The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler system for two-layer stratified flows in an infinite two-dimensional channel. The Hamiltonian structure of the averaged equations is obtained directly from that of the Euler equations through the process of Hamiltonian reduction. Long-wave asymptotics together with the Boussinesq approximation of neglecting the fluids' inertia is then applied to reduce the leading order vertically averaged equations to the shallow-water Airy system, albeit in a non-trivial way. The full non-Boussinesq system for the dispersionless limit can then be viewed as a deformation of this well known equation. In a perturbative study of this deformation, a family of approximate constants of the motion are explicitly constructed and used to find local solutions of the evolution equations by means of hodograph-like formulae. The research that led to the present paper was partially supported by a grant of the group GNFM of INdAM.
Camassa, R., Falqui, G., & Ortenzi, G. (2017). Two-layer interfacial flows beyond the Boussinesq approximation: a Hamiltonian approach. NONLINEARITY, 30(2), 466-491 [10.1088/1361-6544/aa4ff7].
Citazione: | Camassa, R., Falqui, G., & Ortenzi, G. (2017). Two-layer interfacial flows beyond the Boussinesq approximation: a Hamiltonian approach. NONLINEARITY, 30(2), 466-491 [10.1088/1361-6544/aa4ff7]. | |
Tipo: | Articolo in rivista - Articolo scientifico | |
Carattere della pubblicazione: | Scientifica | |
Presenza di un coautore afferente ad Istituzioni straniere: | Si | |
Titolo: | Two-layer interfacial flows beyond the Boussinesq approximation: a Hamiltonian approach | |
Autori: | Camassa, R; Falqui, G; Ortenzi, G | |
Autori: | FALQUI, GREGORIO (Secondo) ORTENZI, GIOVANNI (Ultimo) (Corresponding) | |
Data di pubblicazione: | 2017 | |
Lingua: | English | |
Rivista: | NONLINEARITY | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1088/1361-6544/aa4ff7 | |
Appare nelle tipologie: | 01 - Articolo su rivista |
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