Related papers: Probabilistic representation of helicity in viscou…
We have explored here the case of three-dimensional non-stationary flows of helical type for the incompressible couple stress fluid with given Bernoulli-function in the whole space (the Cauchy problem). In our presentation, the case of…
A method is proposed to estimate the velocity field of an unsteady flow using a limited number of flow measurements. The method is based on a non-linear low-dimensional model of the flow and on expanding the velocity field in terms of…
We analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space…
We prove local well-posedness in regular spaces and a Beale-Kato-Majda blow-up criterion for a recently derived stochastic model of the 3D Euler fluid equation for incompressible flow. This model describes incompressible fluid motions whose…
A recently introduced model describing -on a 1d lattice- the velocity field of a granular fluid is discussed in detail. The dynamics of the velocity field occurs through next-neighbours inelastic collisions which conserve momentum but…
In this paper, we investigate the global well-posedness of three-dimensional Navier-Stokes equations with horizontal viscosity under a special symmetric structure: helical symmetry. More precisely, by a revised Ladyzhenskaya-type inequality…
The effect of kinetic helicity (velocity--vorticity correlation) on turbulent momentum transport is investigated. The turbulent kinetic helicity (pseudoscalar) enters the Reynolds stress (mirrorsymmetric tensor) expression in the form of a…
Context. Magnetic helicity is an important quantity in studies of magnetized plasmas as it provides a measure of the geometrical complexity of the magnetic field in a given volume. A more detailed description of the spatial distribution of…
A diffuse-interface model that describes the dynamics of nonhomogeneous incompressible two-phase viscous flows is investigated in a bounded smooth domain in ${\mathbb R}^3.$ The dynamics of the state variables is described by the…
In the Eulerian approach, the motion of an incompressible fluid is usually described by the velocity field which is given by the Navier--Stokes system. The velocity field generates a flow in the space of volume-preserving diffeomorphisms.…
In this paper, we are interested in the dynamics of charged particles interacting with the incompressible viscous flow. More precisely, we consider the Vlasov-Poisson or Vlasov-Poisson-Fokker-Planck equation coupled with the incompressible…
In an inviscid and incompressible fluid in dimension 3, we prove the existence of several helical filaments, or vortex helices, collapsing into each others.
Chemin has shown that solutions of the Navier-Stokes equations in the plane for an incompressible fluid whose initial vorticity is bounded and lies in L^2 converge in the zero-viscosity limit in the L^2-norm to a solution of the Euler…
Following a restriction argument in the Euclidean space, we derive a geometric invariant formula for a possible viscosity operator for an incompressible fluid flow on an ellipsoid embedded in $\mathbb R^3$. We also give an asymptotic…
Vortex line and magnetic line representations are introduced for description of flows in ideal hydrodynamics and MHD, respectively. For incompressible fluids it is shown that the equations of motion for vorticity ${\bf \Omega}$ and magnetic…
Smoothed particle hydrodynamics is a particle-based, fully Lagrangian, method for fluid-flow simulations. In this work, fundamental concepts of the method are first briefly recalled. Then, we present a thorough comparison of three different…
Previous work has introduced scale-split energy density \psi for a given vector field B in order to quantify the field stochasticity S(t). Application to turbulent magnetic fields leads to the prediction that tangling magnetic field by…
We consider the interface problem between two incompressible and inviscid fluids in the presence of surface tension. Following the geometric approach of [Shatah,J.;Zeng,C. A priori estimates for Fluid Interface Problems. CPAM, vol.16, no.6,…
The paper deals with the existence and almost periodic homogenization of some model of generalized Navier-Stokes equations. We first establish an existence result for non-stationary Ladyzhenskaya equations with a given non constant density.…
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…