Critical speed for capillary-gravity surface flows in the dispersive shallow water limit

Physics of Fluids

Volumn 17, Issue 6, 2005, Pages 1-13

  Pham, Chi Tuong ^a   Nore, Caroline ^a,b   Brachet, Marc Étienne ^a  

^a CNRS   (France)

^b UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY LAYERS; CHEBYSHEV APPROXIMATION; COMPRESSIBLE FLOW; CONTACT ANGLE; GRAVITATIONAL EFFECTS; POLYNOMIALS;

CHEBYCHEV POLYNOMIALS; EULER EQUATIONS; FOURIER PSEUDOSPECTRAL METHODS; STATIONARY SOLUTIONS;

CAPILLARY FLOW;

FLUID FLOW;

EID: 21244488981     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1926267     Document Type: Article

References (25)

1. L. D. Landau and E. M. Lifshitz, Fluid Mechanics, 2nd ed. (Butterworth-Heinemann, Oxford, 1995).
2. G. B. Whitham, Linear and Nonlinear Waves (Wiley-Interscience, New York, 1999).
3. E. Raphaël and P.-G. de Gennes, "Capillary gravity waves caused by a moving disturbance: Wave resistance," Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.53.3448 53, 3448 (1996).
4. J. Browaeys, J.-C. Bacri, R. Perzynski, and M. Shliomis, "Capillary-gravity wave resistance in ordinary and magnetic fluids," Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2001-00138-7 53, 209 (2001).
5. T. Burghelea and V. Steinberg, "Onset of wave drag due to generation of capillary-gravity waves by a moving object," Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.2557 86, 2557 (2001).
6. T. Burghelea and V. Steinberg, "Wave drag due to generation of capillary-gravity surfaces waves," Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.051204 66, 051204 (2002).
7. F. Chevy and E. Raphaël, "Capillary gravity waves: A fixed-depth analysis," Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/ i2003-00304-5 61, 796 (2003).
8. Y. Pomeau and S. Rica, "Model of superflow with rotons," Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.247 71, 247 (1993).
9. T. Frisch, Y. Pomeau, and S. Rica, "Transition to dissipation in a model of superflow," Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/ PhysRevLett.69.1644 69, 1644 (1992).
10. C. Huepe and M. Brachet, "Solutions de nucléation tourbillonnaires dans un modèle d'écoulement superfluide," C. R. Acad. Sci., Ser. IIb: Mec., Phys., Chim., Astron. CMCAEK 1251-8069 10.1016/S1251-8069(97)88278-4 325, 195 (1997).
11. C. Huepe and M. E. Brachet, "Scaling laws for vortical nucleation solutions in a model of superflow," Physica D PDNPDT 0167-2789 10.1016/S0167-2789(99)00229-8 140, 126 (2000).
12. C. Raman, M. Köhl, R. Onofrio, D. S. Durfee, C. E. Kuklewicz, Z. Hadzibabic, and W. Ketterle, "Evidence for a critical velocity in a Bose-Einstein condensed gas," Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.2502 83, 2502 (1999).
13. E. P. Gross, "Structure of a quantized vortex in boson systems," Nuovo Cimento NUCIAD 0029-6341 20, 454 (1961).
14. V. L. Ginzburg and L. P. Pitaevskii, "On the theory of superfluidity," Sov. Phys. JETP SPHJAR 0038-5646 7, 858 (1958).
15. F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, "Theory of Bose-Einstein condensation in trapped gases," Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.71.463 71, 463 (1999).
16. É. Guyon, J.-P. Hulin, and L. Petit, Hydrodynamique Physique, 2nd ed. (EDP Sciences, Les Ulis, 2001).
17. C.-T. Pham, "Stabilité et dynamique d'écoulements de fluides parfaits barotropes autour d'un obstacle en présence de dispersion" Ph.D. thesis, Université Paris 6, 2003.
18. R. Seydel, From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis (Elsevier, New York, 1988).
19. S. Rica, "A remark on the critical speed for vortex nucleation in the nonlinear Schrödinger equation," Physica D PDNPDT 0167-2789 148, 221 (2001).
20. T. Podgorski, J.-M. Flesselles, and L. Limat, "Dry arches within flowing films," Phys. Fluids PHFLE6 1070-6631 10.1063/1.869956 11, 845 (1999).
21. D. Gottlieb and S. A. Orszag, Numerical Analysis of Spectral Methods (SIAM, Philadelphia, 1977).
22. C. Nore, M. Abid, and M. Brachet, "Decaying Kolmogorov turbulence in a model of superflow," Phys. Fluids PHFLE6 1070-6631 10.1063/ 1.869473 9, 2644 (1997).
23. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge University Press, Cambridge, 1992), Chap. 9, p. 372.
24. L. S. Tuckerman and D. Barkley, "Bifurcation analysis for time-steppers," Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems, edited by E. Doedel and L. S. Tuckerman (Springer, New York, 2000), Vol. 7, pp. 452-466.
25. H. A. Van Der Vorst, "BI-CGSTAB: A fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems," SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. SIJCD4 0196-5204 13, 631 (1992).