193 research outputs found
Entropy production and multiple equilibria: the case of the ice-albedo feedback
Nonlinear feedbacks in the Earth System provide mechanisms that can prove
very useful in understanding complex dynamics with relatively simple concepts.
For example, the temperature and the ice cover of the planet are linked in a
positive feedback which gives birth to multiple equilibria for some values of
the solar constant: fully ice-covered Earth, ice-free Earth and an intermediate
unstable solution. In this study, we show an analogy between a classical
dynamical system approach to this problem and a Maximum Entropy Production
(MEP) principle view, and we suggest a glimpse on how to reconcile MEP with the
time evolution of a variable. It enables us in particular to resolve the
question of the stability of the entropy production maxima. We also compare the
surface heat flux obtained with MEP and with the bulk-aerodynamic formula.Comment: 29 pages, 12 figure
Statistical optimization for passive scalar transport: maximum entropy production vs maximum Kolmogorov-Sinay entropy
We derive rigorous results on the link between the principle of maximum
entropy production and the principle of maximum Kolmogorov-Sinai entropy using
a Markov model of the passive scalar diffusion called the Zero Range Process.
We show analytically that both the entropy production and the Kolmogorov-Sinai
entropy seen as functions of f admit a unique maximum denoted fmaxEP and
fmaxKS. The behavior of these two maxima is explored as a function of the
system disequilibrium and the system resolution N. The main result of this
article is that fmaxEP and fmaxKS have the same Taylor expansion at _rst order
in the deviation of equilibrium. We find that fmaxEP hardly depends on N
whereas fmaxKS depends strongly on N. In particular, for a fixed difference of
potential between the reservoirs, fmaxEP (N) tends towards a non-zero value,
while fmaxKS (N) tends to 0 when N goes to infinity. For values of N typical of
that adopted by Paltridge and climatologists we show that fmaxEP and fmaxKS
coincide even far from equilibrium. Finally, we show that one can find an
optimal resolution N_ such that fmaxEP and fmaxKS coincide, at least up to a
second order parameter proportional to the non-equilibrium uxes imposed to the
boundaries.Comment: Nonlinear Processes in Geophysics (2015
Phase transitions and marginal ensemble equivalence for freely evolving flows on a rotating sphere
The large-scale circulation of planetary atmospheres like that of the Earth
is traditionally thought of in a dynamical framework. Here, we apply the
statistical mechanics theory of turbulent flows to a simplified model of the
global atmosphere, the quasi-geostrophic model, leading to non-trivial
equilibria. Depending on a few global parameters, the structure of the flow may
be either a solid-body rotation (zonal flow) or a dipole. A second order phase
transition occurs between these two phases, with associated spontaneous
symmetry-breaking in the dipole phase. This model allows us to go beyond the
general theory of marginal ensemble equivalence through the notion of Goldstone
modes.Comment: 7 pages, 3 figures; accepted for publication in Physical Review
Last Glacial Maximum CO2 and δ13C successfully reconciled
During the Last Glacial Maximum (LGM, ∼21,000 years ago) the cold climate was strongly tied to low atmospheric CO2 concentration (∼190 ppm). Although it is generally assumed that this low CO2 was due to an expansion of the oceanic carbon reservoir, simulating the glacial level has remained a challenge especially with the additional δ13C constraint. Indeed the LGM carbon cycle was also characterized by a modern-like δ13C in the atmosphere and a higher surface to deep Atlantic δ13C gradient indicating probable changes in the thermohaline circulation. Here we show with a model of intermediate complexity, that adding three oceanic mechanisms: brine induced stratification, stratification-dependant diffusion and iron fertilization to the standard glacial simulation (which includes sea level drop, temperature change, carbonate compensation and terrestrial carbon release) decreases CO2 down to the glacial value of ∼190 ppm and simultaneously matches glacial atmospheric and oceanic δ13C inferred from proxy data. LGM CO2 and δ13C can at last be successfully reconciled
Modelling and numerical simulation of plasma flows with two-fluid mixing
13 pagesFor the modelling of plasma flows at very high temperature such the ones produced by laser beams, one must account for a bi-temperature compressible Euler system coupled to electron thermal conduction and radiative conduction. Moreover, mixing of two different fluids can occur, the two fluids occupying the same volume. For modelling such a phenomenon, instead of dealing with the conservation of mass, momentum and energy for each fluid, we propose here a simplified model which will be easier to implement in a multi-physics Lagrangian 2D code. The principle is to use a closure for expressing the relative velocity between the two fluids with the help of the gradient of the concentration. So, besides the classical system, the final model consists in a non-linear diffusion equation for the concentration and an equation for the mixing kinetic energy (analogous to the one used in turbulence models). We present also first numerical 2D simulations using this model
Statistical mechanics of quasi-geostrophic flows on a rotating sphere
Statistical mechanics provides an elegant explanation to the appearance of
coherent structures in two-dimensional inviscid turbulence: while the
fine-grained vorticity field, described by the Euler equation, becomes more and
more filamented through time, its dynamical evolution is constrained by some
global conservation laws (energy, Casimir invariants). As a consequence, the
coarse-grained vorticity field can be predicted through standard statistical
mechanics arguments (relying on the Hamiltonian structure of the
two-dimensional Euler flow), for any given set of the integral constraints.
It has been suggested that the theory applies equally well to geophysical
turbulence; specifically in the case of the quasi-geostrophic equations, with
potential vorticity playing the role of the advected quantity. In this study,
we demonstrate analytically that the Miller-Robert-Sommeria theory leads to
non-trivial statistical equilibria for quasi-geostrophic flows on a rotating
sphere, with or without bottom topography. We first consider flows without
bottom topography and with an infinite Rossby deformation radius, with and
without conservation of angular momentum. When the conservation of angular
momentum is taken into account, we report a case of second order phase
transition associated with spontaneous symmetry breaking. In a second step, we
treat the general case of a flow with an arbitrary bottom topography and a
finite Rossby deformation radius. Previous studies were restricted to flows in
a planar domain with fixed or periodic boundary conditions with a beta-effect.
In these different cases, we are able to classify the statistical equilibria
for the large-scale flow through their sole macroscopic features. We build the
phase diagrams of the system and discuss the relations of the various
statistical ensembles.Comment: 48 pages, 16 figures. Accepted for publication in Journal of
Statistical Mechanics: Theory and Experimen
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