RESEARCH DEPARTMENT OF VORTEX MOTIONS

     FROM THE HISTORY OF DEPARTMENT

     The Department of Vortex Motion was established in 1990. From the moment of its formation until 1994, it was managed by Doctor of Physical and Mathematical Sciences Prof. V.V.Meleshko. Since 1994, the department has been headed by Doctor of Physical and Mathematical Sciences O.G.Stetsenko. Currently, the department is headed by Doctor of Physical and Mathematical Sciences Prof. Tatyana Sigizmundivna Krasnopolskaya.

     RESEARCH ACTIVITIES

     The research activity of the department is related to the description of the most common vortex movements in nature, the study of which is of extreme importance for solving many scientific and technical problems. The first one is related to the dynamics of the interaction of vortex structures in the process of mixing fluids in physical systems when disturbances are introduced into the distribution of various types of scalar fields in the area of fluid motion. The most famous in the scientific world are the results of research on the movement of microfluid in a microchannel, which uses the method of superposition and solution of the problem found by the researchers from the department.

     The main scientific results obtained in the department are related to:

• studying the regularities of mixing processes in the velocity field with different spatial and temporal scales given by the system of wave structures in an ideal incompressible fluid, and developing effective numerical models that provide results adequate to reality;
• disclosing features of regular and chaotic regimes of movement of cross-waves in pools of finite dimensions, as well as developing research methods for chaotic steady regimes;
• experimental studies and theoretical analysis with numerical calculations to describe the basic regularities of the dynamics of cross-waves in rectangular basins of finite dimensions;
• proving the existence and identifying parameters of chaotic oscillation modes of cross-shaped surface waves in a rectangular basin of finite dimensions with and without delay;
• developing mathematical models of the excitation of cross-shaped surface waves in "singing glasses" when they emit sound waves;
• determining the parameters of stable modes and establishing theoretical models for describing the excitation of cross-shaped surface waves in "singing glasses";
• determining eigenfrequencies and stability criteria, Lyapunov exponents based on the developed method of increasing the accuracy of the Benettin numerical algorithm for estimating the senior Lyapunov exponent.

     The application of the basic apparatus of the modern theory of complex dynamic systems with chaotic dynamics allows for determining the regularities of steady modes of generation of cross-waves in pools of finite dimensions. The laboratory base of the department includes large and small experimental trays with a complex of measuring equipment providing experimental studies of wave motion.

     The photographs show experiments in a rectangular pool with the wall moving back and forth and the appearance of cross-waves on the side surface across the pool width.

 Trace of cross-shaped waves on the pool wall.

     Some results were obtained in cooperation with foreign scientific centers in the USA, the Netherlands, and Italy and during the implementation of international projects and contracts.

     From 1990 to 2024, the department's employees wrote three scientific monographs and more than 230 articles, a significant part of which was published in prestigious foreign journals.