A numerical study of passive scalar evolution in peripheral regions

Physics of Fluids

Volumn 19, Issue 6, 2007, Pages

  Salman, H ^a,b   Haynes, P H ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b University of North Carolina at Chapel Hill   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; KINEMATICS; MATHEMATICAL MODELS; VELOCITY DISTRIBUTION;

EXPONENTIAL DECAY RATE; FLOW REALIZATION; KINEMATIC FLOW;

FLOW OF FLUIDS;

COMPUTER SIMULATION; FLOW OF FLUIDS; KINEMATICS; MATHEMATICAL MODELS; VELOCITY DISTRIBUTION;

EID: 34447332814     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2736341     Document Type: Article

References (40)

1. G. Batchelor, "Small-scale variation of convected quantities like temperature in turbulent fluid," J. Fluid Mech.JFLSA70022-112010.1017/S002211205900009X 5, 113 (1959).
2. G. Falkovich, K. Gawedzki, and M. Vergassola, "Particles and fields in fluid turbulence," Rev. Mod. Phys.RMPHAT0034-686110.1103/ RevModPhys.73.913 73, 913 (2001).
3. B. I. Schraiman and E. D. Siggia, "Scalar turbulence," NatureNATUAS0028-083610.1038/35015000 405, 639 (2000).
4. Z. Warhaft, "Passive scalars in turbulent flows," Annu. Rev. Fluid Mech.ARVFA30066-418910.1146/annurev.fluid.32.1.203 32, 203 (2000).
5. R. H. Kraichnan, "Inertial ranges in two-dimensional turbulence," Phys. FluidsPFLDAS0031-917110.1063/1.1762301 10, 1417 (1967).
6. R. H. Kraichnan, "Small-scale structure of a scalar field convected by turbulence," Phys. FluidsPFLDAS0031-917110.1063/1.1692063 11, 945 (1968).
7. R. H. Kraichnan, "Inertial-range transfer in two- and three-dimensional turbulence," J. Fluid Mech.JFLSA70022-112010.1017/S0022112071001216 47, 525 (1971).
8. M. Chertkov, G. Falkovich, I. Kolokolov, and V. Lebedev, "Statistics of a passive scalar advected by a large-scale two-dimensional velocity field: Analytic solution," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.51.5609 51, 5609 (1995).
9. T. M. Antonsen, Jr., Z. Fan, E. Ott, and E. Garcia-Lopez, "The role of chaotic orbits in the determination of power spectra of passive scalars," Phys. FluidsPHFLE61070-663110.1063/1.869083 8, 3094 (1996).
10. E. Balkovsky and A. Fouxon, "Universal long-time properties of Lagrangian statistics in the Batchelor regime and their application to the passive scalar problem," Phys. Rev. EPLEEE81063-651X10.1103/ PhysRevE.60.4164 60, 4164 (1999).
11. D. T. Son, "Turbulent decay of a passive scalar in the Batchelor limit: Exact results from a quantum mechanical approach," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.59.R3811 59, R3811 (1999).
12. D. R. Fereday, P. H. Haynes, A. Wonhas, and J. C. Vassilicos, "Scalar variance in chaotic advection and Batchelor-regime turbulence," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.65.035301 65, 035301 (2002).
13. D. R. Fereday and P. H. Haynes, "Scalar decay in two-dimensional chaotic advection and Batchelor-regime turbulence," Phys. FluidsPHFLE61070-663110.1063/1.1807431 16, 4359 (2004).
14. W. Liu and G. Haller, "Strange eigenmodes and decay of variance in the mixing of diffusive tracers," Physica DPDNPDT0167-278910.1016/ S0167-2789(03)00287-2 188, 1 (2004).
15. R. T. Pierrehumbert, "Tracer microstructure in the large-eddy dominated regime," Chaos, Solitons, FractalsCSFOEH0960-077910.1016/ 0960-0779(94)90139-2 4, 1091 (1994).
16. J.-L. Thiffeault and S. Childress, "Chaotic mixing in a torus map," ChaosCHAOEH1054-150010.1063/1.1568833 13, 502 (2003).
17. P. H. Haynes and J. Vanneste, "What controls the decay of passive scalars in smooth flows?," Phys. FluidsPHFLE61070-663110.1063/ 1.2033908
18. J. Sukhatme and R. T. Pierrehumbert, "Decay of passive scalars under the action of single scale smooth velocity fields in bounded two-dimensional domains: From non-self-similar probability distribution functions to self-similar eigenmodes," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.66.056302 66, 056302 (2002).
