Inscrição na biblioteca: Guest
Portal Digital Begell Biblioteca digital da Begell eBooks Diários Referências e Anais Coleções de pesquisa
International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.5

ISSN Imprimir: 2152-5102
ISSN On-line: 2152-5110

Volume 46, 2019 Volume 45, 2018 Volume 44, 2017 Volume 43, 2016 Volume 42, 2015 Volume 41, 2014 Volume 40, 2013 Volume 39, 2012 Volume 38, 2011 Volume 37, 2010 Volume 36, 2009 Volume 35, 2008 Volume 34, 2007 Volume 33, 2006 Volume 32, 2005 Volume 31, 2004 Volume 30, 2003 Volume 29, 2002 Volume 28, 2001 Volume 27, 2000 Volume 26, 1999 Volume 25, 1998 Volume 24, 1997 Volume 23, 1996 Volume 22, 1995

International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v46.i4.20
pages 295-308


N. S. Gorodetska
Institute of Hydromechanics of National Academy of Sciences of Ukraine, 8/4, Zhelyabov St., Kyiv, 03057, Ukraine
T. M. Shcherbak
National Transport University of Ukraine, 1, M. Omelianovycha-Pavlenka St., Kyiv, 01010, Ukraine
V. I. Nikishov
Institute of Hydromechanics of National Academy of Sciences of Ukraine, 8/4, Zhelyabov St., Kyiv, 03057, Ukraine


The paper considers a 2D linear problem on scattering of the low-amplitude surface wave in an incompressible fluid that propagates over the bottom obstacle in form of a vertical rectangular wall of the finite of infinitesimal length. The bottoms of the channel and obstacle walls are absolutely rigid. The solution is found by the method of partial domains implying the subdivision of the complex geometry of the overall domain of wave field existence into the subdomains of canonical shapes. This approach allows the formal representing of the corresponding general solutions as the series with respect to eigenfunctions satisfying part of the boundary conditions in each subdomain. The unknown coefficients present in these general solutions may be found from matching conditions that postulate continuity of pressure and normal velocity fields at the boundaries of adjacent subdomains. Applying algebraization procedure to matching conditions for the corresponding general solutions leads to generation of infinite systems of linear equations with respect to the unknown coefficients. The obtained systems possess slow convergence that is determined by the presence of velocity singularities in angular points of the obstacle. To accelerate the convergence, the method of improved reduction is applied in analyzing the infinite systems. It is based on the a priori hypotheses about the asymptotic behavior of the unknown coefficients in general solutions that is controlled by the order of field singularity in the vicinity of the corresponding angular point. The dependence of calculated energy discrepancy on the amount of considered terms in the reduced system is assessed. The method of improved reduction is shown to provide the better convergence quality at moderate number of kept terms (50 to 70), in comparison with the ordinary reduction. The use of the improved reduction also leads to some widening of the region for which the numerical error remains within acceptable limits.


  1. Abul-Azm, A.G., Wave Diffraction through Submerged Breakwater, J. Waterway, Port, Coast., Ocean Eng., vol. 119, no. 6, pp. 587-605,1993.

  2. Abul-Azm, A.G., Diffraction through Wide Submerged Breakwater under Oblique Waves, Ocean Eng., vol. 21, no. 7, pp. 683-706, 1994.

  3. Bartholomeusz, E.F., The Reflexion of Long Waves at a Step, Math. Proc. Cambridge Philos. Soc., vol. 54, no. 1, pp. 106-118, 1958.

  4. Bender, Ch.J. and Dean, R.G., Wave Transformation by Two-Dimensional Bathymetric Anomalies with Sloped Transitions, Coast. Eng., vol. 50, pp. 61-84,2003.

  5. Chakraborty, R. and Mandal, B.N., Water Wave Scattering by a Rectangular Trench, J. Eng. Math., vol. 89, pp. 101-112,2014.

  6. Dalrymple, R.A. and Martin, P.A., Wave Diffraction through Offshore Breakwaters, J. Waterway, Port, Coast., Ocean Eng., vol. 116, no. 6, pp. 727-741,1990.

  7. Dean, R.G. and Dalrymple, R.A., Water Wave Mechanics for Engineers and Scientists, Singapore: World Scientific, 1991.

  8. Grinchenko, V.T. and Gorodetska, N.S., Features of Energy Transformation in an Elastic Waveguide with an Insert at its Forced Vibrations, Acoustic Bulletin, vol. 8, no. 3, pp. 34-43,2005 (in Russian).

  9. Grinchenko, V.T. and Ulitko, A.P., On the Local Features in the Mathematical Models of Physical Fields, Mathemat. Methods Physicomechan. Fields, vol. 41, no. 1, pp. 12-34,1998 (in Russian).

