Universality and imaginary potentials in advection-diffusion equations in closed flows

Journal of Fluid Mechanics

Volumn 513, Issue , 2004, Pages 221-237

  Giona, M ^a   Cerbelli, S ^a   Vitacolonna, V ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION; EIGENVALUES AND EIGENFUNCTIONS; EQUATIONS OF MOTION; KINEMATICS; MATHEMATICAL MODELS; PROBLEM SOLVING;

ADVECTION-DIFFUSION EQUATIONS; HOMOGENIZATION DYNAMICS; SCALING EXPONENT CONTROL; SPECTRAL PROPERTIES;

STEADY FLOW;

ADVECTION-DIFFUSION EQUATION; SPECTRAL ANALYSIS; STEADY FLOW;

EID: 4344643142     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S002211200400984X     Document Type: Article

References (21)

1. AGMON, S. 1962 On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems. Commun. Pure Appl. Maths 15, 119-147.
2. AGMON, S. 1965 Lectures on Elliptic Boundary Value Problems. Van Nostrand.
3. BATCHELOR, G. K. 1956 On steady laminar flow with closed streamlines at large Reynolds number. J. Fluid Mech. 1, 177-190.
4. BENSOUSSAN, A., LIONS, J.-L. & PAPANICOLAU, G. 1978 Asymptotic Analysis for Periodic Structures. North-Holland.
5. CASTIGLIONE, P., MAZZINO, A., MURATORE-GIANNESCHI, P. & VULPIANI, A. 1999 On strong anomalous diffusion. Physica D 134, 75-93.
6. CERBELLI, S., ADROVER, A. & GIONA, M. 2003 Enhanced diffusion regimes in bounded chaotic flows. Phys. Lett. A 312, 355-362.
7. CHILDRESS, S. & SOWARD, A. M. 1989 Scalar transport and alpha-effect for a family of cat's-eye flows. J. Fluid Mech. 205, 99-133.
8. FANNJIANG, A. & PAPANICOLAU, G. 1994 Convection enhanced diffusion for periodic flows. SIAM J. Appl. Maths 54, 333-408.
9. FEIGENBAUM, M. J. 1979 The universal metric properties of nonlinear transformations. J. Statist. Phys. 21, 669-706.
10. GIONA, M. & ADROVER, A. 1998 Nonuniform stationary measure of the invariant unstable foliation in hamiltonian and fluid mixing systems. Phys. Rev. Lett. 81, 3864-3867.
11. GIONA, M., ADROVER, A., CERBELLI, S. & VITACOLONNA, V. 2004 Spectral properties and transport mechanisms of partially chaotic bounded flows in the presence of diffusion. Phys. Rev. Lett., 92, 114101.
12. GIONA, M., CERBELLI, S. & ADROVER, A. 2002 Quantitative analysis of mixing structures in chaotic flows generated by infinitely fast reaction in the presence of diffusion. J. Phys. Chem. 106, 5722-5736.
13. GOLDSHEID, I. YA. & KHORUZHENKO, B. A. 2000 Eigenvalue curves of asymmetric tridiagonal random matrices. Electronic J. Prob. 5, 1-28.
14. GUPTA, V. K. & BHATTACHARYA, R. N. 1986 Solute dispersion in multidimensional periodic saturated porous media. Water. Resour. Res. 22, 156-164.
15. HATANO, N. & NELSON, D. R. 1996 Localization Transition in non-hermitian quantum mechanics. Phys. Rev. Lett. 77, 570-573.
16. HOLMES, M. H. 1995 Introduction to Perturbation Methods. Springer-Verlag.
17. LIU, M., MUZZIO, F. J. & PESKIN, R. L. 1994 Quantification of mixing in aperiodic flow. Chaos, Solitons and Fractals 4, 869-893.
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. OTTINO, J. M. 1989 The Kinematics of Mixing - Stretching, Chaos, and Transport. Cambridge University Press.
20. TOUSSAINT, V., CARRIERE, P. & RAYNAL, F. 1995 A numerical Eulerian approach to mixing by chaotic advection. Phys. Fluids 7, 2587-2600.
21. TOUSSAINT, V., CARRIERE, P., SCOTT, J. & GENCE, J.-N. 2000 Spectral decay of a passive scalar in chaotic mixing. Phys. Fluids 12, 2834-2844.