Journal article
Overturned internal capillary–gravity waves
European journal of mechanics, B, Fluids, v 57, pp 143-151
May 2016
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
A vortex sheet formulation of irrotational, incompressible Euler flow is used to compute periodic traveling waves at the interface between two constant-density, two-dimensional fluids, including waves with overturned crests. Branches of traveling waves are computed via numerical continuation, which are jointly continuous in the physical parameters: Bond number, Atwood number and mean shear. Global branches are computed, for various choices of parameters, illustrating the termination criteria of the global bifurcation theorem of Ambrose et al. (2015). The dependence of the branches, and their termini, on the physical parameters are probed via a boundary continuation method. Bifurcation surfaces are computed; these surfaces are both overturned and self-intersecting. The connection between the second harmonic of a Stokes’ wave expansion and the shape of these surfaces is discussed.
•Global bifurcation branches of internal capillary–gravity waves are computed.•All possible behaviors from a global bifurcation theorem are realized.•A numerical method is developed for computing the boundary of bifurcation surfaces.•The role of the waves’ second harmonic in its bifurcation structure is discussed.•Steep waves limited by self-intersection at both crests and troughs are computed.
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Details
- Title
- Overturned internal capillary–gravity waves
- Creators
- Benjamin F. Akers - Air Force Institute of TechnologyDavid M. Ambrose - Drexel UniversityKevin Pond - Air Force Institute of TechnologyJ. Douglas Wright - Drexel University
- Publication Details
- European journal of mechanics, B, Fluids, v 57, pp 143-151
- Publisher
- Elsevier
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000375361300013
- Scopus ID
- 2-s2.0-84956863125
- Other Identifier
- 991019168356404721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mechanics
- Physics, Fluids & Plasmas