ar X iv : m at h - ph / 0 50 70 44 v 1 1 8 Ju l 2 00 5 Remarks on the K 41 scaling law in turbulent fluids
نویسندگان
چکیده
A definition of K41 scaling law for suitable families of measures is given and investigated. First, a number of necessary conditions are proved. They imply the absence of scaling laws for 2D stochastic Navier-Stokes equations and for the stochastic Stokes (linear) problem in any dimension, while they imply a lower bound on the mean vortex stretching in 3D. Second, for 3D stochastic Navier-Stokes equations necessary and sufficient conditions for K41 are proved, translating the problem into bounds for energy and enstrophy of high and low modes respectively. The validity of such conditions in 3D remains open. Finally, a stochastic vortex model with such properties is presented.
منابع مشابه
ar X iv : m at h - ph / 0 60 70 40 v 1 2 0 Ju l 2 00 6 Invariant Form of BK - factorization and its Applications
متن کامل
ar X iv : m at h - ph / 0 50 70 42 v 1 1 7 Ju l 2 00 5 Polygamma theory , the Li / Keiper constants , and
The Riemann hypothesis is equivalent to the Li criterion governing a sequence of real constants {λk}k=1, that are certain logarithmic derivatives of the Riemann xi function evaluated at unity. We investigate a related set of constants cn, n = 1, 2, . . ., showing in detail that the leading behaviour (1/2) ln n of λn/n is absent in cn. Additional results are presented, including a novel explicit...
متن کاملar X iv : m at h - ph / 0 00 20 29 v 2 1 6 Fe b 20 00 A Note on the Intermediate Region in Turbulent Boundary Layers
We demonstrate that the processing of the experimental data for the average velocity profiles obtained by J. M. ¨ Osterlund (www.mesh.kth.se/∼jens/zpg/) presented in [ 1 ] was incorrect. Properly processed these data lead to the opposite conclusion: they confirm the Reynolds-number-dependent scaling law and disprove the conclusion that the flow in the intermediate ('overlap') region is Reynolds...
متن کامل