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Warianty tytułu
Języki publikacji
Abstrakty
The paper concerns the non-linear problem of description of shallow-water waves of finite amplitude. The description is based on the conservation-law formulation, which seems to be particularly convenient in constructing an approximate solution of the problem considered. The analysis is confined to the one-dimensional case of waves propagating in water of constant depth. In the model considered, vertical acceleration of the fluid is taken into account, and thus, the fundamental equations of the problem are similar to those given by Boussinesq (Abbott 1979). The equations differ from those frequently used in shallow-water hydrodynamics which are based on the assumption of hydrostatic pressure. An approximate solution of the problem is constructed by means of a perturbation scheme with the third order expansion of the equations with respect to a small parameter. It is demonstrated that the solution procedure may be successfully applied only within a certain range of the two ratios defining wave height to water depth and the depth to wave length, respectively.
Słowa kluczowe
Rocznik
Tom
Strony
269--285
Opis fizyczny
Bibliogr. 16 poz., il.
Twórcy
autor
- Institute of Hydro-Engineering of the Polish Academy of Sciences, ul. Waryńskiego 17, 71-310 Szczecin, Poland, jks@hydros.ibwpan.szczecin.pl
Bibliografia
- Abbot M. B. (1979), Computational Hydraulics — Elements of the Theory of Free Surface Flows, Pitman Publishing Limited, London.
- Abbott M. B., McCowan A. D. and Warren I. R. (1984), Accuracy of Short-wave Numerical Models, J. Hydraulic Engineering, Vol. 110, No. 10, 1287-1301.
- Abbott M. B., Petersen H. M. and Skovgaard (1978), On the Numerical Modelling of Short Waves in Shallow Water, J. Hydraulic Research, 16, No. 3, 173-203.
- Ambrosi D. (1995), Approximation of Shallow Water Equations by Roe's Riemann Solver, Int. J. for Numerical Methods in Fluids, Vol. 20, 157-168.
- Jha A. K., Akiyama J. and Ura M. (2000), Flux-difference Splitting Schemes for 2D Flood Flows, J. Hydraulic Engineering, 33-42.
- Madsen P. A., Murray R. and Sorensen 0. R. (1991), A New Form of the Boussinesq Equations with Improved Linear Dispersion Characteristics, Coastal Engineering, 15, 371-388.
- Mei C. C. (1983), The Applied Dynamics of Ocean Surface Waves, J. Wiley & Sons, New York.
- Stoker J. J. (1957), Water Waves, Inerscience, New York.
- Szmidt J. K. (2001), Third Order Approximation to Long Water Waves in Material Description, [in:] Zastosowania mechaniki w budownictwie lądowym i wodnym, Wyd. IBW PAN Gdańsk.
- Szydłowski M. (2001), Two-dimensional Shallow Water Model for Rapidly and Gradually Varied Flow, Archives of Hydro-Engineering and Environmental Mechanics, Vol. 48, No. 1, 35-61.
- Toro E. E (1997), Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer-Verlag, Berlin.
- Ursell F. (1953), The Long-wave Paradox in the Theory of Gravity Waves, Proceedings Cambridge Philosophical Society, Vol. 49, 685-694.
- Van Groesen E. and De Jager E. M. (1994), Mathematical Structures in Continuous Dynamical Systems, North-Holland.
- Weiyan T (1992), Shallow Water Hydrodynamics, Elsevier, Amsterdam.
- Whitham G. B. (1974), Linear and Nonlinear Waves, J. Wiley & Sons Interscience Publications, New York.
- Witting J. M. (1984), A Unified Model for the Evolution of Nonlinear Water Waves, J. Computational Physics, 56, 203-236.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT3-0021-0018