Spectral properties and universal behaviour of advecting-diffusing scalar fields in finite-length channels

Journal of Fluid Mechanics

Volumn 612, Issue , 2008, Pages 387-406

  Giona, M ^a   Cerbelli, S ^a   Creta, F ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

PARALLEL FLOW;

ADVECTION-DIFFUSION OPERATORS; DOMINANT EIGENVALUES; MICRO FLUIDIC APPLICATIONS; MOLECULAR DIFFUSIVITY; RELAXATION TIME SCALE; SPECTRAL PROPERTIES; STAGNATION POINTS; VELOCITY PROFILES;

EIGENVALUES AND EIGENFUNCTIONS;

ADVECTION-DIFFUSION EQUATION; CHANNEL FLOW; EIGENVALUE; SPECTRAL ANALYSIS; THEORETICAL STUDY; VELOCITY PROFILE;

EID: 52749083103     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112008003042     Document Type: Article

References (28)

1. ARIS, R. 1956 On the dispersion of a solute in a fluid flowing through a tube. Proc. R. Soc. Lond. A 235, 67-77.
2. BACKUS, G. 1958 A class of self-sustaining dissipative spherical dynamos. Annals Phys. 4, 372-447.
3. BEIGIE, D., LEONARD, A. & WIGGINS, S. 1991 A global study of enhanced stretching and diffusion in chaotic tangles. Phys. Fluids A 3, 1039-1050.
4. BENDER, C. M. 2007 Making sense of non-Hermitians Hamiltonians. Rep. Prog. Phys. 70, 947-1018.
5. CHERTKOV, M. & LEBEDEV, V. 2003 Boundary effects on chaotic advection-diffusion chemical reactions. Phys. Rev. Lett. 90, 134501.
6. CHOMAZ, J.-M. 2005 Global instabilities in spatially developing flows: Non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357-392.
7. DANCKWERTS, P. V. 1953 Continuous flow systems. Chem. Engng Sci. 2, 1-13.
8. DOREY, P., MILLICAN-SLATER, A. & TATEO, R. Beyond the WKB approximation in PT-symmetric quantum mechanics. J. Phys. A 38 1305-1331.
9. FANNJIANG, A. & PAPANICOLAOU, G. 1994 Convection enhanced diffusion for periodic flows. SIAM J. Appl. Maths 54, 333-408.
10. FANNJIANG, A. & PAPANICOLAOU, G. 1997 Convection-enhanced diffusion for random flows. J. Statist Phys. 88, 1033-1076.
11. FARINA, L. & RINALDI, S. 2000 Positive Linear Systems. Theory and applications. John Wiley and Sons.
12. GILBERT, A. D. 2006 Advected fields in maps - III. Passive scalar decay in baker's maps. Dyn. Syst. 21, 25-71.
13. GIONA, M., ADROVER, A. & CERBELLI, S. 2005 On the use of the pulsed-convection approach for modelling advection-diffusion in chaotic flows - A prototypical example and direct numerical simulations. Physica A 348, 37-73.
14. GIONA, M., ADROVER, A., CERBELLI, S. & VITACOLONNA, V. 2004a Spectral properties and transport machanisms of partially chaotic bounded flows in the presence of diffusion. Phys. Rev. Lett. 92 114101.
15. GIONA, M., CERBELLI, S. & VITACOLONNA, V. 2004b Universality and imaginary potentials in advection-diffusion equations in closed flows. J. Fluid Mech. 513, 221-237.
16. KANDLIKAR, S. G., GARIMELLA, S., LI, D., COLIN, S. & KING, M. R. 2006 Heat Transfer and Fluid Flow in Minichannels and Microchannels Elsevier.
17. KARNIANDAKIS, G., BESKOK, A. & ALURU, N. 2005 Microflows and Nanoflows. Springer.
18. MAJDA, A. J. & KRAMER, P. R. 1999 Simplified models for turbulent diffusion: Theory, numerical modelling and physical phenomena. Phys. Rep. 314, 237-574.
19. MATHEWS, J. H. & FINK, K. K. 2004 Numerical Methods using Matlab. Prentice-Hall.
20. PIERREHUMBERT, R. T. 1994 Tracer microstructure in large-eddy dominated regime. Chaos Solitons Fractals 4, 1091-1110.
21. PIKOVSKY, A. & POPOVYCH, O. 2003 Persistent patterns in deterministic mixing flows. Europhys. Lett. 61, 625-631.
22. POPOVYCH, O. V., PIKOVSKY, A. & ECKHARDT, B. 2007 Abnormal mixing of passive scalars in chaotic flows. Phys. Rev. E 75, 036308.
23. SCHMID, P. J. 2007 Nonmodal stability theory. Annu. Rev. Fluid Mech. 39, 129-162.
24. SMITH, R. 1988 Entry and exit conditions for flow reactors. IMA J. Appl. Maths. 41, 1-20.
25. STRAUBE, A. V. & PIKOVSKY, A. 2007 Mixing-induced global modes in open active flow. Phys. Rev. Lett. 99, 184503.
26. TAYLOR, G. 1953 Dispersion of soluble matter in a solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219, 186-203.
27. TAYLOR, G. 1954 The dispersion of matter in turbulent flow through a pipe. Proc. R. Soc. Lond. A 223, 446-468.
28. TEL, T., DE MOURA, A., GREBOGI, C. & KAROLYI, G. 2005 Chemical and biological activity in open flows: A dynamical system approach. Phys. Rep. 413, 91-196.