Long gravity waves in a canal with a corrugated bottom in the asymptotic description

• Autorzy: Bielski Włodzimierz , Wojnar Ryszard

Identyfikatory

DOI

10.15632/jtam-pl/138855

• Języki publikacji: EN

Abstrakty

EN

We consider the classic Lagrange long gravitational wave of a homogeneous incompressible fluid in a shallow canal with a corrugated bottom. We use the asymptotic expansion method to find the effective depth of a one-dimensional canal and, hence, the effective wave velocity. A flow in a two-dimensional tank with a corrugated bottom is also studied by this method.

Słowa kluczowe

EN

bottom profiles; homogenization approach; effective depth

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2021
• Tom: Vol. 59 nr 3
• Strony: 443–--454
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Bielski Włodzimierz

• Institute of Geophysics, Polish Academy of Sciences, Warsaw, Poland

• https://orcid.org/0000-0003-1708-3546

autor

Wojnar Ryszard

• Institute of Fundamental Technological Research, PAS, Warsaw, Poland

Bibliografia

• 1. Adler P.M., Malevich A.E., Mityushev V.V., 2013, Nonlinear correction to Darcy’s law for channels with wavy walls, Acta Mechanica, 224, 8, 1823-1848.
• 2. Andrianov I.V., Awrejcewicz J., Danishevskyy V.V., 2018, Asymptotical Mechanics of Composites: Modelling Composites without FEM, Springer International Publishing AG, Cham.
• 3. Bakhvalov N.S., Panasenko G.P., 1989, Homogenisation: Averaging Processes in Periodic Media: Mathematical Problems in the Mechanics of Composite Materials, Kluwer, Dordrecht-Boston-London.
• 4. Bensoussan A., Lions J.-L., Papanicolaou G., 1980, Asymptotic Analysis of Periodic Structures, North Holland Publishing Company, Amsterdam-New York-Oxford.
• 5. Dingemans M.W., 1997, Water Wave Propagation Over Uneven Bottoms, Part 1 – Basic Equations, Part 2 – Wave propagation formulation, Advanced Series on Ocean Engineering: Vol. 13, World Scientific, Delft.
• 6. Evangelos K., 2012, The impact of vegetation on the characteristics of the flow in an inclined open channel using the piv method, Water Resources and Ocean Science, 1, 1, 1-6.
• 7. Gill A.E., 1982, Gravity wave, Atmosphere Ocean Dynamics, Academic Press.
• 8. Karaeva D.A., Karaev A.D., Nazaikinskii V.E., 2018, Homogenization method in the problem of long wave propagation from a localized source in a basin over an uneven bottom, Differential Equations, 54, 8, 1057-1072.
• 9. Kubrak E., Kubrak J., Rowiński P.M., 2013, Application of one-dimensional model to calculate water velocity distributions over elastic elements simulating Canadian waterweed plants (Elodea canadensis), Acta Geophysica, 61, 1, 194-210.
• 10. Lagrange J.-L., 1781, Mémoire sur la théorie du mouvement des fluides, Nouveaux mémoires de l’Académie royale des sciences et belles-lettres de Berlin, année 1781, also: Oéuvres complétes, tome 4, 695-748.
• 11. Lamb H., 1916, Hydrodynamics, 4th ed., University Press, Cambridge.
• 12. Landau L.D., Lifshitz E.M., 1987, Fluid Mechanics, transl. by J.B. Sykes and W.H. Reid, 2nd ed., Pergamon Press, Oxford-New York.
• 13. Lighthill J., 2001, Waves in Fluids, Cambridge University Press.
• 14. Malevich A.E., Mityushev V.V., Adler P.M., 2006, Stokes flow through a channel with wavy walls, Acta Mechanica, 182, 3-4, 151-182.
• 15. Mei C.C., Stiassnie M., Yue D.K.-P., 2005, Theory and Applications of Ocean Surface Waves, Advanced Series on Ocean Engineering, World Scientific, Singapore, 1136 pp.
• 16. Mei C.C., Vernescu B., 2010, Homogenization Methods for Multiscale Mechanics, World Scientific Publishers, New Jersey-London-Singapore-Beijing-Shanghai-Hong Kong-Taipei-Chennai.
• 17. Nappo C.J., 2012, An Introduction to Atmospheric Gravity Waves, 2nd ed. Waltham, Elsevier Academic Press, Massachusetts.
• 18. Popescu I., 2014, Computational Hydraulics – Numerical Methods and Modelling, IWA Publishing Alliance House, London.
• 19. Sanchez-Palencia E., 1980, Non-homogeneous Media and Vibration Theory, Springer Verlag, Berlin, Heidelberg, New York.
• 20. Telega J.J., Bielski W., 2003, Flow in random porous media: effective models, Computers and Geotechnics, 30, 4, 271-288.
• 21. Wojnar R., Bielski W., 2014, Flow in the canal with plants on the bottom, [In:] Complex Analysis and Potential Theory with Applications, T. Aliev Azerogly, A. Golberg, S.V. Rogosin (Edit.), Cambridge Scientific Publishers, 167-183.

Uwagi

„Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).”