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.
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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
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DOI: https://doi.org/10.1007/978-3-642-17770-5_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17769-9
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