532.59 Numerical simulation of perturbation of two-layer liquid free surface by a point source localized in the lower layer

Nosov V. N. (Vernadsky Institute of Geochemistry and Analytical Chemistry, RAS), Savin A. S. (Bauman Moscow State Technical University)

LIQUID, POINT SOURCE, WAVES ON THE SURFACE OF THE LIQUID


doi: 10.18698/2309-3684-2019-3-113124


The paper considers a pulse point source in the lower layer of stratified fluid. An expression for the perturbation of its free surface is obtained. It is shown that two waves arise on the surface of the liquid, associated with the presence of a density jump in it. Examples of numerical calculations for real sea conditions are shown. The pulse point source is a model of elementary perturbation of the liquid medium depth, allowing a complete mathematical study in the framework of the approximation of small waves. This approximation is quite justified in cases of simulating real disturbance sources located at considerable depths, since these sources transmit a very weak signal to the sea surface. The main problem in such cases is the isolation of this signal from background noise, such as wind waves. The solution of the problem should be based on the results of mathematical modeling of sea surface disturbances by different sources in the depth of the marine environment. More complex models can be designed by considering real disturbances of the marine environment as some superpositions of model elementary disturbances from point pulse sources. Furthermore, a complete mathematical solution to the problem of a point pulse source gives an idea of the orders of the sea surface disturbance magnitudes, which creates the basis for obtaining various estimates of possible disturbances and therefore is of considerable interest in the development of requirements for sea surface remote sensing equipment.


Nesterov S.V., Shamayev A.S., Shamaev S.I. Metody, protsedury i sredstva aerkosmicheskoy komputernoy radiotomografii pripoverkhnostnykh oblastey Zemli [Methods, procedures and tools in aerospace computer radiotomography of the Earth surficial regions]. Moscow, Nauchnyy mir Publ., 1996, 272 p.
Lavrentyev M.A., Shabat B.V. Problemy gidrodinamiki i ikh matematicheskie modeli [Problems of hydrodynamics and their mathematical models]. Moscow, Nauka Publ., 1977, 407 p.
Milne-Thompson L. M. Theoretical hydrodynamics. London, Macmillan Publ., 1938, 552 p. [Milne-Thompson L. M. Teoreticheskaya gidrodinamika. Moscow, Mir Publ., 1964, 655 p.
Stepanyants Y.A., Sturova I.V., Teodorovich E.V. Linenaya teoriya generatsii poverkhnostnykh i vnutrennikh voln [Linear theory of generation of surface and internal waves]. In: Itogi nauki i tekhniki. Mekhanika zhidkosti i gaza [Outcomes of science and technology. Fluid mechanics]. Moscow, VINITI Publ., 1987, vol.21, pp.93–179.
Bulatov V.V., Vladimirov Yu.V. Vnutrennie gravitatsionnye volny v neodnorodnykh sredakh [Internal gravitational waves in inhomogeneous media]. Moscow, Nauka Publ., 2005, 195 p.
Bulatov V.V., Vladimirov Yu.V. Volny v stratifitsirovannykh sredakh [Waves in stratified media]. Moscow, Nauka Publ., 2015, 735 p.
Vladimirov I.Yu., Korchagin N.N., Doklady Akademii nauk — Proceedings of the Russian Academy of Sciences, 2011, vol.440, no.6, pp.826–829.
Cherkesov, L.V., Poverkhnostnye i vnutrennie volny [Surface and internal waves]. Kyiv, Naukova Dumka Publ., 1973, 248 p.
Landau L.D., Lifshitz E.M. Gidrodynamika [Hydrodynamics]. Moscow, Nauka Publ., 1986, 736 p.
Sretensky L.N. Teoriya volnovykh dvizheniy zhidkosti [The theory of wave motion of a liquid]. Moscow, Nauka Publ., 1977, 815 p.
Lavrentyev M.A., Shabat B.V. Metody teorii funktsiy kompleksnogo peremennogo [Methods of the theory of complex variable functions]. Moscow, Nauka Publ., 1987, 688 p.
Gradshteyn I.S., Ryzhik I.M. Tablitsy integralov, ryadov i proizvedeniy [Tables of integrals, sums, series and products]. Moscow, Nauka Publ., 1971, 1108 p.
Chowdhury R.G., Mandal B.N. Fluid Dynamics Research, 2006, vol.38, no.4, pp.224–240.
Lu D.Q., Dai S.Q. Archive of Applied Mechanics, 2006, vol.76, no.1–2, pp.49–63.
Lu D.Q., Dai S.Q. International Journal of Engineering Science, 2008, vol.46, no.11, pp.1183–1193.
Parkhomenko V.P. Matematicheskoe modelirovanie i chislennye menody — Mathematical Modeling and Computational Methods, 2015, no.1, pp.94–108.
Vladimirov I.Yu., Korchagin N.N., Savin A.S. Matematicheskoe modelirovanie i chislennye menody – Mathematical Modeling and Computational Methods, 2014, no.2, pp.62–76.
Vladimirov I.Yu., Korchagin N.N., Savin A.S. Matematicheskoe modelirovanie i chislennye menody — Mathematical Modeling and Computational Methods, 2014, no.4, pp.74–87.
Plusnin A. V. Matematicheskoe modelirovanie i chislennye menody — Mathematical Modeling and Computational Methods, 2014, no.2, pp.77–100.


Носов В.Н., Савин А.С. Численное моделирование возмущения свободной поверхности двухслойной жидкости точечным источником, локализованным в нижнем слое. Математическое моделирование и численные методы. 2019. № 3. с. 113–124.



Download article

Количество скачиваний: 61