21st Century COE Lecture
Edriss S. Titi
Date : 
March 25 (Thu), 2004, 15:0016:30

Place : 
Room 115, RIMS

Lecturer: 
Edriss S. Titi
(Dept. of Math., Univ. of California, Irvine)

Title : 
The NavierStokesalpha models and Turbulence Theory

Abstract: 
In this talk we will show the global wellposedness of the three dimensional
NavierStokesalpha model (also known as a viscous CamassaHolm equations
or the Lagrangian Averaged NavierStokes equations (LANS)).
The dimension of its global attractor will be esitmated and shown
to be comparable with the number of degrees of freedom suggested by
classical theory of turbulence. We will present semirigorous arguments
showing that up to a certain wave number, in the inertial range,
the translational energy power specturm obeys the Kolmogorov power
law for the energy decay of the three dimensional turbulent flow.
However, for the rest the inertial range the energy spectrum of this
model obeys the Kraichnan power law for the energy decay
of the two dimensional turbulent follows. This observation makes the
NavierStokesalpha model more computable than the NavierStokes
equations. Furthermore, we will show that by using the
NavierStokesalpha model as a closure model to the Reynolds averaged
equations of the NavierStokes one gets very good agreement with
empirical and numerical data of turbulent flows in infinite pipes and
channels. We observe that similar results hold also to other
turbulence models: the Lerayalpha and the Clark models.


