Main field of study: 011200 Physics
Area of specialization: Statistical Theory of Inhomogeneous Media
Department of Statistical Physics
Scientific advisor: ph. D., prof. L.Ts. Adzhemyan
Reviewer: ph. D., prof. N.V. Antonov

The principle of maximum randomness in the theory of developed turbulence: A model with maximum parity violation
Kulikov Anatoly

In the present work we apply methods of quantum field theory and statistical physics to the theory of developed homogeneous isotropic turbulence. Considered model is based on the principle of maximum randomness of velocity field with fixed mean energy spectral flux. Model with a maximum violation of parity, similar to considered in the theory of weak interactions, is presented. Diagram technique and closed set of equations for parameters of the model, allowing one to determine an important experimental value – Kolmogorov constant, is constructed using set of self-consistent equations. Analytical expressions for one-loop 1-irreducible diagrams of the model are obtained by means of computer calculation. Solution found of the closed set of equations yields Kolmogorov index of the velocity fields correlator power dependence on the wave number.
Ultraviolet divergences of 2-loop diagrams of the model were analyzed. The existence of anomalous scaling (small shift from Kolmogorov index) is demonstrated. Analytical expressions for the leading order of the expansion over the small parameter of two-loop 1-irreducible diagrams of the model are obtained by means of computer calculation. Through analyzing self-consistent equations in two-loop approximation the values of anomalous scaling and Kolmogorov constant are obtained.

The list of the publications:
1.	A.B. Kulikov, L.Ts. Adzhemyan. Spontaneous parity violation in theory of developed turbulence: multiloop approximation // Book of abstracts, International Youth Conference «PhysicA.SPb» (Saint Petersburg, 28-30 october 2014).
2.	A.B. Kulikov. Spontaneous parity violation in the theory of developed turbulence // Book of abstracts, XIX International Conference of Young Scientists (Dubna, 16-20 February, 2015).