Elements of the theory of local similarity of hydrodynamic phenomena and the selection of optimal parameters for a wave attenuator with a vortex well based on this theory

by

A.E. Shchodro1, Yu.E. Shishkin1,2

1Institute of Natural and Technical Systems, RF, Sevastopol, Lenin St., 28

2Sevastopol State University, RF, Sevastopol, Universitetskaya St., 33

E-mail: ashodro@ya.ru

DOI: 10.33075/2220-5861-2026-1-53-61

UDC 532.54                          

EDN: https://elibrary.ru/oubiov

Abstract:     

The paper introduces the concept of local similarity of hydrodynamic processes and phenomena based on the general concept of similarity of mechanical systems formulated by Academician M. V. Kirpichev and K. Konakov (1949). Different approaches to similarity analysis are examined. Three levels of locality of similarity are considered. The first level is locality in which, near a certain segment of the flow-domain boundary, hydrodynamic processes of the same type should be observed, with their gradual attenuation or transition to other processes as the distance from this region increases. The second level concerns local similarity of hydrodynamic systems in a generalized coordinate system where, in addition to the spatial coordinates x, y, z and time t, essential (control) parameters of the system are also chosen as independent coordinates. The third, most significant level is when the similarity of processes in a local region is described by a mathematical structure that admits a certain Lie group and the corresponding Lie algebra. On the basis of this theory, conclusions were drawn regarding the optimal parameter values of a wave attenuator with a vortex well–swirler (VKZ).

Keywords: vortex well, bed sediments, rational parameters, Lie groups and Lie algebras, systems of hydrodynamic equations

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