Convectons and secondary snaking in three-dimensional natural doubly diffusive convection

Physics of Fluids

Volumn 25, Issue 2, 2013, Pages

  Beaume, Cédric ^a,b   Bergeon, Alain ^a,b   Knobloch, Edgar ^c  

^a UNIVERSITÉ PAUL SABATIER   (France)

^b IMFT   (France)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FLUIDS; PHYSICS;

CONDUCTION STATE; DIFFUSIVE CONVECTION; HOMOCLINIC SNAKING; NO-SLIP BOUNDARY CONDITIONS; NUMERICAL CONTINUATION; SQUARE CROSS-SECTION; THREE-DIMENSIONAL EQUATIONS; VERTICAL ENCLOSURES; VERTICAL WALL;

THREE DIMENSIONAL;

EID: 84874727494     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4792711     Document Type: Article

References (44)

1. Knobloch E. Moore D.R. Toomre J. Weiss N.O. Transitions to chaos in two-dimensional double-diffusive convection. J. Fluid Mech. 1986, 166:409-448. 10.1017/S0022112086000216
2. Barten W. Lücke M. Kamps M. Schmitz R. Convection in binary fluid mixtures. II. Localized traveling waves. Phys. Rev. E 1995, 51:5662-5680. 10.1103/PhysRevE.51.5662
3. Spina A. Toomre J. Knobloch E. Confined states in large-aspect-ratio thermosolutal convection. Phys. Rev. E 1998, 57:524-545. 10.1103/PhysRevE.57.524
4. Batiste O. Knobloch E. Simulations of oscillatory convection in 3He-4He mixtures in moderate aspect ratio containers. Phys. Fluids 2005, 17:064102. 10.1063/1.1920349
5. Beaume C. Bergeon A. Knobloch E. Homoclinic snaking of localized states in doubly diffusive convection. Phys. Fluids 2011, 23:094102. 10.1063/1.3626405
6. Turner J.S. The coupled turbulent transports of salt and heat across a sharp density interface. Int. J. Heat Mass Transfer 1965, 8:759-760. 10.1016/0017-9310(65)90022-0
7. Turner J.S. Double diffusive phenomena. Annu. Rev. Fluid Mech. 1974, 6:37-54. 10.1146/annurev.fl.06.010174.000345
8. Turner J.S. Multicomponent convection. Annu. Rev. Fluid Mech. 1985, 17:11-44. 10.1146/annurev.fl.17.010185.000303
9. Schmitt R.W. Double diffusion in oceanography. Annu. Rev. Fluid Mech. 1994, 26:255-285. 10.1146/annurev.fl.26.010194.001351
10. Hansen U. Yuen D.A. Nonlinear physics of double-diffusive convection in geological systems. Earth-Sci. Rev. 1990, 29:385-399. 10.1016/0012-8252(90)90050-6
11. Knobloch E. Nonlinear diffusive instabilities in differentially rotating stars. Geophys. Astrophys. Fluid Dyn. 1982, 22:133-158. 10.1080/03091928208221740
12. Tsitverblit N. Kit E. The multiplicity of steady flows in confined double-diffusive convection with lateral heating. Phys. Fluids A 1993, 5:1062-1064. 10.1063/1.858671
13. Tsitverblit N. Bifurcation phenomena in confined thermosolutal convection with lateral heating: Commencement of the double-diffusive region. Phys. Fluids 1995, 7:718-736. 10.1063/1.868776
14. Xin S. Le Quéré P. Tuckerman L.S. Bifurcation analysis of double-diffusive convection with opposing horizontal thermal and solutal gradients. Phys. Fluids 1998, 10:850-858. 10.1063/1.869608
15. Wilcox W.R. Transport phenomena in crystal growth from solution. Prog. Cryst. Growth Charact. Mater. 1993, 26:153-194. 10.1016/0960-8974(93)90014-U
16. Ghorayeb K. Mojtabi A. Double diffusive convection in a vertical rectangular cavity. Phys. Fluids 1997, 9:2339-2348. 10.1063/1.869354
17. Bergeon A. Knobloch E. Spatially localized states in natural doubly diffusive convection. Phys. Fluids 2008, 20:034102. 10.1063/1.2837177
18. Bergeon A. Knobloch E. Natural doubly diffusive convection in three-dimensional enclosures. Phys. Fluids 2002, 14:3233-3250. 10.1063/1.1493790
19. Burke J. Knobloch E. Localized states in the generalized Swift-Hohenberg equation. Phys. Rev. E 2006, 73:056211. 10.1103/PhysRevE.73.056211
20. Burke J. Knobloch E. Snakes and ladders: Localized states in the Swift-Hohenberg equation. Phys. Lett. A 2007, 360:681-688. 10.1016/j.physleta.2006.08.072
21. Burke J. Knobloch E. Homoclinic snaking: Structure and stability. Chaos 2007, 17:037102. 10.1063/1.2746816