  10. Grinchenko, V.T., Vovk, I.V., and Matsipura, V.T., Wave Problems of Acoustics, Kiev: Interservis, 2013 (in Russian).

  11. Hudspeth, R.T., Waves and Wave Forces on Coastal and Ocean Structures, Singapore: World Scientific, 2006.

  12. Kanoria, M., Dolai, D.P., and Mandal, B.N., Water-Wave Scattering by Thick Vertical Barriers, J. Eng. Math, vol. 35, pp. 361-384, 1999.

  13. Kirby, J.T. and Dalrymple, R.A., Propagation of Obliquely Incident Water Waves over a Trench, J. Fluid Mech, vol. 133, pp. 47.

  14. Lee, J.-J. and Ayer, R.M., Wave Propagation over a Rectangular Trench, J. Fluid Mech., vol. 110, pp. 335-347,1981.

  15. Linton, C.M. and McIver, P., Handbook of Mathematical Techniques for Wave/Structure Interactions, New York, NY: Chapman & Hull/CRC, 2001.

  16. Losada, I.J., Losada, M.A., and Roldan, A.J., Propagation of Oblique Incident Waves past Rigid Vertical Thin Barriers, Appl. Ocean Res, vol. 14, pp. 191-199,1992.

  17. Mandal, B.N. and De, S., Water Wave Scattering, Boca Raton, FL: CRC Press, 2015.

  18. McIver, P., Scattering of Water Waves by Two Surface-Piercing Vertical Barriers, IMA J. Appl. Math., vol. 35, pp. 339-355,1985.

  19. Mei, C.C. and Black, J., Scattering of Surface Waves by Rectangular Obstacle in Water of Finite Depth, J. Fluid Mech., vol. 38, no. 3, pp. 499-511,1969.

  20. Mei, C.C., Stiassnie, M., and Yue, D.K.-P., Theory and Applications of Ocean Surface Waves, Singapore: World Scientific, 2005.

  21. Miles, J.W., Surface-Wave Scattering Matrix for a Shelf, J. Fluid Mech, vol. 28, no. 4, pp. 755-767,1967.

  22. Mobaraken, P.S. and Grinchenko, V.T., Construction Method of Analytical Solutions to the Mathematical Physics Boundary Problems for Non-Canonical Domains, Rep. Math. Phys, vol. 75, no. 3, pp. 417-436,2015.

  23. Newman, J.N., Propagation of Water Waves over an Infinite Step, J. Fluid Mech, vol. 23, no. 2, pp. 399-415,1965.

  24. Newman, J.N., Propagation of Water Waves past Long Two-Dimensional Obstacles, J. Fluid Mech., vol. 23, no. 1, pp. 23-29, 1965.

  25. Porter, R. and Evans, D.V., Complementary Approximations to Wave Scattering by Vertical Barriers, J. Fluid Mech., vol. 294, pp. 155-180,1995.

  26. Sneddon, I.N., Mixed Boundary Value Problems in Potential Theory, Amsterdam: North-Holland, 1966.

  27. Takano, K., Effets d'un Obstacle Parailelepipedique sur la Propagation de la Houle, La Houille Blanche, no. 3, pp. 247-267,1960.

  28. Takano, K. and Nakazawa, H., Effets d'un Obstacle de Parallelepipedique Rectangle sur la Propagation de la Houle, J. Oceanogr. Soc. Japan, vol. 22, no. 5, pp. 1-9,1966.

  29. Xie, J.-J., Liu, H.-W., and Liu, P., Analytical Solution for Long-Wave Reflection by a Rectangular Obstacle with Two Scour Trenches, J. Eng. Mech, vol. 137, no. 12, pp. 919-930,2011.

Articles with similar content:

Investigation of Stationary Convective Flows in a Cylindrical Domain by the Galerkin Method
Journal of Automation and Information Sciences, Vol.37, 2005, issue 8
Nikolay N. Salnikov
Telecommunications and Radio Engineering, Vol.69, 2010, issue 8
T. M. Ahmedov, E. I. Veliev, M. V. Ivakhnichenko
Investigation of Parametric Iterative Processes for Solving Nonlinear Equations
Journal of Automation and Information Sciences, Vol.32, 2000, issue 1
Mikhail Ya. Bartish, Stepan M. Shakhno
Shanwu Wang, Nan Zong, Vigor Yang
Algorithms and the Multiplicative Complexity of the Modulo Arbitrary Polynomial Reduction of the Generalised KN-convolution and of the Fast Vandermonde Transform
Telecommunications and Radio Engineering, Vol.54, 2000, issue 11&12
Aleksandr Mikhaylovich Krot