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
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
SN - 0010-3616
VL - 290
SP - 679
EP - 717
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 2
ER -