The Problem of Large Local Fluctuations Appearance

The question of the appearance of fluctuations of physical quantities is considered on the basis of a hydrodynamic model. A possible mechanism for the formation of large fluctuations is discussed in the framework of a hydrodynamic model based on the Burgers equation. Solutions of the Burgers equation in a complex-valued space are considered. A transformation to a system of differential equations of the first order is carried out with a further study of the behavior of the system's solutions on the entire set of fixed points. An analysis is made of two different cases of system behavior for different values of the divergence of the vector field of the original system. The case of the occurrence of turbulence in a system with perturbations having a different type of solution is considered in more detail - in the form of a solitary wave, in the form of a switching wave, and in the form of a wave packet with many oscillations. A bifurcation mechanism for the appearance of turbulence is considered, based on two hypotheses - Landau's hypothesis and the hypothesis of strange attractors. It is shown that there are critical values of physical quantities at which their small fluctuations can generate large local fluctuations, which can be another mechanism for the appearance of dynamic chaos. #CSOC1120. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.