@inproceedings{3d49bfcf01fd4022973cad0050abf9d4,

title = "Modeling collision of 3D moderately long disturbances of small but finite amplitude in viscous fluid layer",

abstract = "This paper deals with the combined approach to describing the interaction of weakly nonlinear three-dimensional disturbances of a free surface of the shallow viscous fluid layer. The initial system of hydrodynamic equations is reduced to the novel model system of equations. The first of them is integro-differential equation for disturbance of small but finite amplitude, taking into account non-stationary shear stress on a weakly sloping bottom. Another equation is an auxiliary linear equation for determining the liquid horizontal velocity vector, averaged over the layer depth. This vector is present in the main equation only in the term of the second order of smallness. The proposed model is suitable for nonlinear waves, traveling at any angles in the horizontal plane. Some problems of interactions and collisions of such disturbances over the horizontal and weakly sloping bottom are solved numerically.",

keywords = "WAVES, EQUATION, WATER",

author = "Khabakhpashev, {Georgy A.} and Arkhipov, {Dmitry G.}",

year = "2019",

month = jul,

day = "24",

doi = "10.1063/1.5113990",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

editor = "T.E. Simos and Ch. Tsitouras",

booktitle = "International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2018",

note = "International Conference on Numerical Analysis and Applied Mathematics 2018, ICNAAM 2018 ; Conference date: 13-09-2018 Through 18-09-2018",

}