balanced by both the steady and transient fluxes. The overturning circulations that average to give the Hadley Cell are confined to specific longitudinal regions, as are the steady and transient momentum fluxes. In these regions, both intraâseasonal and synoptic variations are important. The dominant contributor to the Hadley Cell is from the Indian Ocean and W Pacific regions, and the maxima in OLR variability and meridional wind in these regions have a characteristic structure associated with the Westwardâmoving Mixed RossbyâGravity wave. Much of the upper tropospheric motion into the winter hemisphere occurs in filaments of air from the summer equatorial region. These filaments can reach the winter subâtropical jet, leading to the strengthening of it and of the eddies on it, implying strong tropicalâextratropical interaction
Asymmetric Squares as Standing Waves in Rayleigh-Benard Convection
Possibility of asymmetric square convection is investigated numerically using
a few mode Lorenz-like model for thermal convection in Boussinesq fluids
confined between two stress free and conducting flat boundaries. For relatively
large value of Rayleigh number, the stationary rolls become unstable and
asymmetric squares appear as standing waves at the onset of secondary
instability. Asymmetric squares, two dimensional rolls and again asymmetric
squares with their corners shifted by half a wavelength form a stable limit
cycle.Comment: 8 pages, 7 figure
On the importance of nonlinear modeling in computer performance prediction
Computers are nonlinear dynamical systems that exhibit complex and sometimes
even chaotic behavior. The models used in the computer systems community,
however, are linear. This paper is an exploration of that disconnect: when
linear models are adequate for predicting computer performance and when they
are not. Specifically, we build linear and nonlinear models of the processor
load of an Intel i7-based computer as it executes a range of different
programs. We then use those models to predict the processor loads forward in
time and compare those forecasts to the true continuations of the time seriesComment: Appeared in "Proceedings of the 12th International Symposium on
Intelligent Data Analysis
Galerkin Method in the Gravitational Collapse: a Dynamical System Approach
We study the general dynamics of the spherically symmetric gravitational
collapse of a massless scalar field. We apply the Galerkin projection method to
transform a system of partial differential equations into a set of ordinary
differential equations for modal coefficients, after a convenient truncation
procedure, largely applied to problems of turbulence. In the present case, we
have generated a finite dynamical system that reproduces the essential features
of the dynamics of the gravitational collapse, even for a lower order of
truncation. Each initial condition in the space of modal coefficients
corresponds to a well definite spatial distribution of scalar field. Numerical
experiments with the dynamical system show that depending on the strength of
the scalar field packet, the formation of black-holes or the dispersion of the
scalar field leaving behind flat spacetime are the two main outcomes. We also
found numerical evidence that between both asymptotic states, there is a
critical solution represented by a limit cycle in the modal space with period
.Comment: 9 pages, revtex4, 10 ps figures; Phys. Rev. D, in pres
A model for interacting instabilities and texture dynamics of patterns
A simple model to study interacting instabilities and textures of resulting
patterns for thermal convection is presented. The model consisting of
twelve-mode dynamical system derived for periodic square lattice describes
convective patterns in the form of stripes and patchwork quilt. The interaction
between stationary zig-zag stripes and standing patchwork quilt pattern leads
to spatiotemporal patterns of twisted patchwork quilt. Textures of these
patterns, which depend strongly on Prandtl number, are investigated numerically
using the model. The model also shows an interesting possibility of a
multicritical point, where stability boundaries of four different structures
meet.Comment: 4 pages including 4 figures, page width revise
Symmetry justification of Lorenz' maximum simplification
In 1960 Edward Lorenz (1917-2008) published a pioneering work on the `maximum
simplification' of the barotropic vorticity equation. He derived a coupled
three-mode system and interpreted it as the minimum core of large-scale fluid
mechanics on a `finite but unbounded' domain. The model was obtained in a
heuristic way, without giving a rigorous justification for the chosen selection
of modes. In this paper, it is shown that one can legitimate Lorenz' choice by
using symmetry transformations of the spectral form of the vorticity equation.
The Lorenz three-mode model arises as the final step in a hierarchy of models
constructed via the component reduction by means of symmetries. In this sense,
the Lorenz model is indeed the `maximum simplification' of the vorticity
equation.Comment: 8 pages, minor correction
Lorenz-like systems and classical dynamical equations with memory forcing: a new point of view for singling out the origin of chaos
A novel view for the emergence of chaos in Lorenz-like systems is presented.
For such purpose, the Lorenz problem is reformulated in a classical mechanical
form and it turns out to be equivalent to the problem of a damped and forced
one dimensional motion of a particle in a two-well potential, with a forcing
term depending on the ``memory'' of the particle past motion. The dynamics of
the original Lorenz system in the new particle phase space can then be
rewritten in terms of an one-dimensional first-exit-time problem. The emergence
of chaos turns out to be due to the discontinuous solutions of the
transcendental equation ruling the time for the particle to cross the
intermediate potential wall. The whole problem is tackled analytically deriving
a piecewise linearized Lorenz-like system which preserves all the essential
properties of the original model.Comment: 48 pages, 25 figure
Noise Can Reduce Disorder in Chaotic Dynamics
We evoke the idea of representation of the chaotic attractor by the set of
unstable periodic orbits and disclose a novel noise-induced ordering
phenomenon. For long unstable periodic orbits forming the strange attractor the
weights (or natural measure) is generally highly inhomogeneous over the set,
either diminishing or enhancing the contribution of these orbits into system
dynamics. We show analytically and numerically a weak noise to reduce this
inhomogeneity and, additionally to obvious perturbing impact, make a
regularizing influence on the chaotic dynamics. This universal effect is rooted
into the nature of deterministic chaos.Comment: 11 pages, 5 figure
On the Hyperbolicity of Lorenz Renormalization
We consider infinitely renormalizable Lorenz maps with real critical exponent
and combinatorial type which is monotone and satisfies a long return
condition. For these combinatorial types we prove the existence of periodic
points of the renormalization operator, and that each map in the limit set of
renormalization has an associated unstable manifold. An unstable manifold
defines a family of Lorenz maps and we prove that each infinitely
renormalizable combinatorial type (satisfying the above conditions) has a
unique representative within such a family. We also prove that each infinitely
renormalizable map has no wandering intervals and that the closure of the
forward orbits of its critical values is a Cantor attractor of measure zero.Comment: 63 pages; 10 figure
On the recurrence and robust properties of Lorenz'63 model
Lie-Poisson structure of the Lorenz'63 system gives a physical insight on its
dynamical and statistical behavior considering the evolution of the associated
Casimir functions. We study the invariant density and other recurrence features
of a Markov expanding Lorenz-like map of the interval arising in the analysis
of the predictability of the extreme values reached by particular physical
observables evolving in time under the Lorenz'63 dynamics with the classical
set of parameters. Moreover, we prove the statistical stability of such an
invariant measure. This will allow us to further characterize the SRB measure
of the system.Comment: 44 pages, 7 figures, revised version accepted for pubblicatio
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