TY - JOUR

T1 - On the helicity in 3D-periodic Navier-stokes equations II

T2 - The statistical case

AU - Foias, Ciprian

AU - Hoang, Luan

AU - Nicolaenko, Basil

N1 - Copyright:
Copyright 2009 Elsevier B.V., All rights reserved.

PY - 2009/7

Y1 - 2009/7

N2 - We study the asymptotic behavior of the statistical solutions to the Navier-Stokes equations using the normalization map [9]. It is then applied to the study of mean energy, mean dissipation rate of energy, and mean helicity of the spatial periodic flows driven by potential body forces. The statistical distribution of the asymptotic Beltrami flows are also investigated. We connect our mathematical analysis with the empirical theory of decaying turbulence. With appropriate mathematically defined ensemble averages, the Kolmogorov universal features are shown to be transient in time. We provide an estimate for the time interval in which those features may still be present.

AB - We study the asymptotic behavior of the statistical solutions to the Navier-Stokes equations using the normalization map [9]. It is then applied to the study of mean energy, mean dissipation rate of energy, and mean helicity of the spatial periodic flows driven by potential body forces. The statistical distribution of the asymptotic Beltrami flows are also investigated. We connect our mathematical analysis with the empirical theory of decaying turbulence. With appropriate mathematically defined ensemble averages, the Kolmogorov universal features are shown to be transient in time. We provide an estimate for the time interval in which those features may still be present.

UR - http://www.scopus.com/inward/record.url?scp=70350635678&partnerID=8YFLogxK

U2 - 10.1007/s00220-009-0827-z

DO - 10.1007/s00220-009-0827-z

M3 - Article

AN - SCOPUS:70350635678

VL - 290

SP - 679

EP - 717

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -