Quantum field renormalization group in the theory of fully developed turbulence
L.T. Adzhemyan a
N.V. Antonov a
A.N. Vasil’ev a, b, c
a Department of Theoretical Physics, Institute of Physics, St. Petersburg State University, ul. Ulyanovskaya 1, Petrodvorez, St. Petersburg, 198904, Russian Federation
b Lomonosov Moscow State University, Vorobevy Gory, Moscow, 119991, Russian Federation
c Lomonosov Moscow State University, Department of Physics, Leninskie Gory 1 build. 2, Moscow, 119991, Russian Federation
Quantum field renormalisation group results of the theory of developed turbulence are reviewed. Background information about quantum field renormalisation theory, including operator expansion and the renormalisation of composite operators is given. As an example problem, the stochastic model of isotropic homogeneous turbulence is considered for which, using the renormalisation technique, the existence of infrared scaling with Kholmogorov dimensions is proved. The dimension of composite operators and the infrared asymptotic behaviour of various correlation functions are discussed, and numerical amplitude factors of scaling laws are calculated.