4,907 research outputs found
Derivation of Delay Equation Climate Models Using the Mori-Zwanzig Formalism
Models incorporating delay have been frequently used to understand climate
variability phenomena, but often the delay is introduced through an ad-hoc
physical reasoning, such as the propagation time of waves. In this paper, the
Mori-Zwanzig formalism is introduced as a way to systematically derive delay
models from systems of partial differential equations and hence provides a
better justification for using these delay-type models. The Mori-Zwanzig
technique gives a formal rewriting of the system using a projection onto a set
of resolved variables, where the rewritten system contains a memory term. The
computation of this memory term requires solving the orthogonal dynamics
equation, which represents the unresolved dynamics. For nonlinear systems, it
is often not possible to obtain an analytical solution to the orthogonal
dynamics and an approximate solution needs to be found. Here, we demonstrate
the Mori-Zwanzig technique for a two-strip model of the El Nino Southern
Oscillation (ENSO) and explore methods to solve the orthogonal dynamics. The
resulting nonlinear delay model contains an additional term compared to
previously proposed ad-hoc conceptual models. This new term leads to a larger
ENSO period, which is closer to that seen in observations.Comment: Submitted to Proceedings of the Royal Society A, 25 pages, 10 figure
Ultrashort filaments of light in weakly-ionized, optically-transparent media
Modern laser sources nowadays deliver ultrashort light pulses reaching few
cycles in duration, high energies beyond the Joule level and peak powers
exceeding several terawatt (TW). When such pulses propagate through
optically-transparent media, they first self-focus in space and grow in
intensity, until they generate a tenuous plasma by photo-ionization. For free
electron densities and beam intensities below their breakdown limits, these
pulses evolve as self-guided objects, resulting from successive equilibria
between the Kerr focusing process, the chromatic dispersion of the medium, and
the defocusing action of the electron plasma. Discovered one decade ago, this
self-channeling mechanism reveals a new physics, widely extending the frontiers
of nonlinear optics. Implications include long-distance propagation of TW beams
in the atmosphere, supercontinuum emission, pulse shortening as well as
high-order harmonic generation. This review presents the landmarks of the
10-odd-year progress in this field. Particular emphasis is laid to the
theoretical modeling of the propagation equations, whose physical ingredients
are discussed from numerical simulations. Differences between femtosecond
pulses propagating in gaseous or condensed materials are underlined. Attention
is also paid to the multifilamentation instability of broad, powerful beams,
breaking up the energy distribution into small-scale cells along the optical
path. The robustness of the resulting filaments in adverse weathers, their
large conical emission exploited for multipollutant remote sensing, nonlinear
spectroscopy, and the possibility to guide electric discharges in air are
finally addressed on the basis of experimental results.Comment: 50 pages, 38 figure
Triple cascade behaviour in QG and drift turbulence and generation of zonal jets
We study quasigeostrophic (QG) and plasma drift turbulence within the Charney-Hasegawa-Mima (CHM) model. We focus on the zonostrophy, an extra invariant in the CHM model, and on its role in the formation of zonal jets. We use a generalized Fjørtoft argument for the energy, enstrophy, and zonostrophy and show that they cascade anisotropically into nonintersecting sectors in k space with the energy cascading towards large zonal scales. Using direct numerical simulations of the CHM equation, we show that zonostrophy is well conserved, and the three invariants cascade as predicted by the Fjørtoft argument
Extreme sensitivity and climate tipping points
A climate state close to a tipping point will have a degenerate linear
response to perturbations, which can be associated with extreme values of the
equilibrium climate sensitivity (ECS). In this paper we contrast linearized
(`instantaneous') with fully nonlinear geometric (`two-point') notions of ECS,
in both presence and absence of tipping points. For a stochastic energy balance
model of the global mean surface temperature with two stable regimes, we
confirm that tipping events cause the appearance of extremes in both notions of
ECS. Moreover, multiple regimes with different mean sensitivities are visible
in the two-point ECS. We confirm some of our findings in a physics-based
multi-box model of the climate system.Comment: 11 figure
Magnetic Flux Transport at the Solar Surface
After emerging to the solar surface, the Sun's magnetic field displays a
complex and intricate evolution. The evolution of the surface field is
important for several reasons. One is that the surface field, and its dynamics,
sets the boundary condition for the coronal and heliospheric magnetic fields.
Another is that the surface evolution gives us insight into the dynamo process.
In particular, it plays an essential role in the Babcock-Leighton model of the
solar dynamo. Describing this evolution is the aim of the surface flux
transport model. The model starts from the emergence of magnetic bipoles.
Thereafter, the model is based on the induction equation and the fact that
after emergence the magnetic field is observed to evolve as if it were purely
radial. The induction equation then describes how the surface flows --
differential rotation, meridional circulation, granular, supergranular flows,
and active region inflows -- determine the evolution of the field (now taken to
be purely radial). In this paper, we review the modeling of the various
processes that determine the evolution of the surface field. We restrict our
attention to their role in the surface flux transport model. We also discuss
the success of the model and some of the results that have been obtained using
this model.Comment: 39 pages, 15 figures, accepted for publication in Space Sci. Re
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