Geodesic
Hyperbolic model of strongly nonlinear waves in two-layer flows of an inhomogeneous fluid
Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 4, pp. 71-85

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A mathematical model of propagation of nonlinear long waves in a two-layer shear flow of an inhomogeneous liquid with a free boundary is proposed, taking into account the effects of dispersion and mixing. The equations of fluid motion are presented in the form of a hyperbolic system of quasi-linear equations of the first order. Solutions describing damped oscillations of the internal interface are constructed in the class of traveling waves. The parameters of a two-layer flow at which the formation of large-amplitude waves is possible are found. Numerical simulation of nonstationary flows arising during the flow around a local obstacle is performed. It is shown that, depending on the velocity of the incoming flow and the shape of the obstacle, disturbances propagate upstream in the form of a monotone or wave boron.
Keywords: equations of long waves, hyperbolicity, inhomogeneous fluid, mixing
Mots-clés : dispersion. . 
@article{SJIM_2022_25_4_a5,
     author = {V. E. Ermishina},
     title = {Hyperbolic model of strongly nonlinear waves in two-layer flows of an inhomogeneous fluid},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {71--85},
     publisher = {mathdoc},
     volume = {25},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2022_25_4_a5/}
}
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V. E. Ermishina. Hyperbolic model of strongly nonlinear waves in two-layer flows of an inhomogeneous fluid. Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 4, pp. 71-85. http://geodesic.mathdoc.fr/item/SJIM_2022_25_4_a5/