St-Petersburg State University Research Institute of Physics Faculty of Physics High Energy and Elementary Particles Physics
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Fully  developed hydrodynamical turbulence
is  a  special  state  of  fluids,  described by
interesting  and  universal laws. In particular,
correlation  functions  of  the velocity exhibit
scaling   behaviour   with   infinite   set   of
"anomalous  exponents."  Theoretical description
of  that  phenomenon on the basis of a dynamical
micromodel  remains an open problem. Recently it
was  solved  for  a related problem of turbulent
advection  of  a  scalar  field  (temperature or
impurity)  by  a  velocity field with prescribed
Gaussian  statistics  (Obukhov-Kraichnan model).
In  our  approach, the key role is played by the
field-theoretic methods of renormalization group
and    operator-product   expansion,   and   the
anomalous exponents are identified with negative
scaling  dimensions  of certain composite fields
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March 2009