R. Dascaliuc

Coherent Vortex Structures and 3D Enstrophy Cascade

Existence of 2D enstrophy cascade in a suitable mathematical setting, and under suitable conditions compatible with 2D turbulence phenomenology, is known both in the Fourier and in the physical scales. The goal of this paper is to show that the same geometric condition preventing the formation of singularities –

Energy Cascades and Flux Locality in Physical Scales of the 3D Navier-Stokes Equations

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Anomalous Dissipation and Energy Cascade in 3D Inviscid Flows

-Hölder coherence of the vorticity direction – coupled with a suitable condition on a modified Kraichnan scale, and under a certain modulation assumption on evolution of the vorticity, leads to existence of 3D enstrophy cascade in physical scales of the flow.

Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations.

A mathematical evidence—in a statistically significant sense—of a geometric scenario leading to criticality of the Navier-Stokes problem is presented.

On Energy Cascades in the Forced 3D Navier–Stokes Equations

Rigorous estimates for the total – (kinetic) energy plus pressure – flux in

Estimates on enstrophy, palinstrophy, and invariant measures for 2-D turbulence ✩

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