On the description of non-equilibrium transport processes and formation of dynamic structures in liquid media

Abstract

The paper discusses the problems associated with the description of the complicated motions of liquid media, which are accompanied by a multi-scale complex of non-equilibrium processes, including relaxation and inertial effects. The approach is based on the nonlocal theory of non-equilibrium transport processes using the methods of cybernetical physics, which allows one to go beyond the limits of continuum mechanics, to describe the self-organization and evolution of dynamic vortex-wave structures during non-equilibrium momentum transport in a liquid. In the framework of this approach, an algorithm is proposed for determining the scale spectrum of dynamic structures formed in non-equilibrium fluid flows due to the conditions imposed on the system by actions from the side of its environment. The temporal evolution of the flow is described using the Speed Gradient principle developed in the control theory of adaptive systems. The control parameters are the average sizes of the dynamic structure of the liquid medium, and the goal function is determined by the maximum entropy that the system can produce under the constraints imposed on it. In this case, feedback is formed between the structural evolution of the system and the dynamics of the flow, which stabilizes the flow regime. Without taking them into account, the evolution of dynamic structures can lead to various types of instabilities and a change in the flow regime. An example is the high-speed Rayleigh flow, where it is shown that, due to the transition to a turbulent regime, the liquid minimizes irreversible loss of mechanical energy.