We revisit the issue of whether thermal fluctuations are relevant for incompressible fluid
turbulence and estimate the scale at which they become important. As anticipated by …

The high-order statistics of fluctuations in velocity gradients in the crossover range from the
inertial to the Kolmogorov and sub-Kolmogorov scales are studied by direct numerical …

Intermittency is one of the central obstacles for understanding small-scale dynamics in the
fully developed hydrodynamic turbulence. The modern approach is largely based on the …

The dispute on whether the three-dimensional (3D) incompressible Euler equations develop
an infinitely large vorticity in a finite time (blowup) keeps increasing due to ambiguous …

Turbulent flows frequently accompany physical, chemical and biological processes, such as
mixing, two-phase flow, combustion and even foraging by bacteria and plankton larvae, all …

We construct semi-integral curves which bound the projection of the global attractor of the 2-
D Navier–Stokes equations in the plane spanned by enstrophy and palinstrophy. Of …

We provide an observation suggesting a strong correlation between helicity and enstrophy
in fluid turbulence. Helicity statistics were obtained in a direct numerical simulation of forced …

A systematic study of the influence of the viscous effect on both the spectra and the
nonlinear fluxes of conserved as well as nonconserved quantities in Navier–Stokes …

We revisit the issue of whether thermal fluctuations are relevant for incompressible fluid
turbulence, and estimate the scale at which they become important. As anticipated by …

Exponential integrators are explicit methods for solving ordinary differential equations that
treat linear behaviour exactly. The stiff-order conditions for exponential integrators derived in …