Abstract
This paper deals with the novel approach to the evolution description of nonlinear three-dimensional moderately long disturbances of the liquid free surface. The suggested model consists of one basic second-order differential equation for spatial perturbations and two auxiliary linear differential equations for a determination of the fluid horizontal velocity vector averaged over the layer depth. This vector is contained in the main equation only in the terms of the second order of smallness. The suggested model is suitable for finite-amplitude waves running with any angles. This approach is in essence easier than the known systems of equations, where all equations contain both linear and nonlinear items. Some problems of interactions and collisions of waves were solved numerically. A number of test and demonstrational solutions were found in the pools with different topographies. Expectedly it was observed that not only the change of the wave velocities but also the intensification of disturbances propagating towards the lower liquid depth and otherwise their weakening along with the waves motion to the deeper area. It is seen, that the additional peaks and troughs took place over the bottom irregularities.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Miles, J.W.: J. Fluid Mech. 106, 131–147 (1981)
Kadomtsev, B.B., Petviashvili, V.I.: Sov. Phys. Dokl. 15, 539–542 (1970)
Marchuk, A.G., Chubarov, L.B., Shokin, Y.I.: Numerical Simulation of Tsunami Waves, LA-TR-85, Los-Alamos (1985)
Khakimzyanov, G.S., Shokin, Y.I., Barakhnin, V.B., Shokina, N.Y.: Numerical Simulation of Currents with Surface Waves. Publ. House SB RAS, Novosibirsk (2001) (in Russian)
Kim, K.Y., Reid, R.O., Whitaker, R.E.: J. Comput. Phys. 76, 327–348 (1988)
Pelinovsky, D.E.: Stepanyants Yu.A.: JETP 79, 105–112 (1994)
Khabakhpashev, G.A.: Comput. Technol. 2, 94–102 (1997) (in Russian)
Peregrine, D.H.: J. Fluid Mech. 27, 815–827 (1967)
Karpman, V.I.: Nonlinear Waves in Dispersive Media. Pergamon Press, N.Y (1975)
Green, A.E., Naghdi, P.M.: J. Fluid Mech. 78, 237–246 (1976)
Arkhipov, D.G., Khabakhpashev, G.A.: Doklady Physics 51, 418–422 (2006)
Johnson, R.S.: J. Fluid Mech. 323, pp. 65–78 (1996)
Khabakhpashev, G.A.: Fluid Dyn. 22, pp. 430–437 (1987)
Litvinenko, A.A., Khabakhpashev, G.A.: Comput. Technologies 4, 95–105 (1999) (in Russian)
Ostrovsky, L.A., Potapov, A.I.: Modulated Waves: Theory and Applications. Johns Hopkins Univ. Press, Baltimore (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Arkhipov, D.G., Khabakhpashev, G.A., Safarova, N.S. (2011). Combined Approach to Numerical Simulation of Spatial Nonlinear Waves in Shallow Water with Various Bottom Topography. In: Krause, E., Shokin, Y., Resch, M., Kröner, D., Shokina, N. (eds) Computational Science and High Performance Computing IV. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 115. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17770-5_22
Download citation
DOI: https://doi.org/10.1007/978-3-642-17770-5_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17769-9
Online ISBN: 978-3-642-17770-5
eBook Packages: EngineeringEngineering (R0)