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].

Two-layer interfacial flows beyond the Boussinesq approximation: a Hamiltonian approach

FALQUI, GREGORIO
Secondo
;
ORTENZI, GIOVANNI
Ultimo
2017

Abstract

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.
Articolo in rivista - Articolo scientifico
channel flow; Hamiltonian structures; integrable systems; perturbation theory; stratified fluids
English
466
491
26
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].
Camassa, R; Falqui, G; Ortenzi, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/139278
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