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

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.

preprint2011arXivOpen access
R. DascaliucZ. Grujic
math.APmath-phmath.MPphysics.flu-dyn
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R. DascaliucZ. Grujic

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