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.
|Citazione:||Camassa, R., Falqui, G., & Ortenzi, G. (2017). Two-layer interfacial flows beyond the Boussinesq approximation: a Hamiltonian approach. NONLINEARITY, 30(2), 466-491.|
|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|
FALQUI, GREGORIO (Secondo)
ORTENZI, GIOVANNI (Ultimo) (Corresponding)
|Data di pubblicazione:||2017|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1088/1361-6544/aa4ff7|
|Appare nelle tipologie:||01 - Articolo su rivista|