19. A. A. Schekochihin, P. H. Haynes, and S. C. Cowley, "Diffusion of a passive scalar in a fine-scale random flow," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.70.046304 70, 046304 (2004).
20. M. Chertkov and V. Lebedev, "Decay of scalar turbulence revisited," Phys. Rev. Lett.PRLTAO0031-900710.1103/ PhysRevLett.90.034501 90, 034501 (2003).
21. M. Chertkov and V. Lebedev, "Boundary effects on chaotic advection-diffusion chemical reactions," Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.90.134501 90, 134501 (2003).
22. V. V. Lebedev and K. S. Turitsyn, "Passive scalar evolution in peripheral region," Phys. Rev. EPLEEE81063-651X10.1103/ PhysRevE.69.036301 69, 036301 (2004).
23. R. Camassa and S. Wiggins, "Chaotic advection in a Rayleigh-Bénard flow," Phys. Rev. APLRAAN1050-294710.1103/ PhysRevA.43.774 43, 774 (1991).
24. S. Ghosh, A. Leonard, and S. Wiggins, "Diffusion of a passive scalar from a no-slip boundary into a two-dimensional chaotic advection field," J. Fluid Mech.JFLSA70022-112010.1017/S0022112098002249 372, 119 (1998).
25. K. Shariff, T. H. Pulliam, and J. M. Ottino, "A dynamical systems analysis of kinematics in the time-periodic wake of a circular cylinder," Lect. Appl. Math.ZZZZZZ0075-8485 28, 613 (1991).
26. T. Yuster and W. W. Hackborn, "On invariant manifolds attached to oscillating boundaries of Stokes flows," ChaosCHAOEH1054-150010.1063/1.166274 7, 769 (1997).
27. S. C. Venkataramani, T. M. Antonsen, Jr., and E. Ott, "Lévy flights in fluid flows with no Kolmogorov-Arnold-Moser surfaces," Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.78.3864 78, 3864 (1997).
28. S. C. Venkataramani, T. M. Antonsen, Jr., and E. Ott, "Anomalous diffusion in bounded temporally irregular flows," Physica DPDNPDT0167-278910.1016/S0167-2789(97)00184-X 112, 412 (1998).
29. E. R. Weeks, J. S. Urbach, and H. L. Swinney, "Anomalous diffusion in asymmetric random walks with a quasi-geostrophic flow example," Physica DPDNPDT0167-278910.1016/0167-2789(96)00082-6 97, 291 (1996).
30. T. Burghelea, E. Segre, and V. Steinberg, "Mixing by polymers: Experimental test of decay regime of mixing," Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.92.164501 92, 164501 (2004).
31. A. Groisman and V. Steinberg, "Efficient mixing at low Reynolds numbers using polymer additives," NatureNATUAS0028-083610.1038/ 35073524 410, 905 (2001).
32. T. Burghelea, E. Segre, I. Bar-Joseph, A. Groisman, and V. Steinberg, "Chaotic flow and efficient mixing in a microchannel with a polymer solution," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.69.066305 69, 066305 (2004).
33. T. H. Solomon and J. P. Gollub, "Passive transport in steady Rayleigh-Bénard convection," Phys. FluidsPFLDAS0031-917110.1063/1.866729 31, 1372 (1988).
34. T. H. Solomon and J. P. Gollub, "Chaotic particle transport in time-dependent Rayleigh-Bénard convection," Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.38.6280 38, 6280 (1988).
35. L. Biferale, A. Crisanti, M. Vergassola, and A. Vulpiani, "Eddy diffusivities in scalar transport," Phys. FluidsPHFLE61070-663110.1063/1.868651 7, 2725 (1995).
36. A. J. Majda and P. R. Kramer, "Simplified models for turbulent diffusion: Theory, numerical modelling and physical phenomena," Phys. Rep.PRPLCM0370-157310.1016/S0370-1573(98)00083-0 314, 237 (1999).
37. R. T. Pierrehumbert, "Lattice models of advection-diffusion," ChaosCHAOEH1054-150010.1063/1.166476 10, 61 (2000).
38. A. Staniforth and J. Côté, "Semi-Lagrangian integration schemes for atmospheric models - A review," Mon. Weather Rev.MWREAB0027-064410.1175/1520-0493(1991) 119<2206:SLISFA>2.0.CO;2 119, 2206 (1991).
39. G. Haller, "Exact theory of unsteady separation for two-dimensional flows," J. Fluid Mech.JFLSA70022-1120 512, 257 (2004).
40. N. J. Balmforth and W. R. Young, "Diffusion-limited scalar cascades," J. Fluid Mech.JFLSA70022-112010.1017/S0022112003003914 482, 91 (2003).