arxiv: 1101.2193 · v2 · pith:I22Z2P5Mnew · submitted 2011-01-11 · 🧮 math.AP · math-ph· math.MP· physics.flu-dyn

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

R. Dascaliuc , Z. Grujic This is my paper

classification 🧮 math.AP math-phmath.MPphysics.flu-dyn

keywords energyfluxscalesconditionequationslocalitynavier-stokesobtained

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

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