Geodesic
Numerical study of the Kelvin-Helmholtz instability resolution in a~floodplain channel flow
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 4, pp. 417-428

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Models of water flows with different velocities in the river channel are studied. The tangential velocity discontinuity causes development of the so-called Kelvin and Helmholtz instability. The mathematical statement of the problem of studying instability based on the two-dimensional planimetric equations of the turbulent flow hydrodynamics was formulated. When constructing a numerical model, a finite difference scheme of a high spatial resolution is used, providing a possibility of the direct description of large eddies generated in the turbulence field on the line of separation. Analysis of energy transformations in the system “channel-floodplain” is made, the possibility of realization of the antigradient transport, known as negative viscosity phenomenon, is shown. 
@article{SJVM_2007_10_4_a7,
     author = {V. A. Shlychkov},
     title = {Numerical study of the {Kelvin-Helmholtz} instability resolution in a~floodplain channel flow},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {417--428},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2007_10_4_a7/}
}
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V. A. Shlychkov. Numerical study of the Kelvin-Helmholtz instability resolution in a~floodplain channel flow. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 4, pp. 417-428. http://geodesic.mathdoc.fr/item/SJVM_2007_10_4_a7/