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A parametrization of two-dimensional turbulence based on a maximum entropy production principle with a local conservation of energy
Pierre-Henri Chavanis
In the context of two-dimensional (2D) turbulence, we apply the maximum entropy production principle (MEPP) by enforcing a local conservation of energy. This leads to an equation f…
Statistical mechanics of two-dimensional point vortices: relaxation equations and strong mixing limit
Pierre-Henri Chavanis
We complete the literature on the statistical mechanics of point vortices in two-dimensional hydrodynamics. Using a maximum entropy principle, we determine the multi-species Boltzm…
Supernovae: an example of complexity in the physics of compressible fluids
Yves Pomeau, Martine Le Berre, Pierre-Henri Chavanis +1
The supernovae are typical complex phenomena in fluid mechanics with very different time scales. We describe them in the light of catastrophe theory, assuming that successive equil…
Phase transitions and marginal ensemble equivalence for freely evolving flows on a rotating sphere
Corentin Herbert, Bérengère Dubrulle, Pierre-Henri Chavanis +1
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…
Statistical mechanics of Fofonoff flows in an oceanic basin
A. Naso, P. H. Chavanis, B. Dubrulle
We study the minimization of potential enstrophy at fixed circulation and energy in an oceanic basin with arbitrary topography. For illustration, we consider a rectangular basin an…
Statistical mechanics of Beltrami flows in axisymmetric geometry: Equilibria and bifurcations
Aurore Naso, Simon Thalabard, Gilles Collette +2
We characterize the thermodynamical equilibrium states of axisymmetric Euler-Beltrami flows. They have the form of coherent structures presenting one or several cells. We find the…
Statistical mechanics of Beltrami flows in axisymmetric geometry: Theory reexamined
Aurore Naso, Romain Monchaux, Pierre-Henri Chavanis +1
A simplified thermodynamic approach of the incompressible axisymmetric Euler equations is considered based on the conservation of helicity, angular momentum and microscopic energy.…
Statistical mechanics of two-dimensional Euler flows and minimum enstrophy states
A. Naso, P. H. Chavanis, B. Dubrulle
A simplified thermodynamic approach of the incompressible 2D Euler equation is considered based on the conservation of energy, circulation and microscopic enstrophy. Statistical eq…
Relaxation equations for two-dimensional turbulent flows with a prior vorticity distribution
P. H. Chavanis, A. Naso, B. Dubrulle
Using a Maximum Entropy Production Principle (MEPP), we derive a new type of relaxation equations for two-dimensional turbulent flows in the case where a prior vorticity distributi…
Statistical mechanics of 2D turbulence with a prior vorticity distribution
Pierre-Henri Chavanis
We adapt the formalism of the statistical theory of 2D turbulence in the case where the Casimir constraints are replaced by the specification of a prior vorticity distribution. A p…
Fluctuation-Dissipation Relations and statistical temperatures in a turbulent von Kármán flow
Romain Monchaux, Pierre-Philippe Cortet, Pierre-Henri Chavanis +4
We experimentally characterize the fluctuations of the non-homogeneous non-isotropic turbulence in an axisymmetric von Kármán flow. We show that these fluctuations satisfy relation…
Statistical mechanics of the shallow-water system with a prior potential vorticity distribution
P. H. Chavanis, B. Dubrulle
We adapt the statistical mechanics of the shallow-water equations to the case where the flow is forced at small scales. We assume that the statistics of forcing is encoded in a pri…
Statistical mechanics of 2D turbulence with a prior vorticity distribution
P. H. Chavanis
We adapt the formalism of the statistical theory of 2D turbulence in the case where the Casimir constraints are replaced by the specification of a prior vorticity distribution. A n…
Dynamics and thermodynamics of axisymmetric flows: I. Theory
Nicolas Leprovost, Bérengère Dubrulle, Pierre-Henri Chavanis
We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that the…
Thermodynamics of MHD flows with axial symmetry
Nicolas Leprovost, Pierre-Henri Chavanis, Berengere Dubrulle
We present strategies based upon extremization principles, in the case of the axisymmetric equations of magnetohydrodynamics (MHD). We study the equilibrium shape by using a minimu…
Statistical mechanics of the shallow water system
P. H. Chavanis, J. Sommeria
We extend the formalism of the statistical theory developed for the 2D Euler equation to the case of shallow water system. Relaxation equations towards the maximum entropy state ar…
Quasilinear theory of the 2D Euler equation
Pierre-Henri Chavanis
We develop a quasilinear theory of the 2D Euler equation and derive an integro-differential equation for the evolution of the coarse-grained vorticity. This equation respects all t…