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Title: Self-contained two-layer shallow water theory of strong internal bores.

We show that interfacial gravity waves comprising strong hydraulic jumps
(bores) can be described by a two-layer hydrostatic shallow-water (SW)
approximation without invoking additional front conditions. The theory is based
on a new SW momentum equation which is derived in locally conservative form
containing a free parameter $\alpha.$ This pa [...]

Authors: Jānis Priede

Link: http://arxiv.org/abs/1806.06041

Title: Self-contained two-layer shallow water theory of strong internal bores.

We show that interfacial gravity waves comprising strong hydraulic jumps
(bores) can be described by a two-layer hydrostatic shallow-water (SW)
approximation without invoking additional front conditions. The theory is based
on a new SW momentum equation which is derived in locally conservative form
containing a free parameter $\alpha.$ This pa [...]

Authors: Jānis Priede

Link: http://arxiv.org/abs/1806.06041

Title: Lock-exchange problem for Boussinesq fluids revisited: exact shallow-water solution.

An exact solution to the lock-exchange problem, which is a two-layer analogue
of the classical dam-break problem, is obtained in the shallow-water (SW)
approximation for two immiscible fluids with slightly different densities. The
problem is solved by the method of characteristics using analytic expressions
for [...]

Authors: Gerasimos Politis, Jānis Priede

Link: http://arxiv.org/abs/2002.02699