Related papers: Compressible helical turbulence: Fastened-structur…
A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the velocity vector is orthogonal to the gradient of the…
A simplified thermodynamic approach of the incompressible axisymmetric Euler equations is considered based on the conservation of helicity, angular momentum and microscopic energy. Statistical equilibrium states are obtained by maximizing…
A model of fully developed turbulence of a compressible fluid is briefly reviewed. It is assumed that fluid dynamics is governed by a stochastic version of Navier-Stokes equation. We show how corresponding field theoretic-model can be…
Percolation theory is usually applied to lattices with a uniform probability p that a site is occupied or that a bond is closed. The more general case, where p is a function of the position x, has received less attention. Previous studies…
This work deals with a number of questions relative to the discrete and continuous adjoint fields associated with the compressible Euler equations and classical aerodynamic functions. The consistency of the discrete adjoint equations with…
We study the phenomenon of turbulence from the point of view of statistical physics. We discuss what makes the turbulent states different from the thermodynamic equilibrium and give the turbulent analog of the partition function. Then,…
Homological equations of tensor type associated to periodic flows on a manifold are studied. The Cushman intrinsic formula is generalized to the case of multivector fields and differential forms. Some applications to normal forms and the…
The appearance of a geometric flow in the conservation law of particle number in classical particle diffusion and in the conservation law of probability in quantum mechanics is discussed in the geometrical environment of a two-dimensional…
We investigate the turbulence-induced dissipation of the large scales in a statistically homogeneous flow using an "optimal closure," which one of us (BT) has recently exposed in the context of Hamiltonian dynamics. This statistical closure…
In a helical flow there is a subrange of the inertial range in which there is a cascade of both energy and helicity. In this range the scaling exponents associated with the cascade of helicity can be defined. These scaling exponents are…
We present hydrodynamic equations of compressible fluids in gravity as a generalization of those in the Boussinesq approximation used for nearly incompressible fluids. They account for adiabatic processes taking place throughout the cell…
These lecture notes present an overview of equilibrium statistical mechanics of classical fluids, with special applications to the structural and thermodynamic properties of systems made of particles interacting via the hard-sphere…
We consider compressible fluid flow on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ both an energetic variational approach and the first law of thermodynamics to make a…
Helicity, a measure of the breakage of reflectional symmetry representing the topology of turbulent flows, contributes in a crucial way to their dynamics and to their fundamental statistical properties. We review several of their main…
We derive the exact relation for the energy transfer in three-dimensional compressible two-fluid plasma turbulence. In the long-time limit, we obtain an exact law which expresses the scale-to-scale average energy flux rate in terms of two…
Continuum modelling of granular flow has been plagued with the issue of ill-posed equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation,…
Tropical convective clouds evolve over a wide range of temporal and spatial scales, and this makes them difficult to simulate numerically. Here, we propose that their statistical properties can be derived within a simplified…
The uniform shear flow for the rarefied gas is governed by the time-dependent spatially homogeneous Boltzmann equation with a linear shear force. The main feature of such flow is that the temperature may increase in time due to the shearing…
The theory of mesoscopic fluctuations is applied to inhomogeneous solids consisting of chaotically distributed regions with different crystalline structure. This approach makes it possible to describe statistical properties of such mixture…
The probability density function (PDF) of the gas density in turbulent supersonic flows is investigated with high-resolution numerical simulations. In a systematic study, we compare the density statistics of compressible turbulence driven…