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Vanishing characteristic speeds and critical dispersive points in nonlinear interfacial wave problems
journal contribution
posted on 2018-11-12, 13:56 authored by Daniel RatliffCriticality plays a central role in the study of reductions and stability of hydrodynamical systems. At critical points, it is often the case that nonlinear reductions with dispersion arise to govern solution behavior. By considering when such models become bidirectional and lose their initial dispersive properties, it will be shown that higher order dispersive models may be supported in hydrodynamical systems. Precisely, this equation is a two-way Boussinesq equation with sixth order dispersion. The case of two layered shallow water is considered to illustrate this, and it is reasoned why such an environment is natural for such a system to emerge. Further, it is demonstrated that the regions in the parameter space for nontrivial flow, which admit this reduction, are vast and in fact form a continuum. The reduced model is then numerically simulated to illustrate how the two-way and higher dispersive properties suggest more exotic families of solitary wave solutions can emerge in stratified flows.
Funding
The author is in receipt of a fully funded Ph.D studentship under the EPSRC Grant No. EP/L505092/1.
History
School
- Science
Department
- Mathematical Sciences
Published in
Physics of FluidsVolume
29Issue
11Pages
112104 - 112104Citation
RATLIFF, D.J., 2017. Vanishing characteristic speeds and critical dispersive points in nonlinear interfacial wave problems. Physics of Fluids, 29 (11), 112104.Publisher
AIP Publishing © The AuthorVersion
- AM (Accepted Manuscript)
Acceptance date
2017-10-24Publication date
2017Notes
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in RATLIFF, D.J., 2017. Vanishing characteristic speeds and critical dispersive points in nonlinear interfacial wave problems. Physics of Fluids, 29 (11), 112104 and may be found at https://doi.org/10.1063/1.4998803.ISSN
1070-6631eISSN
1089-7666Publisher version
Language
- en