Three-dimensional global instability modes associated with a localized hot spot in Rayleigh-Bénard-Poiseuille convection

Journal of Fluid Mechanics

Volumn 551, Issue , 2006, Pages 275-301

  Martinand, Denis ^a,b   Carrière, Philippe ^a   Monkewitz, Peter A ^b  

^a UNIVERSITÉ LYON 1   (France)

^b EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; HEATING; THERMODYNAMIC STABILITY; WALL FLOW;

CONVECTION ROLLS; TEMPERATURE BUMP;

HEAT CONVECTION;

COMPUTER SIMULATION; HEAT CONVECTION; HEATING; THERMODYNAMIC STABILITY; WALL FLOW;

THERMAL CONVECTION; THREE-DIMENSIONAL MODELING;

EID: 33646802271     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112005008323     Document Type: Article

References (25)

1. Bender, C. M. & Orszag, S. A. 1978 Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill.
2. Carrière, P. & Monkewitz, P. A. 1999 Convective versus absolute instability in mixed Rayleigh-Bénard-Poiseuille convection. J. Fluid Mech. 384, 243-262.
3. Carrière, P. & Monkewitz, P. A. 2001 Transverse-roll global modes in a Rayleigh-Bénard-Poiseuille system with streamwise variable heating. Eur. J. Mech. B/Fluids 20, 751-770.
4. Carrière, P., Monkewitz, P. A. & Martinand, D. 2004 Envelope equation for the Rayleigh-Bénard-Poiseuille system. Part 1. Spatially homogeneous case. J. Fluid Mech. 502, 153-174.
5. Chomaz, J.-M., Huerre, P. & Redekopp, L. G. 1991 A frequency selection criterion in spatially developing flows. Stud. Appl. Maths 84, 119-144.
6. Crighton, D. & Gaster, M. 1976 Stability of slowly diverging jet flow. J. Fluid Mech. 77, 397-413.
7. Gilbert, N. 1988 Transition von der laminaren in die turbulente Kanalströmung. PhD thesis, DFVLR Institut für Strömungsmechanik Göttingen.
8. Huerre, P. & Monkewitz, P. A. 1985 Absolute and convective instabilities in free shear layers. J. Fluid Mech. 159, 151-168.
9. Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473-537.
10. Jammer, M. 1966 The Conceptual Development of Quantum Mechanics. McGraw-Hill.
11. Kelly, R. E. 1994 The onset and development of thermal convection in fully developed shear flows. Adv. Appl. Mech. 31, 35-112.
12. Kleiser, L. & Schumann, U. 1980 Treatment of incompressibility and boundary conditions in 3-D numerical spectral simulations of plane channel flows. In Proc. Third GAMM Conf. on Numerical Methods in Fluid Mechanics.
13. Kleiser, L. & Schumann, U. 1984 Spectral simulations of the laminar-turbulent transition process in plane Poiseuille flow. In Spectral Methods for Partial Differential Equations (ed. R. G. Voigt, D. Gottlieb & M. Y. Hussaini), pp. 141-163. SIAM, Philadelphia.
14. Le Dizès, S., Huerre, P., Chomaz, J.-M. & Monkewitz, P. A. 1996 Linear global modes in spatially developing media. Phil. Trans. R. Soc. Lond. A 354, 169-212.
15. Lighthill, J. 1978 Waves in Fluids. Cambridge University Press.
16. Martinand, D. 2003 Détermination analytique des modes globaux tridimensionnels en écoulement de convection mixte du type Rayleigh-Bénard-Poiseuille. PhD thesis, Université Claude Bernard Lyon I. http://tel.ccsd.cnrs.fr/documents/archives0/00/00/34/61/ index.html.
17. Martinand, D., Carrière, P. & Monkewitz, P. A. 2004 Envelope equation for the Rayleigh-Bénard-Poiseuille system. Part 2. Linear global modes in the case of two-dimensional non-uniform heating. J. Fluid Mech. 502, 175-197.
18. Monkewitz, P. A., Huerre, P. & Chomaz, J.-M. 1993 Global linear stability analysis of weakly non-parallel shear flows. J. Fluid Mech. 288, 1-20.
19. Newell, A. C. & Whitehead, J. A. 1969 Finite bandwidth, finite amplitude convection. J. Fluid Mech. 38, 279-303.
20. Nicolas, X. 2002 Bibliographical review on the Poiseuille-Rayleigh-Bénard flows: The mixed convection flows in horizontal rectangular ducts heated from below. Intl J. Therm. Sci. 41(10).
21. Pier, B., Huerre, P. & Chomaz, J.-M. 2001 Bifurcation to fully nonlinear synchronized structures in slowly varying media. Physica D 148, 49-96.
22. Provansal, M., Mathis, C. & Boyer, L. 1987 Bénard-von Kármán instability: Transient and forced regimes. J. Fluid Mech. 182, 1-22.
23. Roussopoulos, K. & Monkewitz, P. A. 1996 Nonlinear modelling of vortex shedding control in cylinder wakes. Physica D 97, 264-273.
24. Segel, L. A. 1969 Distant side-walls cause slow amplitude modulation of cellular convection. J. Fluid Mech. 38, 203-224.
25. Wasow, W. 1985 Linear Turning Point Theory. Springer.