ИСТИНА

https://igafd.sciencesconf.org/ Differential fluid mechanics Yuli D Chashechkin Laboratory of Fluid Mechanics A.Yu.Ishlinskiy Institute for Problems in Mechanics of the RAS 101/1 prospect Vernadskogo Moscow 119526, Russia The system of equations of a state and for the conservation of matter, momentum, energy and concentration of matter with physically justified boundary conditions on solid walls and a free surface analyzed taking into account the compatibility condition determining its rank and the order of the linearized version. In a media with a weak dissipation, the complete solution of the linearized system includes regularly and singularly perturbed functions that describe dynamics, global and fine structure of flows. Some effects of non-linearity leading to generation of new components were analyzed. The constructed solutions of the theory of internal wave problems agree with the data of numerical solutions of the complete set and laboratory experiments on the generation of periodic or attached waves and patterns of flow around obstacles. Limiting cases and extrapolations on the environment are discussed. Reference Chashechkin Yu. D. Differential fluid mechanics – harmonization of analytical, numerical and laboratory models of flows. // Mathematical Modeling and Optimization of Complex Structures. Springer Series “Computational Methods in Applied Sciences” V. 40. 2016. P. 61-91. DOI: 10.1007/978-3-319-23564-6-5 Kistovich A. V. and Chashechkin Yu. D. Fine Structure of a Conical Beam of Periodical Internal Waves in a Stratified Fluid // Izvestiya, Atmospheric and Oceanic Physics, 2014, Vol. 50, No. 1, pp. 103–110. Kalinichenko V.A., Soe A.N., Chashechkin Yu.D. Circulation Flow Patterns in the Faraday Waves in the Presence of Damper Plates // Fluid Dynamics, 2016, Vol. 51, No. 5, pp. 639–646. DOI: 10.1134/S0015462816050082