The practice of using the fourier transform in processing the results of mathematical modeling of the hydrodynamics of getaways

• Published in: Journal of physics. Conference series 2021-12, Vol.2131 (3), p.32029
• Main Authors: Lipatov, I, Molchanova, M, Lebedev, O
• Format: Article
• Language: English
• ISSN: 1742-6588; 1742-6596
• DOI: 10.1088/1742-6596/2131/3/032029

The article deals with the actual aspects of practical mathematical modeling of hydro-dynamic processes in the chambers of navigational locks. The use of direct and inverse Fourier transforms has been tested to obtain the representations of non-stationary graphs acceptable for analysis. Cross-sections of the water flow filling the chamber of a typical lock in the Volga-Don shipping channel were used as reference data (VDSC). The control sections in the flow were selected with a qualitatively different hydrodynamic nature of motion. A two-dimensional array of non-stationary data results were decomposed into Fourier series. The resulting graph of the amplitude-frequency spectrum was analyzed by the harmonics forming it. Its amplitude was taken as the criterion for the harmonics’ selection. After zeroing the insignificant harmonics, the inverse Fourier transform was performed. The quality of the data array approximation was controlled by visual overlay of the original graphs on the processed one. In all cases, it was possible to obtain the acceptable approximation results. This created a reliable basis for the scientific analysis and development of engineering measures for the implementation of safe ship passage through gateways. At the end of the article, a number of the data processing specific features are presented, caused by a variety of hydrodynamic features of the flow in various sections.