22. Beck M. Knobloch J. Lloyd D.J. B. Sandstede B. Wagenknecht T. Snakes, ladders and isolas of localized patterns. SIAM J. Math. Anal. 2009, 41:936-972. 10.1137/080713306
23. Hunt G.W. Peletier M.A. Champneys A.R. Woods P.D. Wadee M.A. Budd C.J. Lord G.J. Cellular buckling in long structures. Nonlinear Dyn. 2000, 21:3-29. 10.1023/A:1008398006403
24. Skryabin D.V. Instabilities of cavity solitons in optical parametric oscillators. Phys. Rev. E 1999, 60:R3508-R3511. 10.1103/PhysRevE.60.R3508
25. Blanchflower S. Magnetohydrodynamic convectons. Phys. Lett. A 1999, 261:74-81. 10.1016/S0375-9601(99)00573-3
26. Lo Jacono D. Bergeon A. Knobloch E. Magnetohydrodynamic convectons. J. Fluid Mech. 2011, 687:595-605. 10.1017/jfm.2011.402
27. Schneider T.M. Gibson J.F. Burke J. Snakes and ladders: Localized solutions of plane Couette flow. Phys. Rev. Lett. 2010, 104:104501. 10.1103/PhysRevLett.104.104501
28. Lo Jacono D. Bergeon A. Knobloch E. Spatially localized binary fluid convection in a porous medium. Phys. Fluids 2010, 22:073601. 10.1063/1.3439672
29. Mercader I. Batiste O. Alonso A. Knobloch E. Convectons, anticonvectons and multiconvectons in binary fluid convection. J. Fluid Mech. 2011, 667:586-606. 10.1017/S0022112010004623
30. Mercader I. Batiste O. Alonso A. Knobloch E. Localized pinning states in closed containers: Homoclinic snaking without bistability. Phys. Rev. E 2009, 80:025201(R). 10.1103/PhysRevE.80.025201
31. Tuckerman L.S. Steady-state solving via Stokes preconditioning: Recursion relations for elliptic operators. Proceedings of the 11th International Conference on Numerical Methods in Fluid Dynamics 1989, 573-577. D. Dwoyer, M. Hussaini, R. Voigt, in edited by and (Springer, Berlin), Lecture Notes in Physics 323
32. Mamun C.K. Tuckerman L.S. Asymmetry and Hopf bifurcation in spherical Couette flow. Phys. Fluids 1995, 7:80-91. 10.1063/1.868730
33. Karniadakis G.E. Israeli M. Orszag S.A. High-order splitting methods for the incompressible Navier-Stokes equations. J. Comp. Phys. 1991, 97:414-443. 10.1016/0021-9991(91)90007-8
34. Henry D. Ben Hadid H. Multiple flow transitions in a box heated from the side in low-Prandtl-number fluids. Phys. Rev. E 2007, 76:016314. 10.1103/PhysRevE.76.016314
35. Paliwal R.C. Chen C.F. Double-diffusive instability in an inclined fluid layer. Part 1. Experimental investigation. J. Fluid Mech. 1980, 98:755-768. 10.1017/S0022112080000377
36. Paliwal R.C. Chen C.F. Double-diffusive instability in an inclined fluid layer. Part 2. Stability analysis. J. Fluid Mech. 1980, 98:769-785. 10.1017/S0022112080000389
37. Thangam S. Zebib A. Chen C.F. Double-diffusive convection in an inclined fluid layer. J. Fluid Mech. 1982, 116:363-378. 10.1017/S0022112082000500
38. Houghton S.M. Knobloch E. Homoclinic snaking in bounded domains. Phys. Rev. E 2009, 80:026210. 10.1103/PhysRevE.80.026210
39. Bergeon A. Burke J. Knobloch E. Mercader I. Eckhaus instability and homoclinic snaking. Phys. Rev. E 2008, 78:046201. 10.1103/PhysRevE.78.046201
40. Mercader I. Batiste O. Alonso A. Knobloch E. Convectons in periodic and bounded domains. Fluid Dyn. Res. 2010, 42:025505. 10.1088/0169-5983/42/2/025505
41. Burke J. Houghton S.M. Knobloch E. Swift-Hohenberg equation with broken reflection symmetry. Phys. Rev. E 2009, 80:036202. 10.1103/PhysRevE.80.036202
42. Lloyd D.J. B. Sandstede B. Avitabile D. Champneys A.R. Localized hexagons patterns of the planar Swift-Hohenberg equation. SIAM J. Appl. Dyn. Syst. 2008, 7:1049-1100. 10.1137/070707622
43. Bardan G. Bergeon A. Knobloch E. Mojtabi A. Nonlinear doubly diffusive convection in vertical enclosures. Physica D 2000, 138:91-113. 10.1016/S0167-2789(99)00195-5
44. Suslov S.A. Paolucci S. Stability of non-Boussinesq convection via the complex Ginzburg-Landau model. Fluid Dyn. Res. 2004, 35:159-203. 10.1016/j.fluiddyn.2004.06.002