Helicity in dispersive fluid mechanics

By dispersive models of fluid mechanics we are referring to the Euler–Lagrange equations for the constrained Hamilton action functional where the internal energy depends on high order derivatives of unknowns. The mass conservation law is considered as a constraint. The corresponding Euler–Lagrange e...

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Bibliographic Details
Published in:International journal of non-linear mechanics 2024-06, Vol.162, p.104705, Article 104705
Main Authors: Gavrilyuk, S.L., Gouin, H.
Format: Article
Language:English
Subjects:
Analysis of PDEs
Bubbly fluids
Capillary fluids
Dispersive fluid mechanics
Engineering Sciences
Long free-surface gravity waves
Mathematical Physics
Mathematics
Mechanics
Physics
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Summary:By dispersive models of fluid mechanics we are referring to the Euler–Lagrange equations for the constrained Hamilton action functional where the internal energy depends on high order derivatives of unknowns. The mass conservation law is considered as a constraint. The corresponding Euler–Lagrange equations include, in particular, the van der Waals–Korteweg model of capillary fluids, the model of fluids containing small gas bubbles and the model describing long free-surface gravity waves. We obtain new conservation laws generalizing the helicity conservation for classical barotropic fluids. •New conservation laws for the equations of dispersive fluids are found.•Generalized helicity integrals are formulated for the second gradient fluids.•Generalized helicity integrals are obtained for fluids with internal inertia.
ISSN:0020-7462
1878-5638
DOI:10.1016/j.ijnonlinmec.2024.104705