Reappraisal of criticality for two-layer flows and its role in the generation of internal solitary waves

Physics of Fluids

Volumn 19, Issue 7, 2007, Pages

  Bridges, Thomas J ^a   Donaldson, Neil M ^a  

^a UNIVERSITY OF SURREY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL GEOMETRY; FLOW PATTERNS; MASS TRANSFER; SOLITONS;

CRITICAL FLOW; INTERNAL SOLITARY WAVES; MULTILAYER FLOWS; TWO-LAYER FLOWS; UNIFORM FLOWS;

TWO PHASE FLOW;

COMPUTATIONAL GEOMETRY; FLOW PATTERNS; MASS TRANSFER; SOLITONS; TWO PHASE FLOW;

EID: 34547780584     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2750541     Document Type: Article

References (22)

1. R. H. J. Grimshaw, "Internal solitary waves," in Advances in Fluid Mechanics V (WIT, Southampton, 2004), Vol. 40, pp. 209-218.
2. K. R. Helfrich and W. K. Melville, "Long nonlinear internal waves," Annu. Rev. Fluid Mech. ARVFA30066-418910.1146/ annurev.fluid.38.050304.092129 38, 395 (2006).
3. L. Armi, "The hydraulics of two flowing layers with different densities," J. Fluid Mech.JFLSA70022-112010.1017/S0022112086002197 163, 27 (1986).
4. P. G. Baines, Topographic Effects in Stratified Flows (Cambridge University Press, Cambridge, UK, 1995).
5. J. Bühler, "Simple internal waves and bores," J. Hydraul. Eng.JHEND80733-942910.1061/(ASCE)0733-9429(1994)120:5(638) 120, 638 (1994).
6. T. B. Benjamin, "Internal waves of finite amplitude and permanent form," J. Fluid Mech.JFLSA70022-112010.1017/S0022112066001630 25, 241 (1966).
7. W. Choi and R. Camassa, "Fully nonlinear internal waves in a two-fluid system," J. Fluid Mech.JFLSA70022-112010.1017/ S0022112099005820 396, 1 (1999).
8. F. Dias and J.-M. Vandenbroeck, "On internal fronts," J. Fluid Mech. JFLSA70022-112010.1017/S0022112002003609 479, 145 (2003).
9. M. Funakishi and M. Oikawa, "Long internal waves of large amplitude in a two-layer fluid," J. Phys. Soc. Jpn.JUPSAU0031-901510.1143/ JPSJ.55.128 55, 128 (1986).
10. O. Laget and F. Dias, "Numerical computation of capillary-gravity interfacial solitary waves," J. Fluid Mech.JFLSA70022-112010.1017/ S0022112097006861 349, 221 (1997).
11. R. R. Long, "Solitary waves in the one and two-fluid system," TellusTELLAL0040-2826 8, 460 (1956).
12. D. I. Pullin and R. H. J. Grimshaw, "Finite-amplitude solitary waves at the interface between two homogeneous fluids," Phys. FluidsPFLDAS0031-917110.1063/1.866922 31, 3550 (1988).
13. T. J. Bridges and N. M. Donaldson, "Secondary criticality of water waves. Part 1. Definition, bifurcation and solitary waves," J. Fluid Mech.JFLSA70022-112010.1017/S002211200600187X 565, 381 (2006).
14. T. B. Benjamin and M. J. Lighthill, "On cnoidal waves and bores," Proc. R. Soc. London, Ser. APRLAAZ1364-5021 224, 448 (1954).
15. M. J. Sewell and D. Porter, "Constitutive surfaces in fluid mechanics," Math. Proc. Cambridge Philos. Soc.MPCPCO0305-0041 88, 517 (1980).
16. M. J. Sewell, Maximum and Minimum Principles (Cambridge University Press, Cambridge, UK, 1987).
17. T. J. Bridges and N. M. Donaldson, "Degenerate periodic orbits and homoclinic torus bifurcation," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.95.104301 95, 104301 (2005).
18. See EPAPS Document No. E-PHFLE6-19-048706 for color versions of Figs. This document can be reached via a direct link in the online article's HTML reference section or via the EPAPS homepage (http://www.aip.org/ pubservs/epaps.html).
19. N. M. Donaldson, "Criticality theory and conformal mapping techniques for single and two-layer water-wave systems," Ph.D. thesis, University of Surrey (2006).
20. V. I. Arnold, S. M. Gusein-Zade, and A. N. Varchenko, Singularities of Differentiable Maps (Birkhäuser, Boston, 1985), Vol. I.
21. T. B. Benjamin and T. J. Bridges, "Reappraisal of the Kelvin-Helmholtz instability. Part 1. Hamiltonian structure," J. Fluid Mech.JFLSA70022-112010.1017/S0022112096004272 333, 301 (1997).
22. W. Craig, P. Guyenne, and H. Kalisch, "Hamiltonian long-wave expansions for free surfaces and interfaces," Commun. Pure Appl. Math.CPMAMV0010-364010.1002/cpa.20098 58, 1587 (2005).