Related papers: Equilibrium and nonequilibrium properties of Euler…
Deformation of material lines drives transport and dissipation in many industrial and natural flows. Here we report an exact Eulerian formula for the stretching rate of a material line, also known as the topological entropy, in a prototype…
We elaborate the statistical field theory of Turbulence suggested in the previous paper \cite{M20a}. We clarify and simplify the basic Energy pumping equation of that theory and study mathematical properties of singular field configuration…
The dynamics of the truncated Euler equations with helical initial conditions are studied. Transient energy and helicity cascades leading to Kraichnan helical absolute equilibrium at small scales are obtained for the first time. The results…
While it is well known that constant rotation induces linear dispersive effects in various fluid models, we study here its effect on long time nonlinear dynamics in the inviscid setting. More precisely, we investigate stability in the 3d…
Two-dimensional turbulence self-organizes through a process of energy accumulation at large scales, forming a coherent flow termed a condensate. We study the condensate in a model with local dynamics, the large-scale quasi-geostrophic…
Coherent vortices are often observed to persist for long times in turbulent 2D flows even at very high Reynolds numbers and are observed in experiments and computer simulations to potentially be asymptotically stable in a weak sense for the…
Singularity formation of the 3D incompressible Euler equations is known to be extremely challenging. In [18], Elgindi proved that the 3D axisymmetric Euler equations with no swirl and $C^{1,\alpha}$ initial velocity develops a finite time…
We consider the three-dimensional Euler equations in a domain with a free boundary with no surface tension. We assume that $u_0 \in H^{2.5+\delta }$ is such that $\mathrm{curl}\,u_0 \in H^{2+\delta }$ in an arbitrarily small neighborhood of…
This paper develops the geometry and analysis of the averaged Euler equations for ideal incompressible flow in domains in Euclidean space and on Riemannian manifolds, possibly with boundary. The averaged Euler equations involve a parameter…
The statistical properties of the $E \times B$ flux in different types of plasma turbulence simulations are investigated using probability density distribution functions (PDF). The physics included in the models ranges from two dimensional…
The dynamics of the two-dimensional (2D) state in driven tridimensional (3D) incompressible magnetohydrodynamic turbulence is investigated through high-resolution direct numerical simulations and in the presence of an external magnetic…
The Euler equations on a three-dimensional periodic domain have a family of shear flow steady states. We show that the linearised system around these steady states decomposes into subsystems equivalent to the linearisation of shear flows in…
We revisit, both numerically and analytically, the finite-time blowup of the infinite-energy solution of 3D Euler equations of stagnation-point-type introduced by Gibbon et al. (1999). By employing the method of mapping to regular systems,…
Direct and large eddy simulations of hydrodynamic and hydromagnetic turbulence have been performed in an attempt to isolate artifacts from real and possibly asymptotic features in the energy spectra. It is shown that in a hydrodynamic…
We analyse the scaling properties of the energy spectra in fully developed incompressible turbulence in forced, rotating fluids in three dimensions (3D), which are believed to be characterised by universal scaling exponents in the inertial…
We demonstrate the existence of smooth three-dimensional vector fields where the cross product between the vector field and its curl is balanced by the gradient of a smooth function, with toroidal level sets that are not invariant under…
We present results of large-scale three-dimensional simulations of supersonic Euler turbulence with the piecewise parabolic method and multiple grid resolutions up to 2048^3 points. Our numerical experiments describe non-magnetized driven…
Based upon the formalism of conformal field theory with a boundary, we give a description of the boundary effect on fully developed two dimensional turbulence. Exact one and two point velocity correlation functions and energy power spectrum…
An inviscid two-dimensional fluid model with nonlinear dispersion that arises simultaneously in coarse-grained descriptions of the dynamics of the Euler equation and in the description of non-Newtonian fluids of second grade is considered.…
We report results on the geometrical statistics of the vorticity vector obtained from experiments in electromagnetically forced rotating turbulence. A range of rotation rates $\Omega$ is considered, from non-rotating to rapidly rotating…