Energy cascades and flux locality in physical scales of the 3D Navier-Stokes equations

Details Energy cascades and flux locality in physical scales of the 3D Navier-Stokes equations Energy cascades and flux locality in physical scales of the 3D Navier-Stokes equations

2011-01-11

arxiv.org/abs/1101.2193v2

Mathematics

Analysis of PDEs

21 pages, 2 figures; accepted to Comm. Math. Phys

Scientific paper

Rigorous estimates for the total - (kinetic) energy plus pressure - flux in R^3 are obtained from the three dimensional Navier-Stokes equations. The bounds are used to establish a condition - involving Taylor length scale and the size of the domain - sufficient for existence of the inertial range and the energy cascade in decaying turbulence (zero driving force, non-increasing global energy). Several manifestations of the locality of the flux under this condition are obtained. All the scales involved are actual physical scales in R^3 and no regularity or homogeneity/scaling assumptions are made.

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