Direct and Inverse Problems of Dynamics of Surface Waves Caused by Flow around Underwater Obstacle

D. Yu. Knyazkov; Князьков Д. Ю.; V. G. Baydulov; Байдулов В. Г.; A. S. Savin; Савин А. С.; A. S. Shamaev; Шамаев А. С.

doi:10.31857/S0032823523030074

Direct and Inverse Problems of Dynamics of Surface Waves Caused by Flow around Underwater Obstacle

Authors: Knyazkov D.Y.¹, Baydulov V.G.¹, Savin A.S.², Shamaev A.S.¹
Affiliations:
1. Ishlinsky Institute for Problems in Mechanics of the RAS
2. Bauman Moscow State Technical University
Issue: Vol 87, No 3 (2023)
Pages: 442-453
Section: Articles
URL: https://journals.rcsi.science/0032-8235/article/view/138870
DOI: https://doi.org/10.31857/S0032823523030074
EDN: https://elibrary.ru/ZTOFFW
ID: 138870

Cite item

Full Text

Open Access
Restricted Access

Access granted
Restricted Access

Subscription Access

Abstract
About the authors
References
Supplementary files
Statistics

Abstract

The paper presents algorithms and results of calculations of the dynamics of the surface layer of a liquid under the action of currents that have emerged from the depth. Several approaches to modeling the velocity field in a horizontal flow round a fixed underwater obstacle are investigated. Formulas for calculating the velocity field on the free surface of an ideal homogeneous liquid are proposed. A computer program has been developed that makes it possible to simulate the interaction of a stratified fluid flow with an underwater obstacle. The possibility of using asymptotic formulas for the far-field approximation to calculate the velocity field in a uniformly stratified fluid is studied.

Keywords

stratified fluid, ideal fluid, flow around, velocity field, surface wave

References

Nesterov S.V., Shamaev A.S., Shamaev S.I. Methods, Algorithms and Means of Aerospace Computed Tomography of the Near-Surface Layer of the Earth. Moscow: Nauchnyi Mir, 1996. 272 p. (in Russian)
Gavrikov A., Knyazkov D., Romanova A., Chernik V., Shamaev A. Simulation of influence of the surface disturbance on the ocean self radiation spectrum // Progr. Syst.: Theory&Appl., 2016, vol. 7, iss. 2. pp. 73–84. https://doi.org/10.25209/2079-3316-2016-7-2-73-84
Bulatov M.G., Kravtsov Yu.A. Lavrova O.Yu. et al. Physical mechanisms of aerospace radar imaging of the ocean // Phys. Usp., 2003, vol. 46, no. 1, pp. 63–79.
Jackson C.R., da Silva J.C.B., Jeans G. et al. Nonlinear internal waves in synthetic aperture radar imagery // Oceanogr., 2013, vol. 26, no. 2, pp. 68–79.
Baydulov V.G., Knyazkov D., Shamaev A.S. Motion of mass source in stratified fluid // J. Phys.: Conf. Ser., 2021, vol. 2224, 2nd Int. Symp. on Automation, Information and Computing (ISAIC 2021) 03/12/2021–06/12/2021 Online. pp. 012038.
Ulaby F.T., Moore R.K., Fung A.K. Microwave Remote Sensing. Active and Passive. Massachusetts: Addison-Wesley Pub., 1981. 456 p.
Knyazkov D. Web-interface for HPC computation of a plane wave diffraction on a periodic layer // Lobachevskii J. Math., 2017, vol. 38, no. 5, pp. 936–939.
Knyazkov D. Diffraction of plane wave at 3-dimensional periodic layer // AIP Conf. Proc., 2018, vol. 1978, pp. 470075-1-4. https://doi.org/10.1063/1.5044145
Baydulov V.G. On the solution of the inverse problem of the motion of a source in a stratified fluid // in: Proc. 12th Int. Conf. – School of Young Sci. Waves and Vortices in Complex Media. Moscow, Dec. 01–03, 2021. Moscow: ISPOPrint, 2021. S. 31–35.
Matyushin P.V. Process of the formation of internal waves initiated by the start of motion of a body in a stratified viscous fluid // Fluid Dyn., 2019, vol. 54, no. 3, pp. 374–388. https://doi.org/10.1134/S0015462819020095
Voisin B. Internal wave generation in uniformly stratified fluids. Pt. 2. Moving point sources // J. Fluid Mech., 1994, vol. 261, pp. 333–374.
Voisin B. Lee waves from a sphere in a stratified flow // J. Fluid Mech., 2007, vol. 574, pp. 273–315.
Scase M.M., Dalziel S.B. Internal wave fields and drag generated by a translating body in a stratified fluid // J. Fluid Mech., 2004, vol. 498, pp. 289–313.
Scase M.M., Dalziel S.B. Internal wave fields generated by a translating body in a stratified fluid: an experim ental comparison // J. Fluid Mech., 2006, vol. 564, pp. 305–331.
Loitsyanskii L.G. Mechanics of Liquids and Gases. Oxford: Pergamon, 1966. 803 p.
Sretenskii L.N. Theory of Wave Motions in a Fluid. Moscow: Nauka, 1977. 816 p. (in Russian)
Gorelov A.M., Nosov V.N., Savin A.S. et al. Method of calculating surface disturbances over a point source and a dipole // Fluid Dyn., 2009, vol. 44, no. 1, pp. 170–174. https://doi.org/10.1134/S0015462809010177
Bulatov V.V., Vladimirov Yu.V. A General Approach to Ocean Wave Dynamics Research: Modelling, Asymptotics, Measurements. Moscow: OntoPrint, 2019. 587 p.
Galassi M., Davies J., Theiler J. et al. GNU Scientific Library Reference Manual (3rd Ed.). Network Theory Ltd., 2009. 592 p.
Saad Y., Schultz M.H. GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems // SIAM J. on Sci.&Statist. Comput., 1986, vol. 7, no. 3, pp. 856–869.
Chashechkin Y., Gumennik E., Sysoeva E. Transformation of a density field by a three-dimensional body moving in a continuously stratified fluid // J. Appl. Mech.&Tech. Phys., 1995, vol. 36, pp. 19–29.