Abstract
In this paper, the two-layer viscous shallow-water equations are derived from the three-dimensional Navier-Stokes equations under the hydrostatic assumption. It is noted that the combination of upper and lower equations in the two-layer model produces the classical one-layer equations if the density of each layer is the same. The two-layer equations are approximated by a finite element method which follows our numerical scheme established for the one-layer model in 1978. Finally, it is numerically demonstrated that the interfacial instability generated when the densities are the same can be eliminated by providing a sufficient density difference.
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Kanayama, H., Dan, H. A finite element scheme for two-layer viscous shallow-water equations. Japan J. Indust. Appl. Math. 23, 163 (2006). https://doi.org/10.1007/BF03167549
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DOI: https://doi.org/10.1007/BF03167549